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8/12/2019 IJFM Journal
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Chief Editor
Dr. Balwinder Singh,Associate Professor, Department of Commerce & Business Management, Guru Nanak Dev University, Amritsar, India
Associate Editors
Dr. Revti Raman,Victoria University of Wellington, New Zealand
Dr. Mahesh Joshi,RMIT University, Melbourne, Australia
Dr. Kapil Gupta,Professor, Management Department, Punjab Technical University, Kapurthala
Editorial Coordinator
Ms. Rekha Handa, Assistant Professor, Department of Commerce & Business Management, Guru Nanak Dev University, Amritsar, India
Editorial Advisory Board
Dr. C.P.Gupta, Professor, Dept. of Commerce, Delhi University, New Delhi, IndiaDr. Ravinder Vinayak, Professor, Maharishi Dayanand University, Rohtak, Haryana, India
Dr. Sanjay Rastogi, Indian Institute of Foreign Trade, New Delhi, India
Dr. H. Venkateshwarlu, Professor, Osmania University, Hyderabad, A.P., India
Dr. Bala Balachandran, La trobe University, Australia
Dr. Golaka C Nath, Vice President, Clearing Corporation of India, Mumbai, India
Dr. N. Panchanatham, Prof., Dept. of Business Administration, Annamalai University, Tamil Nadu
Dr. Annalisa Prencipe, Universita Bocconi, Milan(Italy)
Dr. Bhagwan Khanna, Victoria University of Wellington, New Zealand
Samanthala Hettihewa, University of Ballarat, Ballarat
Editorial Review Board
Dr. Ashok Bhardwaj Abbott, Associate Professor, West Virginia University, United States
Dr. Sourendra Nath Ghosal, Director, Nicco Financial Services Ltd., Kolkata, India
Dr M.R. Vanitha Mani, Director, MBA Dept., SSK College of Engineering & Tech., Coimbatore, India
Samuel Gil Martin, Faculty, Universidad Autonoma de San Luis Potos, MexicoDr. Syed Hussain Ashraf, Senior Professor, Dept. of Commerce, Aligarh Muslim University, India
Dr. Sanjay Jayantilal Bhayani, Associate Prof., Saurashtra University, Rajkot, Gujarat, India
Mr. Moid U Ahmad, Assistant Professor, Jaipuria Institute of Management, Noida, India
Mr. Kushankur Dey, Faculty, Institute of Rural Management, Anand, Gujarat, India
Dr. Shafali Nagpal, Director, UGC-Academic Staff College, BPS Mahila Vishwavidhyalaya, Sonepat
Dr. Punit Kumar Dwivedi, Assistant Professor, Prestige Institute of Mgt. and Research, Indore, India
Prof. Amrit Lal Ghosh, Professor, Department of Business Admn., Assam University, Assam, India
Dr. Ritu Gupta, Assistant Professor, Kamla Lohtia S.D. College, Ludhiana, India
Prof. S.L. Gupta, Professor, Birla Institute of Technology, Mesra, Ranchi, India
Mrs. Maithreye Sunil Holeyachi, Assistant Professor, City college, Bangalore, India
Dr Pawan Jain, Assistant Professor, Institute of Management Technology, Nagpur, India
Dr. Sudhanshu Joshi, Assistant Professor, School of Management, Doon Univ., Uttrakhand, India
Badar Alam Iqbal, Professor, Department of Commerce, A.M.U., Aligarh, India
Mrs. Sonal Gupta, Faculty, CMRIT, Bangalore, India
Mr Pankaj Varshney, Associate Professor, Apeejay School of Mgt., Dwarka, New Delhi, India
Dr Jaideep Gulabrao Jadhav, Associate Professor, MIT School of Telecom Management, Pune, India
Dr. Sri kanth, Associate Professor, PES Institute of Technology, Bangalore, India
Dr. (Mrs.) Parul Khanna, Associate Professor, Institute of Mgt. & Technology, Faridabad, India
Mr. Nitin Kulkarni, Faculty, MET Institute of Management, India
Mr. Anandadeep Mandal, Assistant Professor, KIIT School of Management, Orissa, India
Ratna Shanker Mishra, Assistant Professor, Banaras Hindu University, Varanasi, India
Akhil Mishra, Associate Professor, Faculty Of Commerce, BHU, Varanasi, India
Mr. Debabrata Mitra, Faculty, Department of Commerce, Univ. of North, Bengal, Darjeeling, India
Dr. Chimun Kumar Nath, Assistant Professor, Dept. of Commerce, Dibrugarh University, India
Prof. Nikunjkumar Ramnikbhai Patel, Associate Prof., S.V. Institute of Management, Gujarat, India
Mr. Sudhakar T Paul, Assistant Prof., Dept. of MBA, MVJ College of Engineering, Bangalore, India
Dr.Raja Ram, Faculty, Kalasalingam University, India
Prakash shanmugasundaram, Faculty, Department of MBA, Anna University, Coimbatore, India
Prof Subhash Chander Sharma, Professor, Dept of Commerce and Business Mgt., GNDU, Amritsar,
Dr Sajeev Surendranath, Senior Lecturer, Institute of Mgt. in Government, Trivandrum, India
International Journal of Financial Management
Journal tends to bring about a revolution in the nancial research through its unparalleled quality, undaunted approach and panoptic coverage of
the research efforts being undertaken all around the globe. The journal intends to provide the super ordinate podium to the researchers to share their
ndings with the global community after having crossed the quality checks and legitimacy criteria, which in no way promise to be liberal.
8/12/2019 IJFM Journal
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Editorial Message
Greetings for the newly dawned year! Hope it lends us umpteen opportunities to learn and align with the dynamic learn
ing environment. The advent of New Year has lent me the privilege to add another volume to the growing glory of our
journal. The International Journal of Financial Management having found a strong foothold with readers, contributor
and reviewers has taken a betting leap to its next volume. The joy I experience is the shared credit of not only the jour
nals editorial and reviewing team but also the silent yet strong inputs of our valued critics and suggestion makers.
The present issue is a ne blend of seven research papers which could take the coveted place here surpassing the
quality barriers raised through our rigorous and regularly updated review procedures. The rst paper talks about the
application and development hybrid methodology that combines both ARIMA and Articial neural network model to
model and predict the stock market index returns. The paper next in line purportedly is the rst exhaustive study of itskind on linkages and the interrelationship between the Asian stock markets and other stock markets during and after
the crisis employing sophisticated and procedurally sound analytical techniques like Granger Causality test based on
Vector Error Correction Model and Co-Integration It concludes that the linkages between the Asian and the US stock
markets are stronger in the post-crisis period. Islamic banking, elimination of gharar, two prominent Islamic banking
nancing instruments Bay al-Inah and Bay al-Dayn and the legal implications of the presence of gharar on the validity
of these contracts is the central thought in the next research compilation. Critical investigation into the jurists views to
examine the revisiting of gharar have been essayed which lend the desired distinctiveness to the work. In line with the
contemporary talks of intellectual capital and its enormous role in building value the next paper analyses the intellectua
capital and physical capital of selected companies and their impact on corporate performance using multiple regression
technique. Performance of both public sector and private sector banks through multivariate analysis has been evaluated
in the next empirical work using comprehensive measures of performance. Analyzing threadbare the performances ofve major bank in India the study makes signicant contributions in the eld of banking and nance. The literature
review on a unique research area regarding the role of human capital management in economic value addition of large
scale organizations also has been made a part of this issue. The culminating paper of this issue relates to construction
of appropriate benchmark index for mutual funds involving an empirical analysis with specic reference to tax saver
funds The methodology focuses on estimating the risk adjusted abnormal return generated by the fund that exhibits the
predictive ability of the fund manager.
I sincerely hope that the issue and its comprehensive contents meet the quality standards set by our previous issues.
Being positively receptive to all your valued comments, observations and feedbacks I stand committed to our promises
of dissemination of quality research in nance.
Warm wishes,
Balwinder Singh
Editor IJFM
8/12/2019 IJFM Journal
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Within Volume 1 Issue 1, January 2012
ISSN No. 2229-5682(P) ISSN No. 2229-5690(O)Online Access www.publishingindia.com
1. Stock Index Return Forecasting and Trading Strategy Using
Hybrid ARIMA-Neural Network Model
Manish Kumar and M. Thenmozhi 1-14
2. A Study on the Linkages of Asian and the US Stock Markets
S.M. Tariq Zafar, D.S. Chaubey and S.R. Sharma 15-32
3. Revisiting the Principles of Gharar (Uncertainty) in Islamic Banking
Financing Instruments with Special Reference to Bay Al-Inah and
Bay Al-Dayn Towards a New Modied Model
Siti Salwani Razali 33-43
4. The Role of Intellectual Capital in Creating Value in Indian Companies
Amitava Mondal and Dr. Santanu Kumar Ghosh 44-54
5. Performance Evaluation of Public and Private Sector Banks: A
Multivariate Analysis
K.V.N. Prasad and D. Maheshwara Reddy 55-62
6. Role of Human Capital Management in Economic Value Addition of
Large Scale Organizations: A Literature Review
Sujata Priyambada Dash and Vijay Agarwal 63-74
7. Construction of Appropriate Benchmark Index for Mutual Funds:
Specic Reference to Tax Saver Funds
Venkatesh Kumar and Ashwini Kumar 73-89
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Stock Index Return Forecasting and Trading Strategy Using Hybrid ARIMA-Neural Network Model 1
Abstrac t
This study presents the application and development
of hybrid methodology that combines both ARIMA and
Articial Neural Network model to take advantageof the unique strengths of both linear and non-linear
modeling to model and predict the stock market index
returns. The performance of the hybrid ARIMA Neural
Network model is compared with the performance of
ARIMA and Neural Network model. The performance
of the models are evaluated in terms of widely used
statistical metrics, correctness of sign and direction
change and various trading performance measures like
annualized return, Sharpe ratio, maximum drawdown,
annualized volatility, average gain/loss ratio, etc. via a
trading strategy. The ndings of the study reveal that
the hybrid ARIMA Neural Network model developed is
the best Forecasting model to achieve greater accuracy
and yields better trading results.
Keywords: ARIMA, Articial Neural Network,
Forecasting, Stock market trading
JEL Codes: C22, C45, C52, E17, G15
Stock Index Return Forecasting and Trading
Strategy Using Hybrid ARIMA-Neural
Network Model
Manish Kumar*and M. Thenmozhi**
1. Introducon
In the last two decades, forecasting nancial time series
have been attempted using different linear and non-linear
methods. The most popular and traditional time series
model is Box-Jenkins or ARIMA model. The ARIMA
approach is both simple and yields accurate results which
explains its wide use. Many authors, e.g. Virtanen and
Paavo (1987), Pagan and Schwert (1990), Leseps and
Morell (1997), Crawford and Fratantoni (2003), etc.
have used ARIMA model as proposed by Box-Jenkins to
forecast different time series such as stock index returns,
exchange rates, etc. and compared it with different models
like Markov Switching, Regime Switching GARCH, etc.
The results show that ARIMA model performed well
compared to other models.
However, the major limitation of the ARIMA model is the
pre-assumed linear form of the model. The approximation
of linear models to complex real-world nancial time series
problem is not always satisfactory. Financial time series
are considered as highly non-linear where the mean and
variance of the series changes overtime. Grudnitski and
Osburn (1993) in their study stated that there is noisy non-
linear process present in the prices. Moreover, Refenes
et al. (1994) in their study also indicated that traditional
statistical techniques for forecasting have serious
limitations with respect to applications with non-linearitiesin the data set such as stock indices. Hence, detecting this
hidden non-linear relationship and the application of non-
linear methods may help in improving the forecasting
*Manish Kumar,Research Scholar, Department of Management Studies, Indian Institute of Technology, Madras, Chennai, India**M. Thenmozhi of Management Studies, Indian Institute of Technology, Madras, Chennai, India
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2 International Journal of Financial Management Volume 1 Issue 1 January 2012
accuracy. Recent developments in the theory of Neural
Computation provide interesting mathematical tools for
such a new kind of nancial analysis. One of the popular
and powerful tools in this area is Articial Neural Network.
The major advantage of neural networks is their exiblenon-linear modeling capability (Donaldson and Kamstra,
1996). Neural networks have exible non-linear function
mapping capability, which can approximate any continuous
function with arbitrarily desired accuracy. Due to their
success in nancial forecasting, neural networks have
been adopted as an alternative method in the prediction of
stock prices, exchange rates, etc.
A number of studies (Refenes et al.(1987), Kimoto et al.
(1990), Takashi et al. (1990), Kryzanowski et al.(1993),
McCluskey (1993), Bansal and Vishwanatahn (1993),
Refenes (1994), Donaldson and Kamstra (1996), Zirilli
(1997)) have investigated Neural Network model for
predicting the stock market and the results support the
importance of the model. Castiglianc (2001) and Phua
et al.(2003) have used Neural Network to forecast stock
index increment. Yao et al. (2002) used Neural Network
for forecasting option price; Jasic and Wood (2004)
examined the daily stock market indices of S&P 500,
DAX, TOPIX and FTSE for protability of trades based
on Neural Network prediction. Thus, many studies have
shown that neural networks are better and can serve as a
better prediction model that can overcome many of the
drawbacks associated with the traditional techniques.
In the Indian context, Thenmozhi (2001) examined
the feasibility of Neural Network in predicting the
movement of the daily and weekly returns of BSE
Index. The architecture used four inputs, which are the
four consecutive daily returns and one output being
the prediction of return on the fth day. The study uses
multiplayer perceptron with backpropagation algorithm.
The results show that predictive powers of both the models
(daily and weekly return) were low. Pant and Rao (2003)
in their work used ANN for estimating the daily return of
the BSE Sensex using randomized backpropagation. The
study was based on the daily price time series of BSE
Sensex. It used four different architectures of three-layer
Neural Network that consist of three-input parameters and
one output parameter. Results indicate that ANN based
forecasting method is superior to the nave strategy of
holding the stocks. Manish and Thenmozhi (2004) used
backpropagation neural networks and compared it with
a linear ARIMA model for forecasting exchange rate like
INR/USD and the Stock index return. Results indicate
that ANN based forecasting method is superior to the
linear ARIMA model.
The recent researches have focused on using hybrid model
or combining various models of forecasting to improve
the forecasting accuracy. The idea behind the model
combination is to use the unique advantageous features
of each model to accurately analyse different patterns in
the data (Reid (1968) and Bates and Granger (1969)).
The study of Newbold and Granger (1974), Makridakis
et al.(1982), Makridakis (1989), Clemen, (1989), Palm
and Zellner (1992) and Makridakis et al.(1993) suggests
that by combining several different models, forecasting
accuracy can often be improved. In addition, the combined
model is more robust and exible with regard to the
possible structure change in the data.
There have been some studies suggesting hybrid models,
combining the ARIMA model and neural networks. An
important motivation to combine different forecasting is
that one cannot identify the true process of the time series,
i.e. the time series under examination is generated from
a linear or non-linear underlying process. Moreover,
the time series data often contain both linear and non-
linear patterns. Hence, different models may be tried in
approximating the underlying process. However, the nal
selected model is not necessarily the best for future uses
due to many potential inuencing factors such as sampling
variation, model uncertainty, and structure change.Therefore, combining different models can increase
the chance to capture different patterns in the data with
increased accuracy and improve forecasting performance
drastically. By combining different methods, the problem
of model selection can be eased with little extra effort and
this can serve as a universal model thus saving time and
effort (Zhang, 2003).
Voort et al. (1996) used this combination to forecast
short-term trafc ow. Their technique used a Kohonen
self-organizing map as an initial classier; with each class
having an individually tuned ARIMA model associated
with it. Su et al.(1997) used the hybrid model to forecast
a time series of reliability data with growth trend. Their
results showed that the hybrid model produced better
forecasts than either the ARIMA model or the Neural
Network by itself. Wedding and Cios (1996) described
a combining methodology using radial basis function
networks and the BoxJenkins models. Luxhoj et
al. (1996) presented a hybrid econometric and ANN
approach for sales forecasting. Pelikan et al.(1992) and
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Stock Index Return Forecasting and Trading Strategy Using Hybrid ARIMA-Neural Network Model 3
Ginzburg and Horn (1994) proposed to combine several
feed-forward neural networks to improve time series
forecasting accuracy. Zhang (2003) used the hybrid
methodology to forecast the three well-known data sets
the Wolfs sunspot data, the Canadian lynx data, and theBritish pound/US dollar exchange rate data. Experimental
results with real data sets indicate that the combined model
can be an effective way to improve forecasting accuracy
achieved by either of the models used separately. Hence,
there is strong evidence in the literature that hybrid models
are more robust and are more accurate over the individual
models.
Recently, Tugba and Casey (2005) using Zhang (2003)
approach showed that the combined forecast can
underperforms signicantly compared to its constituents
performances. They demonstrated these using ninemonthly time series data sets, Auto Regressive (AR)
linear and Time Delay Neural Network models (TDNN).
The last 12 values were reserved for testing, the preceding
12 values for validation, whilst the rest were used for
training. For ve of the nine data sets, the linear AR and
TDNN models outperform the ARIMA Neural Network
hybrids, albeit with similar levels of performance for
two of these data sets. They concluded that despite the
popularity of hybrid models, which rely upon the success
of their components, single models themselves can be
sufcient.
Although, different hybrid ARIMA-ANN model has been
developed, in earlier studies related to hybrid models,
auto, regressive terms have been used as input to the
Neural Network. The residuals of ARIMA model has
been modeled using Neural Network. Zhang (2003) in his
study assumed that the non-linear patterns will always be
present in the residuals of the linear ARIMA model, which
can be modeled using articial neural networks. Moreover,
there is an assumption that the relationship between the
linear and non-linear components is additive and this
may degrade performance if the relationship is different,
e.g. multiplicative. Such assumptions are likely to lead
to unwanted degeneration of performance if the opposite
situation occurs Tugba and Casey (2005). Clemen (1989)
and Granger and Ramanathan (1984) in their study states
that the lack of success using the combination models may
be attributed to the performance of benchmark models.
The performance of the benchmark models was so much
weaker than that of the neural network models that it is
unlikely that combining relatively poor models with an
otherwise good one will outperform the good model
alone. Hence, the result of the recent study on the hybrid
ARIMA-ANN model is mixed.
Moreover, the other key problems associated with these
studies are as follows. These studies use simulated
or articial data set for the analysis and the number of
observation for training and the test data were very
low (Zhang (2003). The degree of accuracy and the
acceptability of certain forecasting models are measured
by the estimates deviations from the observed values, i.e.
MAE, RMSE, etc. but turning point forecast capability
using sign and direction test has not been considered
((Zhang (2003), and Tugba and Casey (2005)). Leung
et al. (2000) in their study suggested that depending on
the trading strategies adopted by investors, forecasting
methods based on minimizing forecast error may not beadequate to meet their objectives. In other words, trading
driven by a certain forecast with a small forecast error
may not be as protable as trading guided by an accurate
prediction of the direction or sign of return. Hence, the
competing models must be evaluated not only in terms of
MAE, RMSE etc., but also in terms of sign and direction
test. The other drawback of the previous studies isthat,
none of the studies evaluated their models based on the
trading performance. Statistical measures of performance
are often inappropriate for nancial applications. The
forecast error may have been minimized during model
estimation, but model with a small forecast error may
not be as protable as a model selected using nancial
criteria such as risk adjusted measure of return Leung et
al.(2000) Evaluations of models using nancial criteria
through a trading experiment may be more appropriate.
Although, there are studies addressing the issue of
forecasting nancial time series such as stock market
index most of the empirical ndings are associated with
the developed nancial markets (UK, USA, and Japan).
However, few studies exist in the literature which predicts
the nancial time series of emerging markets. Nowadays,
many international investment bankers and brokerage
rms have major stakes in overseas markets. Harvey
(1995) found emerging market returns are more likely
to be inuenced by local information than developed
markets; in fact, emerging market returns are generally
more predictable than developed market returns. Indian
stock markets have received relatively little attention until
recently. Now there is more interest and research on Indian
market data due to the countrys rapid growth and potential
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4 International Journal of Financial Management Volume 2 Issue 1 January 2012
opportunities for investors. Since the establishment of
National Stock Exchange (NSE), the nancial markets
in this Asian country have attracted considerable global
investments.
Given this notion, this study examines the applicability of
hybrid ARIMA-neural network models for predicting the
daily return of the S&P CNX NIFTY Index and compares
it with isolated ARIMA and neural network model. The
study differs from earlier studies in several ways. Firstly,
the study develops the hybrid ARIMA-ANN models. In the
rst stage of this study, the ARIMA and an articial neural
network model is used to forecast the variable of interest. In
second stage hybrid ARIMA-ANN models are developed.
The hybrid ARIMA-ANN model is similar to the Zhang
(2003). Secondly, the different competing models are
rigorously compared using two approaches. Firstly, thestudy examines the out-of-sample forecasts generated by
different competing models employing non penalty-based
performance criteria such as Root Mean Square Error
(RMSE), Mean Absolute Percentage Error (MAPE) and
Mean Absolute Error (MAE) and performance criteria
based on direction and sign change such as Directional
Symmetry (DS), Correct Up trend (CU) and Correct Down
trend (CD) goodness of Forecast Measures Thirdly, the
different competing models are also examined in terms of
trading performance and economic criteria via a trading
experiment. For example, the study uses the return forecasts
from the different models in a simple trading strategy (buy
when the forecast is positive and sell when forecast is
negative) and compare pay-offs to determine which model
can serve as a useful forecasting tool.
Thus, the major contribution of this study will be (1) to nd
out the appropriate neural network and ARIMA model for
NIFTY return series; (2) to nd out the appropriate hybrid
ARIMA-ANN for NIFTY return series; (3) to demonstrate
and verify the predictability of S&P CNX NIFTY Index
return by applying the hybrid ARIMA-neural network
models; (4) to compare the performance of the hybrid
model with that of individual ARIMA and neural network
model in terms of forecasting accuracy using non penalty-
based performance criteria such as Root Mean Square
Error (RMSE), Normalized Mean Square Error (NMSE)
and Mean Absolute Error (MAE) and performance criteria
based on direction and sign change such as Directional
Symmetry (DS), Correct Up Trend (CU) and Correct
Down trend (CD); (5) to evaluate the three models in
terms of trading performance via a trading experiment.
The remaining portion of this paper is organized as
follows. The data used in the study, the details of hybrid
approach and the benchmark models are introduced in
Section 2. The empirical results from the real data sets
are discussed in Section 3. Finally, Section 4 contains theconcluding remarks.
2. Data and Methodology
The study is based on the daily closing prices for the S&P
CNX NIFTY Index. The series span the period from 1st
January 2000 to 31stMarch 2005 totaling a 1,319 trading
days. The data is divided into two periods- the rst period
runs from 1stJanuary, 2000 to 26thDecember, 2003 (1,000
observations) used for model estimation and is classied
as in-sample, while the second period runs from 27th
December, 2003 to 31stMarch, 2005 (319 observations)is reserved for out-of-sample forecasting and evaluation.
The division amounts to approximately 25 per cent being
retained for out-of-sample purposes.
The use of data in levels in the stock market has many
problems: stock market price movements are generally
non-stationary and quite random in nature, and therefore
not very suitable for learning purposes. To overcome
these problems, the NIFTY series is transformed into
rates of return. Given the price level P1, P2, , Pt , the
rate of return at time t is formed by: Rt= (Pt /Pt 1) 1.
An advantage of using a returns series is that it helpsin making the time series stationary, a useful statistical
property.
2.1 Forecasng Methodology
The premise of this research is to examine the use of hybrid
models in NIFTY returns forecasting and trading models.
Their performance is compared with univariate linear
ARIMA model and a non-linear backpropagation neural
network. As all of these methods are well-documented in
the literature, an outline of the methods is given below.
2.1.1 ARIMA Methodology
Popularly known as Box-Jenkins (BJ) methodology, but
technically known as ARIMA methodology, assumes that
the future values of a time series have a clear and denite
functional relationship with current, past values and white
noise. The mixed auto regressive model of order (p,q)
denoted as ARMA (p,q) is dened as
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Stock Index Return Forecasting and Trading Strategy Using Hybrid ARIMA-Neural Network Model 5
t= q+ F1Zt 1+ F2Zt 2+ FpZtp+ F0at+ F1at 1 + F2at 2+ Fqatq
Where t is the time series and at is an uncorrelated
random error term with zero mean and constant variance
and qrepresents a constant term.
The time series models are based on the assumption that
the time series involved are stationary. But many a time
series are not stationary, that is they are integrated. If
a time series are integrated of order 1 (i.e., it is I (1)),
and its rst difference is I (0), it is said to be stationary.
Similarly, if a time series is I (2), its second difference is I
(0). In general, if a time series is I (d) after differencing it
dtimes. Then I (0) series will be obtained.
If a time series is differenced d times to make it stationary
and then ARMA (p, q) model is applied to it, then theoriginal time series is ARIMA (p, d, q), that is an
autoregressive integrated moving average time series.
The Box-Jenkins models are implemented using
E-Views 4. The correlogram, which are simply the
plots of Autocorrelation Functions (ACFs) and Partial
Autocorrelation Functions (PACFs) against the lag length,
is used in identifying the signicant ACFs and PACFs.
The lags of ACF and PACF whose probability value is less
than 5% are signicant and are identied. The possible
models are developed from these plots for the NIFTY
Index returns series. The best model for forecasting isidentied by considering the information criteria, i.e.
Akaike Information Criteria (AIC) and Schwarz Bayesian
Information Criteria (SBIC). It is also an accepted
statistical paradigm that the correctly specied model
for the historical data will also be the optimal model for
forecasting. Hence, it is reasonable to compare the hybrid
model and the best neural network results with those of
ARIMA models.
2.1.2 Neural Network Methodology
In this study, one of the widely used ANN models, thefeed forward neural network is used for nancial time
series forecasting. Usually, the NN model consists of an
input layer, an output layer and one or more hidden layers.
The hidden layers can capture the non-linear relationship
between variables. Each layer consists of multiple neurons
that are connected to neurons in adjacent layers.
A neural network can be trained by the historical
data of a time series in order to capture the non-linear
characteristics of the specic time series. The model
parameters (connection weights and node biases) will
be adjusted iteratively by a process of minimizing the
forecasting errors. For time series forecasting, the nal
computational form of the ANN model is as
Yt= ao+ Y ao w f a w Y t jj
q
j ij t i t
i
p
= + + +=
-=
1 1
( ) e
where aj(j= 0,1,2, q) is a bias on thejthunit, and wij(i=
1,2,,p;j= 1,2, q) is the connection weight between
layers of the model, f (.) is the transfer function of thehidden layer, p is the number of input nodes and q is the
number of hidden nodes. Actually, the ANN model in (2)
performs a non-linear functional mapping from the past
observation (Yt 1, Yt 2,, Ytp) to the future value Yt,
i.e.,
Yt= j (Yt 1, Yt 2, Yt 3,, Ytp, n) + xt
where v is a vector of all parameters and jis a function
determined by the network structure and connection
weights. Thus, in some senses, the ANN model is equivalent
to a Nonlinear Auto Regressive (NAR) model.
2.1.3 Model Formulaon
This study employs a three-layer backpropagated neural
network to forecast NIFTY Index returns. The return
series of NIFTY Index are fed to the neural network
model to forecast the next period return in this model.
For example, the inputs to a 5x1 neural network are
NXi 4, NXi 3, NXi 2, NXi 1 and NXi while the output
of the neural network is NXi + 1, the next days NIFTY
return, where NXi stands for the current days NIFTY
return. The architecture of the neural network is denoted
byX-Y-Z. TheX-Y-Zstands for a neural network withX
neurons in input layer, Y neurons in hidden layer, andZ
neurons in output layer. Only one output node is deployed
in the output layer since one-step-ahead forecast is made
in this study. The number of input nodes and hidden nodes
are not specied a priori. This will be selected throughexperiment. This study uses tansigmoid function for
the nodes in the input layer for backpropagated neural
network, while tansigmoid function and pure linear
function are used at hidden layers and output layers.
The number of input nodes is probably the most critical
decision variable for a time series-forecasting problem
since it contains important information about the data.
In this study, the number of input nodes corresponds
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6 International Journal of Financial Management Volume 2 Issue 1 January 2012
to the number of lagged returns observations used to
discover the underlying pattern in a time series and to
make forecasts for future values. Currently, there is no
theory suggesting the appropriate number of input nodes.
But ideally it would be better to have a small number ofessential nodes, since this can unveil the unique features
embedded in the data. Too few or too many input nodes
can affect either the learning or prediction capability of
the network. This study resorts to experimentation in the
network construction process. The network construction
process has been evaluated with six levels of the number
of input nodes ranging from 1 to 6.
The number of hidden nodes plays a very important role
too. These hidden neurons enable the network to detect the
feature, to capture the pattern in the data, and to perform
complicated non-linear mapping between input andoutput variables. Hornik et al.(1989) in their theoretical
work found that single hidden layer is sufcient for the
network to approximate any complex non-linear function
with any desired accuracy. Most authors use only one
hidden layer for forecasting purposes. This study employs
three-layer BPN to forecast the daily returns of NIFTY
returns. Five levels of hidden nodes, 1, 2, 3, 4 and 5 have
been experimented. The combination of six input nodes
and ve hidden nodes yields a total of 30 different neural
network architectures. These in turn are being considered
for each in-sample training set for the NIFTY returns the
backpropagation neural network models.
This study uses backpropagation algorithm to train the
BPN. Backpropagation is the most widely used algorithm
for supervised learning with neural networks. The study
uses MATLAB 6.5 to build and train neural network. The
MATLAB program works with default parameter values
of weight, assigned by the MATLAB.
2.1.4 The Hybrid Methodology
This study develops the hybrid models to forecast the S&P
CNX NIFTY Index return. The forecasting method usinghybrid models initiates with the basic time series data on
NIFTY Index return. It may be reasonable to consider
a time series to be composed of a linear autocorrelation
structure and a non-linear component. A hybrid model
comprising a linear and a non-linear component has
been employed in the experiments (Zhang, 2003): It is
represented as
Yt=Lt+Nt
whereLtdenotes the linear component andNtdenotes the
non-linear component. These two components have to be
estimated from the data. These data then enter the rst
stage of the ARIMA to account for a linear component;
hence the residuals from the linear model will containonly the non-linear relationship. Let etdenote the residual
components at time t from the linear model, then
et= YtLt
where Lt is the forecast value for time t. Any signicant
non-linear pattern in the residuals will indicate the
limitation of the ARIMA. By modeling residuals using
ANNs, non-linear relationships can be discovered. With n
input nodes, the ANN model for the residuals will be
et= (et 1, et - 2,, etn) + et
where is a non-linear function determined by the neural
network and etis the random error. Denote the forecast
from ANN as Nt , the combined forecast will be
Yt = Lt + Nt
The proposed methodology of the hybrid system by
Zhang (2003) consists of two stages. In the rst stage, an
ARIMA model is tted to the time series data to capture
the linear part of the problem. In the second stage, an
appropriate neural network model is developed to forecast
the residuals from the ARIMA model. The hybrid model
exploits the unique feature and strength of ARIMA model
as well as ANN model in determining different patterns.
So, the above hybrid ARIMA neural network model
uses the following: (a) forecast residuals Nt (results of
ARIMA model) of neural network and (b) the forecast Lt
(results of ARIMA model).
The optimal architecture of hybrid model that captures
the non-linear patterns of residuals of ARIMA model
is formed in the same way as discussed in the model
formulation of neural network methodology.
2.2 Forecasng Accuracy and Trading
Simulaon
To compare the performance of the models, it is necessary
to evaluate them on previously unseen data. This situation
is likely to be the closest to a true forecasting or trading
situation. To achieve this, all models were maintained
with an identical out-of-sample period allowing a direct
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Stock Index Return Forecasting and Trading Strategy Using Hybrid ARIMA-Neural Network Model 7
comparison of their forecasting accuracy and trading
performance.
2.2.1 Out-of-Sample Forecasng Accuracy
Measures
This study uses six widely used statistical metrics such
as Mean Absolute Percentage Error (MAPE), Mean
Absolute Error (MAE), Root Mean Square Error (RMSE),
Directional Symmetry (DS), Correct Up trend (CU) and
Correct Down trend (CD) to evaluate the forecasting
capabilities between the three models. RMSE, MAPE and
MAE measure the deviation between actual and forecast
value. The smaller the values of MAE, MAPE and RMSE,
the closer are the predicted time series values to that of the
actual value. It is observed that RMSE, MAE or MAPEfunctions that are used for nancial forecasting models
may not make sense in the nancial context. Caldwell
(1992) gives a general review for the performance metrics.
Yao et al. (1996) use the correctness of the trend to judge
the performance of neural network forecasting model.
So this study uses additional evaluation measures, which
includes the calculation of correct matching number of
the actual and predicted values with respect to sign and
directional change. DS measures correctness in predicted
directions while CU and CD measure the correctness of
predicted up and down trend, respectively, in terms of
percentage. Higher value of these metrics indicates betterdirection and time information. The statistical performance
measures used to analyze the forecasting techniques are
presented in Appendix 1.
This study also uses other measures to test the models
ability to predict turning points. A correct turning point
forecast requires that:
Sign (Yt Yt t
- ) = Sign (Yt Yt 1)
Where Ytand Yt represents the actual and predicted value
at time t.
The ability of a model to forecast turning points can be
measured by a fourth evaluation method developed by
Cumby and Modest (1987). This model denes a forecast
direction variable Ftand an actual direction variable At
such that
At= 1 if DYt> 0 andAt= 0 if DYt0
Ft= 1 if DYt > 0 and Ft= 0 if DYt
0
Where DYt is the amount of change in actual variablesbetween time t1 and t; and DYt is the amount of changein forecasting variables between time t1 and t.
Cumby and Modest (1987) suggest the following
regression equation:
Ft= a0+ a1A1+ et
where etis error term; and a1is the slope of this linear
equation. Here, a1 should be positive and signicantly
different from 0 in order to demonstrate those FtandAt
have a linear relationship. This reects the ability of a
forecasting model to capture the turning points of a time
series.
2.2.2 Out-of-Sample Trading PerformanceMeasures
Statistical performance measures are often inappropriate
for nancial applications. Typically, modeling techniques
are optimized using a mathematical criterion, but
ultimately the results are analyzed on a nancial criterion
upon which it is not optimized. In other words, the forecast
error may have been minimized during model estimation,
but the evaluation of the true merit should be based on the
performance of a trading strategy.
Hence, this study uses a simple trading strategy toevaluate the performance of different models. The
operational detail of the trading is as follows. This study
considered an index in place of a single stock to avoid (or
average out) the impact of company-specic news on the
prediction of only one stock, given that the prediction is
performed by taking into account past prices only. In the
simulated market set up for experimenting the proposed
methodology, a virtual trader can buy or sell stock index
fund on the stock index concerned, and both short and
long positions can be taken over the index.
Assume that a certain amount of seed money is used in thistrading experiment. The seed money is used to buy stock
index funds when the prediction shows a rise in the stock
index price. To calculate the prot, the stock index funds
are bought or sold at the same time. It should be noted that
the price of the stock index fund is directly proportional to
the index level so that the virtual investor can gain from
both a fall and rise of the stock index price. The trading
strategy is to go long when the model predicts that the
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8 International Journal of Financial Management Volume 2 Issue 1 January 2012
stock index price will rise, i.e. the forecast is positive and
a sell otherwise. Then the stock index funds will be held at
hand until the next turning point that the model predicts.
For many traders and analysts, market direction is more
important than the value of the forecast itself, as in
nancial markets money can be made simply by knowing
the direction the series will move. The trading performance
measures used to analyze the forecasting techniques are
presented in Appendix 2. Some of the more important
measures include the Annualized return, Annualized
volatility, Sharpe ratio, maximum drawdown and average
gain/loss ratio. The Sharpe ratio is a risk-adjusted measure
of return, with higher ratios preferred to those that are
lower; the maximum drawdown is a measure of downside
risk and the average gain/loss ratio is a measure of overall
gain, for which a value above one is preferred.
The application of these measures may be a better standard
for determining the quality of the forecasts. After all, the
nancial gain from a given strategy depends on trading
performance, not on forecast accuracy.
3. Results
3.1 Summary Stascs
The mean, median, standard deviation, skewness, and
kurtosis for the NIFTY Index return are given in Table
1. The analysis shows that the sample mean of dailyreturns of NIFTY returns is not statistically different from
zero. The measure of skewness and kurtosis indicates
that the distributions of the return series are different
from the standard normal distributions. They reveal a
slight skewness and high kurtosis, which is common in
nancial time series data
Table 1 Descriptive Statistics of NIFTY Returns
Mean Median Std. Dev Skewness Kurtosis Observations
.000306 .001202 .015392 .621756 8.409610 1319
3.2 Staonarity Test
The Augmented Dickey Fuller test and Philip Perrons test
statistics as given in Table 2 indicate that the rate of return
of the NIFTY Index is stationary as the absolute value of
statistics is greater than the critical value and thus, the
time series is suitable for modeling.
Table 2 Unit Root Test for the NIFTY Return
Series
Augmented Dickey Fuller Test Phillip Perron Test
Statistic Critical Value Statistic Critical Value
15.64312 3.4382 32.62406 3.4382
3.3 ARIMA Model
The correlogram is used to identify the number of
signicant spikes of ACF or PACF of the NIFTY
Index return series. The lags of ACF and PACF whose
probability value is less than 5% are signicant and are
identied. Several ARMA specications were tried out.
After considering all possible models and looking at AIC
and SBIC as given in Appendix 3, the ARIMA (1 1 2)model are identied for NIFTY return.
In order to verify the adequacy of ARIMA model, the
study uses one of the popular diagnostics test known as
Breusch-Godfrey LM Test. Here the test is used to check
the presence of serial correlation in the residuals. It allows
us to examine the relationship between residuals and
several of its lagged values at the same time. The Null
Hypotheses to be tested is there is no serial correlation.
If the predictability value is greater than 5% then we can
accept the Null Hypotheses (at 95% condence levels)
which means there is no serial correlation in the series.The Breusch-Godfrey LM Test for serial correlation of
residuals as shown in Table 3 suggests that, in case of
NIFTY return the ARIMA model captures the entire
serial correlation and the residual do not exhibit any serial
correlation.
Table 3 Breusch-Godfrey Serial Correlation LM
Test for the NIFTY return
F-Statistics Probability Obs*R Square Probability
1.004433 0.366624 2.016921 0.364780
3.4 Neural Network Model
The combination of six input nodes and ve hidden nodes
yields a total of 30 different neural network architecture
which are being considered for each in-sample training
set for NIFTY return and the residuals of ARIMA model.
The best network architecture thus obtained from this
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Stock Index Return Forecasting and Trading Strategy Using Hybrid ARIMA-Neural Network Model 9
experiment for NIFTY return and residuals of ARIMA
model on the basis of least error (MSE) associated with
the model is 3-2-1, i.e. three input nodes in input layer,
two nodes in hidden layer and one node in output layer.
The Neural network model 3 2 1 provides better t tothe NIFTY returns and ARIMA residuals series.
3.5 Hybrid Model
One hidden layer is used to develop the hybrid models.
The study experimented with different nodes or neurons
in hidden layer, which varies from one to ve for the
different hybrid models. The output layer has one neuron
or node, which is the forecast value. The study uses
MSE to select the architecture. The hybrid model which
uses forecast results of ARIMA and the forecast residual
(results of ARIMA) of neural network has three hidden
neurons in hidden layer and three input neurons in input
layer.
3.6 Forecast Evaluaon
Out-of-Sample Forecasng Accuracy Results
For the NIFTY return series one-period-ahead forecast
were produced by the three models namely hybrid modes,
ARIMA and neural networks. The predictive performance
of the three models is summarized in Table 4.
it is observed that hybrid model outperforms the other two
models. MAE and RMSE achieved by the hybrid model
is quite low indicating that there is a smaller deviation
between the actual and predicted values in hybrid model.
Between neural network and ARIMA models, the former
performs better in terms of the three most commonly
used criteria i.e. MAE, RMSE and NMSE. The results
of the hybrid model show that by combining two models
together, the overall forecasting errors can be reduced
considerably.
In terms of other performance metrics like correct up
(CU) and correct down (CD), hybrid models yields
better performance than the other models. It is really the
directional symmetry (DS) measure that singles out the
neural network model as the best performer, predicting
most accurately 52.38 per cent of the time. These three
criteria provide a good measure of the consistency in
prediction of the time series direction.
Between hybrid model, neural network and ARIMA
models, the latter performs worst almost all of the times
in terms of performance metrics like direction sign and
change and non penalty based measure like MAE, NMSE
and RMSE. A majority decision rule would therefore
select the hybrid model as the overall best model.
Turning Point Evaluaon
Table 4 Out-of-Sample Prediction Accuracy
Model Performance Metrics
MAE RMSE NMSE DS CU CD
Hybrid Model 0.011063 0.015916 0.937088 0.514285 0.540541 0.481928
Neural Network 0.011107 0.016153 0.965219 0.523809 0.527027 0.481928
ARIMA 0.011125 0.016275 0.979853 0.425396 0.405405 0.439759
The main purpose of any nancial time series modelingis to determine how well forecasts from estimated
models perform based on the non penalty based measure
of performance such as MAE, RMSE and NMSE. The
forecasting accuracy statistics provide very conclusive
results. A glance at these values shows the superiority of
hybrid model over the two other models. Comparing the
forecasting performance of the three models in terms of
MAE, NMSE and RMSE for the NIFTY return time series;
The turning point evaluation method using Cumby andModest (1987) regression equation is shown in Table 5
for all the models.
The tratio of the slope coefcient a1of all the models
shows that it is statistically different from zero for the
NIFTY Index return time series. This implies that all
models have good turning point forecasting ability.
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Stock Index Return Forecasting and Trading Strategy Using Hybrid ARIMA-Neural Network Model 11
The hybrid model has the highest number of transactions
at 213, while the ARIMA model has the lowest at 183.
In addition, the hybrid model has the highest average
gain/loss ratio at 1.43, highest maximum daily prot at
12.24 per cent and lowest maximum daily loss at 3.94per cent, while the ARIMA model has the lowest average
gain/loss at 1.11 and highest maximum daily loss at 8.29
per cent. A simple neural network model outperforms the
hybrid model and ARIMA models in terms of percentage
of winning and per cent of losing trades with a value of
55.44 per cent and 44.55 per cent respectively. As with
statistical performance measures, nancial criteria clearly
single out the hybrid model as the one with the most
consistent performance: it is therefore considered the
best model for this particular application.
Zhang (2003) in their study found that hybrid ARIMA-NN model outperform the individual neural network
and ARIMA model. However, the studies uses only non
penalty based criteria (MAE, RMSE etc) to evaluate the
forecast model. The turning point forecast capability test
has not been considered. Moreover, these studies does
not evaluated their models based on the performance of
trading. The present study generally supports the nding
of the Zhang (2003) and contradicts the ndings of Tugba
and Casey (2005). The results validate the ndings with
real nancial time series data and also using by evaluating
the performance of models using a trading strategy.
4. Conclusion
This study reports an empirical work which investigates the
usefulness of hybrid (ARIMA and neural network) model in
forecasting and trading the S&P CNX NIFTY Index return.
The linear ARIMA model and the non-linear ANN model
are used in combination, aiming to capture different forms
of relationship in the time series data. The performance of
the hybrid model was measured statistically and nancially
via a trading simulation. The logic behind the trading
simulation is that, if prot from a trading simulation is
compared solely on the basis of statistical measures, the
optimum model from a nancial perspective would rarely
be chosen. The hybrid model was benchmarked against
traditional forecasting techniques such as ARIMA and
non-linear technique like neural network to determine any
added value to the forecasting process.
The empirical results with the NIFTY returns clearly
suggest that the hybrid model is able to outperform each
component model used in isolation. A neural network
architecture of 3-2-1 and ARIMA (1 1 2) is the best
identied model for forecasting the returns of NIFTY
Index. With the prediction, signicant prots were
obtained for a chosen testing period.
The results show that useful prediction could be made
for NIFTY without the use of extensive market data or
knowledge. It also shows how an 81.40 per cent annual
return and a Sharpe ratio of 3.15 could be achieved by
using the hybrid model. The present results indicate that
the hybrid ARIMA neural network models is important
in out-of-sample forecasting and trading performance,
and are in line with Wedding and Cios (1996) and Zhang
(2003) who found that hybrid model works well and
found to outperform the isolated models. The results are
in contrary with the results of Tugba and Casey (2005).
Thus, the study shows that hybrid ARIMA-neural network
model outperforms in forecasting stock index returns both
in terms of forecasting accuracy and in generating trading
returns. Probably this type of hybrid model could be used
by policy makers in forecasting nancial and economic
data, apart from traders, borrowers, FIIs and arbitrageurs
developing trading models that leads to better investment
decision and returns.
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Appendix 1
1. NMSE =( )
( )
Y Y
Y Y
t t
t t
-
-
2
2
2. MAE =| |Y Y
N
t t-
3. RMSE =S ( )Y Y
N
t t- 2
4. DS =100
Ndt
t , dt=
1
0
1 1if
Otherwise
( ) ( )Y Y Y Y t t t t- -
- -
5. CU =
d
k
t
t
tt
dt=1 0 0
01 1 1If
Otherwise
( ) ; ( ) ( )Y Y Y Y Y Y t t t t t t - > - -
- - - ,
kt=1 0
01If
Otherwise
( )Y Yt t- >
-
6. CD =
d
k
tt
tt
dt=1 0 0
01 1 1If
Otherwise
( ) ; ( ) ( )Y Y Y Y Y Y t t t t t t - < - -
- - - ,
kt=1 0
01If
Otherwise
( )Y Yt t-
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14 International Journal of Financial Management Volume 2 Issue 1 January 2012
MD= min ( max( ))t N
tc
tc
i t
R R= =
-1 1
8. % Winning trades : WT= 100
F
NT
tt
N
=
1
where Ft= 1 transaction prott> 0
9. % Losing trades :LT= 100
G
NT
tt
N
=
1
where Gt= 1 transaction prott< 0
10. Number of up periods : Nup = number ofRt> 0
11. Number of down periods : Ndown = number ofRt< 0
12. Number of transaction :NT= Ltt
N
=
1
whereLt= 1 if trading signalt= trading signalt 1
13. Total trading days : Number ofRts
14. Avg. gain in up periods : AG = (sum of allRt> 0)/
Nup
15. Avg. loss in down periods : AL = (sum of allRt< 0)/
Ndown
16. Prot T-statistics : T-statistics = N RA
As
17. Number of periods daily returns : NPR = Qtt
N
=
1
rise
where Qt= 1 if Yt> 0 else Qt= 0
18. Number of periods daily returns : NPF = Stt
N
=
1
falls
where St= 1 if Y
t< 0 else S
t= 0
19. Number of winning up periods :NWU= Btt
N
=
1
whereBt= 1 ifRt> 0 and Yt> 0 elseBt= 0
20. Number of winning down periods:NWD= Ett
N
=
1
whereEt= 1 ifRt> 0 and Yt< 0 elseEt= 0
21. Winning up periods (%) : WUP = 100*(NWU/
NPR)
22. Winning down periods (%) : WDP = 100 * (NWD/
NPF)
Appendix 3
Model AIC SBIC
ARIMA (1 1 1) 5.567444 5.552709
ARIMA (2 1 1) 5.571542 5.551880
ARIMA (1 1 2) 5.572746 5.553099
ARIMA (2 1 2) 5.571903 5.547325
ARIMA (1 1 3) 5.570930 5.546371
ARIMA (2 1 3) 5.571832 5.552339
** ARIMA (1 1 2) has the lowest AIC and SBIC value...
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Abstrac t
In the current unpredictable and volatile economic
environment, the investment avenues have been
changing rapidly. The stock market is one of them.There are multiple unpredictable factors which affect
the performance of the global market time to time. In
recent years, we have observed an unprecedented
growth in the complexity of instruments for trading
and risk management in international market and thus
issues of international stock market linkages and the
relationship between the Asian stock markets and
others stock markets deserves to be investigated
to justify the risk and return factor after the Asian
Financial Crisis. This is the first exhaustive study of its
kind on linkages and the interrelationship between the
Asian stock markets and others stock markets namely,
Malaysia (Kuala), Singapore (Strait), Philippines (Pse),
Indonesia (Jakarta), China (Shanghai), Japan (Nikkie),
Korea (Kospi), and the US (Dow) and reveal that stock
markets of Thailand, Japan and China are exogenous
before, during and after the crisis respectively. For the
purpose of study composite sample consisting of all the
stocks based on weekly stock indexes is been used to
construct panels and for the same the total samples
are separated into three sub periods January 2005
to December 2007, January 2008 to December 2008,
January 2009 to December 2009. The first part of
paper gives an insight about the Asian and US stock
markets and its various aspects. The second partconsists of data and their analysis, collected from the
various websites and manuals. The short-term linkage
was tested through granger causality test based on
A Study on the Linkages of Asian and the
US Stock Markets
S.M. Tariq Zafar*, D.S. Chaubey**and S.R. Sharma***
1. Introducon
Over the past decade, business has continued to grow with
pace and became more globalised than ever and resulting
demand for finance in many folds. With the growing
global trade the needs to communicate across the borders
has correspondingly multiplied, consequently there is
globalization of capital markets which became integral
part of economy and also custodian of socio-economic
integrity and play instrumental role in global economic
growth and have a deep impact on overall capitalemployment. Company in one country is borrowing in the
capital market of another country. In an open economic
competition and in the era of globalization performance
* S.M. Tariq Zafar, Director, Charak Institute of Business Management, Lucknow, India. ** Dr D.S. Chaubey, Director, UIBS, Dehradun, India.*** Dr S.R. SharmaDr. S.R.Sharma, Director, MIT, Dehradun, India
Vector Error Correction Model (VECM), and the co
integration or long-term linkage was through Engle-
Granger co integration test. The empirical results show
that the number of significant cointegrating vector is
higher during the crisis periods compared to otherperiods and concludes that the linkages between the
Asian and the US stock markets are stronger in the
post-crisis period
Keywords: VECM, Unit Root, DF test, ADF test,
Shanghai, Nikkie, Kospi, Dow, Stock market
JEl Codes: COI, C22, C51, C53, G12, G14, G15,
H83, F3
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16 International Journal of Financial Management Volume 2 Issue 1 January 2012
of organization changes day by day, investment avenues
became global and expanded gradually with continuous
strength. With growing capital market and introduction
of high breed financial instrument for common benefit
it became important to understand the concept of globalstock markets its investment, risk and return significance
in economic development.
To achieve complete efficiency in stock market may not be
possible because of difference in the economic, political,
legal and cultural environment which cast there shadow
on shareholders return. In general perception, investment
is regarded as a sacrifice of certain present value of the
uncertain future reward or allocation of funds to assets
that are expected to yield some gain over a period of time
which exclusively involves strategic decisions like, where
to invest, when to invest and how to invest. Since every
investor have different behavior with common appetite to
invest in those investment policies which may generate
maximum return with minimum risk. To have return
with safe growth and investment in unpredictable global
capital / financial market, investors have to establish some
diversified policies and procedures to shed the risk and
equate the invested expectations through global portfolio
which is an appropriate selection and collection of
investments held by institutions or a private individual.
In order to attract the investors globally, market reforms
are inevitable which may fuel competition in financial
market with safe return to investors and produce positive
financial vibration which explores capital market efficiency
and zenith the growth. Balance financial employment and
motivating returns on investment need healthy and vibrant
capital market. Positive stock markets encourage common
investors to invest in security market and maximize the
wealth. In order to cater the global economic competition
and varied requirements of savers and investors wide
spectrum of financial intermediaries with high breed
investments offerings both in money market and capital
market with nations central banks as the apex body have
come into existence across the globe. Further in effortsto manage unexplored challenges and capitalize the
global investment opportunities to the fullest, pursuance
of nations policy of liberalization, privatization, and
globalization has fueled overall competitiveness in
global economies and respective stock markets. Global
economies offering tremendous opportunities to stock
market and other financial organizations to explore
expand and diversify their product range and operators
besides improving their operational efficiency. Effective
execution of strategy is contingent upon adoption of new
high breed global financial instrument, technology better
possess of credit and risk appraisal, fund management,
product diversification, responsive structure, internal
control and availability of talented man power.
2. Causes of Recession and Its Impact
The financial crisis which in respect recognized as great
recession was sponsored by greedy uncontrolled fall
of world trade currency the US dollars by 40% which
chopped investors interest earning on their assets by more
than 80% during 2001-2008. It happens due to Federal
Reserve Banks secret mission with no accountability. The
over emphasis upon debt instead of income through hyper
inflating the money supply US dollar began to fall in value
and touched historic low against the major competitivecurrencies. The Federal Reserve Bank printed too many
dollars to cover mounting budget deficit which was $164.7
billion in the third quarter as to avoid a recession which
has created an imbalance between income and assets and
caused drastic inflation a hidden tax which was 4.3% in
2007 and was 1% higher than its GDP. It has been noted
that inflation sabotaged US growth and swallowed 15% of
its economy and its Infection spread and created insecurity
globally. The IMF sees inflation rate nearly doubling by
almost 12 % in emerging and developing world due to
recession impact.
To control inflation you need to control money supply but
in USA money supply exploded astonishingly 3,000%
from $302 billion in 1959 to $11.5 trillion in 2006 and thus
dollars purchasing power collapsed almost by 85% during
the period resulting America becoming largest debtor
on earth which mounted to & 53 trillion. Once largest
creditor nation in the world US became largest debtor
nation and its overall debt observation was considered in
between 70 to 100 trillion dollars with increasing trend
of more than $7.4 billion per day. In the previous year of
recession, its total debt grown almost by & 4.3 trillion,
comparatively 5.5 times larger than US, GDP. Interest onforeign debt rose almost by $2.2 trillion, Business and
financial sector debt grown by 7-11%, Almost 80% of
American debts which stood to around $42 trillion were
created since 1990. Highest debt ratio in world history,
thats $175,154 per man, woman and child or $700,616
per family of four.
In May 2007 trade surplus of US recorded historic
negative trade deficit of $827 billion. Since 1985, its
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A Study on the Linkages of Asian and the US Stock Markets 17
international deficit is approximately 35% larger than
social security spending, almost 50% larger than all
defense spending, and 2.5 times higher than Medicare. Its
merchandise ratio to national income has grown to 18%.
Its overall merchandise trade defi
cit of $815 billion in2007 was due to its trade performance and created history
by establishing second largest negative trade balance. Its
cumulative deficit mounted to 6.6 trillion dollars which
caused negative international net worth of $5 trillion and
its core manufacturing base reduced by 60%,
Americas 27% of the economy depends on international
trade in goods; foreign interests have more control over
the US economy than Americans and interest on foreign
debt rose almost by $2.2 trillion. They own about $9
trillion of US financial assets, including 13% of all stock,
13 % of agencies, and 27 % of corporate bonds. Its
foreign reserve and universal reserve fell from 50% of
the worlds total to 2.4% ratio, a 95% drop. As 2006 SDR
data revealed that USA has $69 billion as compared to
China $1.04 trillion, Japan $882 billion reserves. During
the period China and Japan together own 40% of the total
world international reserve ($5 Trillion) and US share is
just 1% with tremendously growing international debts in
comparison to it mare $69 billion international reserve.
It is also revealed that 80% of worlds official foreign
exchange reserves which is about $2.2 trillion dollars are
held by Asian central banks.
Since 1990s with declining US manufacturing base, its per
capita energy consumption have increased heavily. Each
day the world oil market consumes 76 million barrels,
America, with 5% of the total world population consumes
three times more oil than its total productivity, and it has
consumption of 20 million barrels per day (26 % of world
total oil production). The difference between Americans
production and consumption during the period was almost
75% which produced deficit gap of 15.5 million per day
and collectively 5.7 billion per year. Further, its population
increased 70 million and in its comparison in last 30 years
its oil reserves declined by 42% and it produces only 20billion barrels oil.
In comparison to economic growth its spending ratios and
its employee number increases faster than its population.
Federal government spending ratios reached almost
25% of its total national income which was 10 times
more growth in government spending than its economy
growth since 1930 and consumed 15% of its economy.
During the period education productivity dropped by
71% and unemployment rate increases to it all time
high. There was very unusual situation. The economy
grew at a 0.6% annual rate over the last two quarters, the
slowest pace since 2001 recession. In 2007, US housing
market worsened and were one of the major causes forthe subprime crises that were witnessed and resulted
in collapse of large financial institutions, the bailout of
banks by national government and downturns in stock
markets around the world. Years of easy liquidity and
relatively low interest rate regime fuelled an economic
boom across the globe, driven largely by credit expansion
and magnificent rise in asset prices. Default and losses on
other loan types also increased significantly as the crises
expanded from the housing market to other parts of the
economy. However, the obscure problem of plenty began
to surface in the US mortgage economy, with disastrous
parameter. Mortgage prices in US declined 40% in lessthan a year and impacted the economy of US in large.
Policymakers did not recognize the increasingly important
role played by financial institutions such as investment
banks and hedge funds, also known as the shadow banking
system which resulted number of established and leading
banks collapsed as some of them were not commercial
banks but was connected with commercial banks through
derivatives transactions. Large number of the banks
was heavily dependent for short term funds on money
market mutual fund that provided wholesale fund, fled
the market. In fact banks were not felled losses on theirsubprime loans. They were felled by losses on mortgage
backed securities caused by drying up of liquidity and
by the loss of nerve of market participant, confidence.
Questions regarding banks solvency, declines in credit
availability, and damaged investors confidence had an
impact on global stock markets, where securities suffered
large losses during late 2008 and early 2009.
The US tried to maintain and expands consumption
rather than producing real goods and savings thus facing
uncontrollable debt in relation to size of its economy. In
order to develop stability in overall market it providedfunds to encourage lending and restore faith in commercial
paper markets in addition it also bailout integral financial
institutions and implemented economic stimulus programs
to promote and protect market confidence. The (FED)
chairmen acknowledged that the central bank faced
increasingly contradictory pressure of slowing growth
and rising consumer prices. In past 1 % decline in US
growth impacted growth in emerging economies by 0.5%
to 1 % depending on trade and financial links to US and
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18 International Journal of Financial Management Volume 2 Issue 1 January 2012
Week dollars impacted Asian exports in particular.
Since 1997, Asia attracted almost 50% of the total
capital inflow. It is due to large population which make
Asia darling of investor. The economies of Southeast
Asia handsomely maintained a high interest rate whichattracted investors who are found of high return. With the
support of World Bank, IMF, regional economies of Asia
experienced high growth rates but the recession of US
impacted global market to a large extent and market with
close interrelation suffered in multiple way. In addition to
recession, Asian countries weak domesticfinancial system,
free international capitals flows, fluctuating market and
investors sentiment and hype hazard economic policies
also played supportive role.
3. Literature ReviewLiterature review is an organized and scientific approach
of study which require collection and systematic analysis
of literatures in the selected area of the researchers in
which they have limited or no exposure. A deep survey of
literature exposed the truth that large number of researchers,
independent and professional research institutions and
academicians has carried out extensive research in the
field of international stock market linkages and many
are concerned about the relationship between the Asian
stock markets and others after the Asian Financial Crisis,
Sharpe and Cooper, Basu, Irala,Brown, S.V. RamanaRao, Zafar S.M, Tariq, Naliniprava Tripathy,M. Kabir
Hassan, Neal C. Maroney Hassan Monir El-Sadyand
Ahmad Telfah, Barman and Smanta, Myong Jae Lezand
SooCheong (Shawn) Jang,and they produced important
findings which pave multiple dimensions and set ultimate
standard. It has been noted that large number of the studies
has been carried out in developed economy or developed
countries stock market, few studies in this context is been
carried out in developing economy or countries stock
market. Further outcome of these studies reflects that
studies which are carried out in developing nations are not
scientific and lack authenticity and validity thus keepingdeveloping nations in mind this paper initiate humble
beginning in this, respects.
Ayshanapalli et al. (1995) in his study he examine the
existence of a common stochastic trend between the US
and the Asian stock market movements during pre- and
post-October 1987 periods. For the study he took data
for the time period January 1, 1986 to May 12, 1992
from Singapore, Thailand, Malaysia, Philippines, Hong
Kong Japan and United States. He used cointegration
and error-correction model for his study and found that
influence of the US stock market innovations were in
excess during the post-October 1987 period. The study
concluded with the fact that Asian stock markets are lessintegrated with Japans stock market than they are with
the US stock market, Masih and Masih (1999) in his
study examined the long-term and short-term dynamic
linkages between the international and Asian emerging
stock markets, and tried to quantify the extent of the
Asian stock market fluctuations which are explained
by intra-regional contagion effect. The finding of study
at the global level, confirm the widely flouting doctrine
of united State leadership in short and long term stock
market and its existing relationship between OECD stock
markets along with the emerging Asian stock markets.
At Southeast Asia, the results of the study confirm thedominating role of Hong Kong stock market which was
even expected too, Malliaropulos and Priestly (1999)
in their study investigated the predictable component of
Southeast Asia Stock market. For the purpose data from
January 1988 to December 1995 at weakly frequency
basis was taken as sample and the study findings were
assessed by adjusting stocks returns for potential time
varying expected returns and partial integration of this
emerging market into world capital market. The study
clearly indicated the danger of testing market efficiency
without sufficiently adjusting the stock returns with care,
especially time variation in the expected return and partial
integration of local markets into world class, Sheng and
Tu (2000)in their study they investigated linkages among
national stock markets before and during the period of
their Asian Financial crisis through co-integration and
variance decomposition analysis. For the study they
took data from July 1, 1996 to June 30, 1998 on daily
closing prices basis of the New York S&P 500 and the 11
major Asia-Pacific equity market indexes. The outcomes
of the study reveals that Southeast Asian countries have
strong relationship in comparison to the Northeast Asian
countries and thefi
ndings also indicate that there were nocointegrational relationship prior to Asianfinancial crises.
Further the forecast error variance decomposition finds
that the degree of exogeneity for the stock markets has
been reduced to an extent, Manning (2002)in his study
tried to investigate the co- movement of stock markets in
South Asia, concurrently taking the United States to be
an external stock market. For the study they took the data
compromised weekly and quarterly information on stock
indexes and US dollars series for the US, Hong Kong,
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4.1 Methodology
The study is done with special reference to relationship
between the Asian stock markets and others after the Asian
Financial Crisis. For the purpose, data from January 2005
to December 2009 from Malaysia (Kuala), Singapore
(Strait), Philippines (Pse), Indonesia (Jakarta), China
(Shanghai), Japan (Nikkie), Korea (Kospi), and the US
(Dow) stock markets were mainly extracted. Three panels
namely Panel A, Panel B and panel C containing different
equity prices and their variances listed on the selected stock
exchanges have been drawn. Simple random technique has
been used, analytical and descriptive research design is
been adopted which based on the secondary data collected
from the websites, annual reports and journals, published
periodicals, stock exchange and various other related sites.
A composite sample, consisting of all the stocks is beenused to construct panels and for the same the total samples
are separated into three sub periods. First period is pre-
crises period spanning from January 2005 to December
2007 denoted as panel A. Second period is during crises
period spanning from January 2008 to December denoted
by panel B and third period is post-crises period spanning
from January 2009 to December 2009 denoted by Panel
C. To interpreting the results Dickey-Fuller (ADF) unit
root test, Phillips- Perron (PP) test and Granger- causality
based on Vector Error Correction Model (VECM) are
used.
4.2 Tools Used for Analysis
In this study, for interpreting the results and to determine
stationarity of the data series the statistical and econometric
tools are been used. The very first step is to examine the
stationary of the variables. Further unit root test is applied
to check the stationary of the series by using the Dickey-
Fuller (DF) test, Augmented Dickey-Fuller (ADF) test.
For robustness of unit root test results the series is also
tested by using the Phillip- Perron (PP) test. Then the
cointegration test (Engle-Granger cointegration test) is
used to estimate the long run equilibrium relationshipamong the variables. Finally, Granger causality test is
applied to test the short-run relationship between the
stationary series which deals with financial time series
data.
4.3 Unit Root
Unit Root test is applied to check the stationary of the
series (Gujarati, 2003; and Enders, 2005). The stationary
condition here has been tested using the Dickey Fuller,
Augmented Dickey Fuller and Philip-Peron unit root
tests.
4.4 DickeyFuller Unit Root Test (DF Test)
In statistics, the DickeyFuller test tests whether a unit
root is present in an autoregressive model. It is named
after the statisticians D. A. Dickey and W. A. Fuller, who
developed the test in 1979.).
A simple AR (1) model is
yt= ryt 1+ ut
Where yt is the variable of interest, t is the time index,
ris a coefficient, and utis the error term. A unit root is
present if |r| = 1. The model would be non-stationary inthis case.
The regression model can be written as
yt= (r 1)yt 1+ ut= dyt 1+ ut
Where is the first difference operator
4.5 Augmented Dickey Fuller Test (ADF Test)
In statistics and econometrics, an Augmented Dickey
Fuller test (ADF) is a test for a unit root in a time seriessample. It constructs a parameter correction for higher
order correlation, by adding lag difference of the time
series. It is consists of a regression of the first difference of
the series against the series lagged once, lagged difference
terms, and optionally, a constant and tie trend.
Dyt= a+ bt+ gyt 1+ d1Dyt 1+ + dpDytp+ et,
Consequently, there are three main versions of the test
which are as commonly used in Dickey Fuller unit root
test (DF test) and in Augmented Dickey Fuller test (ADF
test). Each version of the test has its own critical value
which depends on the size of the sample. They are as: 1. Test for a unit root:
yt= dyt 1+ ut
2. Test for a unit root with drift:
yt= a0+ dyt 1+ ut
3. Test for a unit root with drift and deterministic time
trend:
yt= a0+ a1t+ dyt 1+ ut
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A Study on the Linkages of Asian and the US Stock Markets 21
4.6 Philip-Peron Test
In statistics, the Phillips- Perron test is a unit root test. It is
used in time series analysis to test the null hypothesis that
a time series is I