Business Forecasting 1 Dr. Mohammed Alahmed [email protected] (011) 4674108 Dr. Mohammed Alahmed.

Dr. Mohammed Alahmed

Business Forecasting

1

Dr. Mohammed [email protected]

(011) 4674108

Dr. Mohammed Alahmed

Introduction

• What is Forecasting?– A planning tool that helps

management in its attempts to cope with the uncertainty of the future, relying mainly on data from the past and present and analysis of trends.

– The process of predicting a future event based on historical data.

– Forecasting is a tool used for predicting future demand based on past demand information.

2

Dr. Mohammed Alahmed 3

Why is forecasting important?

• We forecast very different things such as weather, traffic, stock market, state of our economy from different perspectives.

• Almost every business attempt is based on forecasting.

• Forecasting is an essential element of most business decisions.

• Forecasting is important in the business decision-making process.

• Forecasting reduces the range of uncertainty about the future.


• Forecasting can be used for:– Strategic planning (long range

planning)

– Finance and accounting (budgets and cost controls)

– Marketing (future sales, new products)

– Production and operations


TimeJan Feb Mar Apr May Jun Jul Aug

Actual demand (past sales)

Predicted demand

We try to predict the future by looking back

at the past

Predicted demand looking back six months


Forecasting Methods

QualitativeBased on subjective opinions from one or

more experts

QuantitativeBased on data and

analytical techniques


Qualitative Forecasting Methods

Judgment Methods

Sales force

composite

Executive Judgemen

t

DelphiMethod

Counting Methods

Market testing

Consumer market survey

Industrial market survey


Advantages

• Do not require mathematical background

• Wide acceptance• Very Long-range

forecasting

Disadvantages

• Biased• Not consistently

accurate over time


Quantitative Forecasting Methods

Time Series

Movin

g

avera

ges

Exponenti

al

smooth

ing

Ad

apti

ve

filt

eri

ng

Tren

d a

naly

sis

Tim

e s

eri

es

deco

mposi

tio

n

Box

-Jenki

ns

Causal Methods

Corr

ela

tion

meth

ods

Regre

ssio

n

models

Leadin

g

indic

ato

rs

Eco

nom

etr

ic

test

s


Selecting a Forecasting Method

• Data availability– Do you have historical data available?

• Time horizon for the forecast– Is the forecast for short-run or long-run

purposes?• Required accuracy

– How much accuracy is desired?– Is there a minimum tolerance level of

error?• Required Resources

– How much time and money are you willing to spend on your forecast?


Who needs forecasts?

• Every organizations, large and small, private and public.

• Needs for forecasts cuts across all functional lines.– It applies to problems such as:

• How much this company worth? (Finance)• Will a new product be successful? (Marketing)• What level of inventories should be kept? (Production) • How can we identify the best job candidates? (Personnel)


Naïve Method 1

• It is based solely on the most recent information available.

• Suitable when there is small data set. • Some times it is called the “no change”

forecast.• The naïve forecast for each period is the

immediately proceeding observation.


Naïve Method 1

• The simplest naïve forecasting model, in which the forecast value is equal to the previous observed value, can be described in algebraic form as follows:

• Since it discards all other observations, it tracks changes rapidly.

1ˆ tt yy


Example: Sales of saws for Acme Tool Company,1994-2000

• The following table shows the sales of saws for the Acme tool Company. These data are shown graphically as well.

• In both forms of presentation you can see that the sales varied considerably throughout this period, from a low of 150 in 1996Q3 to a high of 850 in 2000Q1.

• The Fluctuations in most economic and business series (variables) are best seen after converting the data graphic form.


Year Quarter t sales1994 1 1 500

2 2 3503 3 2504 4 400

1995 1 5 4502 6 3503 7 2004 8 300

1996 1 9 3502 10 2003 11 1504 12 400

1997 1 13 5502 14 3503 15 2504 16 550

1998 1 17 5502 18 4003 19 3504 20 600

1999 1 21 7502 22 5003 23 4004 24 650

2000 1 25 8502 26 6003 27 4504 28 700

0

100

200

300

400

500

600

700

800

900

0 5 10 15 20 25 30

Saw

s

Year

Sales of saws for the Acme Tool Company: 1994-2000



• The forecast for the first quarter of 2000 , using the naïve method is:

650ˆ

ˆ

ˆ

25

2425

1

y

yy

yy tt



Year Quarter t sales Forecast1994 1 1 500

2 2 350 5003 3 250 3504 4 400 250

1995 1 5 450 4002 6 350 4503 7 200 3504 8 300 200

1996 1 9 350 3002 10 200 3503 11 150 2004 12 400 150

1997 1 13 550 4002 14 350 5503 15 250 3504 16 550 250

1998 1 17 550 5502 18 400 5503 19 350 4004 20 600 350

1999 1 21 750 6002 22 500 7503 23 400 5004 24 650 400

2000 1 25 850 6502 26 600 8503 27 450 6004 28 700 450


Example :Sales of saws for Acme Tool Company,1994-2000

0

100

200

300

400

500

600

700

800

900

0 5 10 15 20 25 30

Sale

s

Quarters

Quarterly Sales of Saws for Acm toll Company 1994-2000

sales Forecast


Naïve Method 2

• One might argue that in addition to considering just the recent observation, it would make sense to consider the direction from which we arrived at the latest observation.

• That is: if the series dropped to the latest point, perhaps it is reasonable to assume further drop and if we have observed an increase, it may make sense to factor into our forecast some further increase.


Naïve Method 2• In general algebraic terms the model

becomes

• Where P is the proportion of the change between period t-2 and t-1 that we choose to include in the forecast.

• We call this Naïve method(2).

)(ˆ 211 tttt yyPyy



• The forecast for the first quarter of 2000 using the Naïve method(2) with P = 50% is:

775)400650(5.0650ˆ

)(5.0ˆ

)(5.0ˆ

25

23242425

22512512525

y

yyyy

yyyy



Year Quarter t sales Forecast (N2)1994 1 1 500

2 2 3503 3 250 2754 4 400 200

1995 1 5 450 4752 6 350 4753 7 200 3004 8 300 125

1996 1 9 350 3502 10 200 3753 11 150 1254 12 400 125

1997 1 13 550 5252 14 350 6253 15 250 2504 16 550 200

1998 1 17 550 7002 18 400 5503 19 350 3254 20 600 325

1999 1 21 750 7252 22 500 8253 23 400 3754 24 650 350

2000 1 25 850 7752 26 600 9503 27 450 4754 28 700 375



0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 25 30

Sale

s

Quarters

Quarterlt sales of Saws for Acme Toll Company 1994-2000

sales Forecast (N2)


Evaluating Forecasts

• We have looked at two alternative forecasts of the sales for the Acme Tool Company. Which forecast is best depends on the particular year or years you look at.

• It is not always possible to find one model that is always best for any given set of business or economic data.

• But we need some way to evaluate the accuracy of forecasting models over a number of periods so that we can identify the model that generally works the best.



• Among a number of possible criteria that could be used, five common ones are:

1. Mean absolute error (MAE)2. Mean percentage error (MPE)3. Mean absolute percentage error (MAPE)4. Mean squared Error (MSE)5. Root Mean squared Error (RMSE)6. Theil’s U-statistic



• To illustrate how each of these is calculated, let:• yt = Actual value in period t

• = Forecast value in period t

• n = number of periods used in the calculation

ty


Mean Absolute Error

• The mean absolute error (MAE)• Measures forecast accuracy by averaging

the magnitudes of the forecast errors.

n

ttt yy

n 1

ˆ1

MAE


Mean Percentage Error• The Mean Percentage Error (MPE)• Can be used to determine if a forecasting method is

biased (consistently forecasting low or high)• Large positive MPE implies that the method

consistently under estimates.• Large negative MPE implies that the method

consistently over estimates.• The forecasting method is unbiased if MPE is close to

zero.

n

t t

tt

y

yy

n 1

)ˆ(1MPE


Mean absolute Percentage Error

• The Mean Absolute Percentage Error (MAPE)• Provides an indication of how large the forecast

errors are in comparison to actual values of the series.

• Especially useful when the yt values are large.

• Can be used to compare the accuracy of the same or different methods on two different time series data.

n

t t

tt

y

yy

1

ˆ

n

1MAPE


Mean Squared Error

• This approach penalizes large forecasting errors.

n

ttt yy

n 1

2)ˆ(1

MSE


Root Mean Squared Error

• The RMSE is easy for most people to interpret because of its similarity to the basic statistical concept of a standard deviation, and it is one of the most commonly used measures of forecast accuracy.

n

yyn

ttt

1

2)ˆ(RMSE


Theil’s U-statistic• This statistic allows a relative comparison of

formal forecasting methods with naïve approaches and also squares the errors involved so that large errors are given much more weight than smaller errors.

• Mathematically, Theil’s U-statistic is defined as

1

1

21

1

1

211

)(

)ˆ

(

n

t t

tt

n

t t

tt

y

yyy

yy

U


Theil’s U-statistic

• U = 1 The naïve method is as good as the forecasting technique being evaluated.

• U < 1 The forecasting technique being used is better than the naïve method.

• U > 1 There is no point in using a formal forecasting method since using a naïve method will produce better results


Example: VCR data

• Data was collected on the number of VCRs sold last year for Vernon’s Music store.

Month t Sales Forecast(N1) At - Ft

January 1 123February 2 130 123 7March 3 125 130 -5April 4 138 125 13May 5 145 138 7June 6 142 145 -3July 7 141 142 -1August 8 146 141 5September 9 147 146 1October 10 157 147 10November 11 150 157 -7December 12 160 150 10


Example: VCR data

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14

VC

R S

ales

Months

Monthly VCR Sales

Sales Forecast(N1)


Example: VCR data

Month t Sales Forecast (N2) At - Ft

January 1 123February 2 130March 3 125 133.5 -8.5April 4 138 122.5 15.5May 5 145 144.5 0.5June 6 142 148.5 -6.5July 7 141 140.5 0.5August 8 146 140.5 5.5September 9 147 148.5 -1.5October 10 157 147.5 9.5November 11 150 162 -12December 12 160 146.5 13.5


Example: VCR data

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14

VC

R S

ales

Months

Monthly VCR Sales

Sales Forecast (N2)


Example:VCR data

• Error analysis:Forecast (N1) RMSE = 7.24

Forecast (N2) ) RMSE = 8.97

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14

VC

R S

ale

s

Months

Monthly VCR Sales

Sales Forecast(N1) Forecast (N2)



• We will focus on root-mean-squared error (RMSE) to evaluate the relative accuracy of various forecasting methods.

• All quantitative forecasting models are developed on the basis of historical data.

• When RMSE are applied to the historical data, they are often considered measures of how well various models fit the data (how well they work in the sample).



• To determine how accurate the models are in actual forecast (out of sample) a hold out period is often used for evaluation.

• It is possible that the best model “in sample” may not be the best in “out of sample”.


Using Multiple Forecasts

• When forecasting Sales or some other business economic variables, it is best to consider more than one model.

• In our example of VCR sales, using the two naïve model, we could take the lowest forecast value as the most pessimistic, the highest as the most optimistic, and the average value as the most likely.

• This is the simplest way to combine forecasts.


Sources of Data

• The quantity and type of data needed in developing forecasts can vary a great deal from one situation to another.– Some forecasting techniques require only data

series that is to be forecasted• Naïve method, exponential smoothing, decomposition

method.

– Some , like multiple regression methods require a data series for each variable included in the forecasting model.


Sources of Data

• Sources of data– Internal records of the organization.– Outside of the organization

• Trade associations• Governmental and syndicated services

• There is a wealth of data available on the internet.

Date post:	18-Jan-2016
Category:	Documents
Upload:	edith-robertson
View:	218 times
Download:	1 times

Business Forecasting 1 Dr. Mohammed Alahmed [email protected] (011) 4674108 Dr. Mohammed Alahmed.

Documents