-
Time Series Analysis
1
[email protected]
Teaching assistant: [email protected]
(home page): [email protected] home page:
www.uni-tuebingen.de/uni/wwo/Grammig/veranstaltungengramm/zeitreihenanalyse05.html
• 3 h per week lecture + 1 h „exercise“ or PC lab (given by
Kerstin Kehrle)
• PC lab uses EVIEWS
• Revise ∼2 h + x per week (Assignments)
• Exam: Either oral or written (open book)Material of lectures,
reading list, chapters in textbooks(see course plan in
lecture_ts06.xls (download))
• Prerequisites : Undergraduate Math & Stats &
Economics
•Take notes !
• Textbooks: F. Hayashi (2000) Econometrics, PrincetonJ.
Hamilton (1994) Time Series Analysis, PrincetonW. Enders (1995)
Applied Econometric Time Series, Wiley
•Why follow the course ?
mailto:[email protected]:[email protected]://www.uni-tuebingen.de/uni/wwo/Grammig/veranstaltungengramm/zeitreihenanalyse05.html
-
Why follow the course? Time series techniques are essential in
Economics & Finance
Predictability of returns
Testing and Estimating Asset Pricing models
Properties of price formation processes
Properties of macroeconomic time series
Persistence of macro-shocks
Testing economic theories (PPT, Expectation
Hypothesis of Term Structure)
Transmission of monetary policy
Finance
Economics
2
-
Agenda
Basic concepts of time series analysis: Stationarity,
Ergodicity…
Basic stochastic processes : White Noise, Random Walks,
MovingAverage and Autoregressive Processes and their use in
Economics &Finance.
Modelling univariate time series (ARMA models)
Regression analysis using stationary time series
Structural Vector Autoregressive Systems (SVAR)
Equilibrium Correction and Cointegration
ARCH (Autorregressive Conditional Heteroskedasticity)
(see course plan in lecture_ts06.xls (download))
3
-
4
for methods of analyzingeconomic time series with time-varying
volatility (ARCH)
-
a)Daily close Dow Jones,from 08/23/1988to 08/22/2000,daily
frequency
b) Realisation of
)1,0(~
250/1
2.0
08.0
N
t
ttx
xx
tt
ttt
ttt
∆+
∆+∆+
=∆
=
=
∆+∆=−
ε
σ
µ
εσµ(?)tx
What is it? (1)
5
-
What is it? (2)
a)Daily close Dow Jones,from 08/23/1988to 08/22/2000,daily
frequency
b) Realisation of
)1,0(~
250/1
02.0
08.0
N
t
ttx
xx
tt
ttt
ttt
∆+
∆+∆+
=∆
=
=
∆+∆=−
ε
σ
µ
εσµ(?)tx
6
-
What is it? (3)
)1,0(~
248/1
2.0
N
t
tx
tt
tttt
∆+
∆+∆+
=∆
=
∆=
ε
σ
εσ
a)log of relative DAX change,from 01/02/1996 to 12/27/1996,daily
frequency
b) Realisation of(?)tx
7
-
What is it? (4)
a)log of relative DAX change,from 01/02/1996 to 12/27/1996,daily
frequency
b) Realisation of
)1,0(~
248/1
047.0
N
t
tx
tt
tttt
∆+
∆+∆+
=∆
=
∆=
ε
σ
εσ(?)tx
8
-
What is it? (5)
( )
)1,0(~
4/1
4.1
99.0
3
N
t
xtxxx
tt
ttttt
∆+
∆+
=∆
=
=
=
+∆−−=−
ε
σ
φ
µ
σµφa) Realisation of
b)3 month CHF LIBORfrom 01/01/1974to 01/01/2002,3-month
frequency
(?)tx
t tt ∆+∆ ε
9
-
What is it? (6)
( )
)1,0(~
4/1
4.1
99.0
3
N
t
txtxxx
tt
ttttttt
∆+
∆+∆+
=∆
=
=
=
∆+∆−−=−
ε
σ
φ
µ
εσµφa) Realisation of
b)3 month CHF LIBORfrom 01/01/1974to 01/01/2002,3-month
frequency
(?)tx
10
-
What is it? (7)
( )
)1,0(~
1
9.0
5.0
23
N
t
ttxxx
tt
tttttt
∆+
∆+∆+
=∆
=
=
=
∆+∆−−=−
ε
φ
σ
µ
εσµφ
a)Price-dividend ratio S&P500from 12/31/1947to
12/31/1996,annual frequency
b) Realisation of(?)tx
11
-
What is it? (8)
a)Price-dividend ratio S&P500from 12/31/1947to
12/31/1996,annual frequency
b) Realisation of( )
)1,0(~
1
9.0
5.0
23
N
t
ttxxx
tt
tttttt
∆+
∆+∆+
=∆
=
=
=
∆+∆−−=−
ε
φ
σ
µ
εσµφ(?)tx
12
-
13
AssignmentsReview statistical basics and english term (e.g.
Hamilton, 1994, p.739 ff.)Course dictionary: download from course
page
Random Variables and distributions (distribution function,
densityfunction), especially Normal distribution.Expectation
Operator (mean, variance, higher moments)and properties of
expectation operator
Joint distributions, covariance and correlation, Dependence
andindependence of random variables
Conditional probability and conditional distribution
Conditional expectationIndependence
Hypothesis testing (significance levels, type I and II errors,
null and alternative hypothesis)
Estimation basics: Least Squares (one explanatory variable), law
oflarge numbers, central limit theorems
-
It is important to distinguish the realisation from the
process
stochastic process
( )0
1,0~ ,
0
1
=+= −
YNYY tttt εε
14
Estimate by taking ensembleaverages at each point
( ) 0.991ˆ10000
1ˆ
-0.00410000
1ˆ
210000
111
21
10000
111
=−=
==
∑
∑
=
=
s
s
s
s
Y
Y
µσ
µ
( ) 99.028ˆ10000
1ˆ
023.010000
1ˆ
210000
1100100
2100
10000
1100100
=−=
==
∑
∑
=
=
s
s
s
s
Y
Y
µσ
µ
( ) 25.130ˆ1ˆ
6.3771ˆ
100
1
22
100
1
=−=
==
∑
∑
=
=
tt
tt
YT
YT
µσ
µ
Estimate by taking sample averages
-
15
stochastic process
( ) 1.065ˆ1ˆ
0.0111ˆ
100
1
22
100
1
=−=
−==
∑
∑
=
=
tt
tt
YT
YT
µσ
µ
( ) 1.001ˆ10000
1ˆ
-0.00410000
1ˆ
210000
111
21
10000
111
=−=
==
∑
∑
=
=
s
s
s
s
Y
Y
µσ
µ
Estimate by taking sample averages
Estimate by taking ensembleaverages at each point
( ) 0.996ˆ10000
1ˆ
000.010000
1ˆ
210000
1100100
2100
10000
1100100
=−=
==
∑
∑
=
=
s
s
s
s
Y
Y
µσ
µ
( )0
1,0~ ,
0 ==
YNY ttt εε
It is important to distinguish the realisation from the
process
Time Series AnalysisWhy follow the course? Time series
techniques are essential in Economics & FinanceAgendaIt is
important to distinguish the realisation from the process
![Applied_Econometric_Time_Series[1] enders](https://static.documents.pub/doc/80x56/551abf054a7959580a8b47fe/appliedeconometrictimeseries1-enders.jpg)
