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FORECASTING

A probabilistic estimate

A description of a future value or condition

In general, effective forecasts vital for achieving thestrategic and operational goals of all organisations (publicor private, profit or non-profit, product or service).

In particular eliminating waste, such as inventory shortages,

excesses

missed due dates plant shut downs lost sales lost customers in the long run, missed strategic opportunities.

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FINANCIAL & STRATEGIC IMPORTANCE

Improved strategic information

Improved marketing information

Improved financial information

Improved operations information

Improved customer service

Improved allocation of scarce resources Improved manufacturing and operating efficiency

Improved productivity

Improved stability in planning

Reduced finished goods inventory Elimination of waste

More flexibility to respond to customer preferences

Increased profitability

Increased return on investment.

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INDEPENDENT-VS-DEPENDENT DEMANDS

Only independent demands need to be forecast and themany dependent demands can then be computed.

E.g. An auto firm needs to forecast demand for its finalassembly called its system unit. It is the independentdemand. Its spares & components or the dependentdemands can be computed (i.e. wheels, tyres, axels,gear boxes, engines, carburetors, batteries, wind shield,

electrical fittings, upholstery etc.).

Similarly for bicycles or micro computers, hospitals,educational institutions, wholesalers, retailers etc.

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THE FORECASTING HIERARCHY

Type of Demand Examples of ForecastsMacroeconomy : Forecasts of income, productivity,

employment, interest rates,technology.

Industry Demand : General demand for products of anindustry e.g. automobiles.

Company demand : The companys market share.

Product-line demand : Small cars, mid-sized cars, luxurycars.

Company-wide demand : National demand for each of theproducts.

Demand for each location : Demand for luxury cars inMumbai, Delhi, Chennai etc.

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ANALOGY WITH FISHING

In fishing, as in forecasting, one casts a line forward.The cast is called forward cast. A backcast in fly-fishing is the toss of a line backward overhead.

Analogous to modeling past demands in forecasting.

Past patterns are modeled (backcast) to throw thosepatterns forward to the future.

Often, therefore a good backcast determines a goodforecast.

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FORECASTING METHODS : AN OVERVIEW

TIME SERIES MODELS: Trend fitting Moving averages Exponential smoothing Fourier series ARIMA

CAUSAL MODELS: Multiple regression Econometric Cyclical

Multivariate ARIMA Vector autoregression I-O Models

QUALITATIVE TECHNOLOGICAL: Expert opinion Sales force composite Delphi Historical Analogy S-growth curves

OTHER QUALITATIVE:

Market research Expert systems Artificial Neural Networks

Genetic Algorithms

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THE FORECASTING PROCESS

Problem definition: plans, objectives and decisions

boundaries of a system

Information search:

define the system define possible cause and effects

Hypothesis/Theory/Model formulation: refine causal model graphical exploration postulate direction of causality

consider appropriate methods

Experimental Design: select in-sample fitting data select out-of-sample validation data

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THE FORECASTING PROCESS (Contd.)

Experimental Execution: fit several in-sample models forecast out-of-sample models

Results Analysis: examine the validity of assumptions

examine whether results support theory examine whether experts agree perform out-of-sample validity tests

Ongoing Maintenance & Verification:(Ensure that the model is still valid and effective) incorporate real-time judgment implement model/system monitor model/system.

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TIME SERIES ANALYSIS & FORECASTING

COMPONENTS : TREND (INCOME, CONSUMPTION, EXPORTS,

IMPORTS, PRICE INDEX, STOCK PRICES ETC.) SEASONALITY (SALES, TRAVEL & TOURS,

FESTIVALS/HOLIDAYS AFFECT CERTAINPHENOMENA & PURCHASE PATTERNS)

CYCLICAL (ASSOCIATED WITH BUSINESS CYCLEFLUCTUATIONS)*

RANDOM (IRREGULAR)

* GENERAL MERCHANDISE SALES DIP DURINGRECESSIONS AND REMAIN SLUGGISH FORSEVERAL MONTHS AFTER THE UPTURN HASSTARTED.

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LINEAR TREND :

y = + t CONSTANT RATE OF GROWTH (MOST MACRO

SERIES)NON-LINEAR TRENDS GROWING BUT AT A SLOWER RATE (POPULATION,

DURABLE CONSUMER GOODS ETC.) DECLINING BUT AT A SLOWER RATE (SPIRALLIG

OIL PRICES OF THE 1973-80 PERIOD CAUSING A BIGDECLINE IN THE ENERGY INTENSITY PER UNIT OFGDP. INITIALLY BUT LATER DECLINING MORESLOWLY.

SATURATION CURVE:PERCENTAGE OF MARKET PENETRATIONSTARTING FROM ZERO, SLOWLY RISING, THENACCELERATION, AND LATER LEVELLING OFFNEAR THE STATURATION POINT.

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SOME FORECASTING KEYS :

NAVE MODEL:

NAVE TREND MODEL:

NAVE RATE OF CHANGE MODEL:

NAVE SEASONAL MODEL FOR QUARTERLY DATA :

NAVE TREND & SEASONAL MODEL FOR QUARTERLYDATA:

tt yy 1

)(11 tttt yyyy

1

1

t

t

tt y

y

yy

31

tt yy

4

)(....)(

43131

tttttt

yyyyyy

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SIMPLE AVERAGE

UPDATED SIMPLE AVERAGE NEW PERIOD:

MOVING AVERAGE FOR K TIME PERIODS:

t

i

it yty 11

1

1

11

2

tyyty ttt

k

yyyyy kttttt

)....(

121

1

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DOUBLE MOVING AVERAGE:

AND WHERE

SIMPLE EXPONENTIAL SMOOTHING:

kMMMMM kttttt

)....( 121

ttpty

ttt MM 2

)(1

2ttt MM

k

ttt yyy )1( 1

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Time series or univariate models are used for short-term forecasting as theyare the most cost effective.

They typically relate a dependent variable to its past values or internalpatterns and to random errors that may be serially correlated.

May sales + June sales 1200 + 1000Eg. July sales forecast = ---------------------------- = ---------------- = 1100

2 2

They are in general, not based on any underlying economic behaviour(unlike econometric models)

Earlier, popular in engineering & physical sciences but since a couple ofdecades or so, it is so in Economics as well for the purpose of short-term

forecasting.

It is often modeled as Yt = Tt + St + Ut or Yt = Tt St Ut

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Where Y is the dependent variableT is the trend componentS is the seasonal component

and U is the random error term

A simple linear time trend is Tt = + t

If Yt has been growing exponentially, then it should beconverted first into logarithms.

S, the seasonal component is the one that occurs regularly as

a seasonal phenomenon such as the month or a quarter,week, day, hour, public holidays and so on. Here, seasonaldummies can be used to estimate seasonal patterns.

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Structure of Time Series Models

Auto regressive Models

Yt = 1 Yt-1 + 2 Yt-2+ .. + p Yt-p + Ut

Ut is well behaved error term with zero mean and constantvariance.

Yt is the tth observation on the dependent variable after

subtracting its mean.

Moving Average Models (Moving Average Models of order q)

Yt = 1 + 1t-1 + 2t-2 + qt-q

ARMA ModelsYt = 1 Yt-1 + 2 Yt-2 + .. ++ 1 + 1t-1 + 2t-2 + qt-q

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ARIMA MODEL: It combines two different specifications (processes) intoone equation.

The first being the autoregressive process (AR) and the second beingmoving average (MA).

ARIMA (p, d, q) :

dtt

qtqtt

YYY

*

22111

Where

.....

**

22

*

11

*....

ptpttt yyyoy

The two processes are integrated when the series is non-stationary (consistent

series say like GDP, interest rate, energy consumption, population etc.) Thatis how `d the differencing term appears. If the series is stationary, there isno integration and ARIMA becomes ARMA because d = 0.

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Smoothing a Time Series

Reducing short term volatality of the series or fluctuations around a trend

entails smoothing.

Moving Average

terms.successivem

averagingbyobtainedseriesnewtheisYseries;originaltheisWhere

.....1

t

11

t

mtttt

X

XXXm

Y

Exponential Smoothing

Here, the new series is obtained as a weighted average of present and pastvalues of the series with geometrically declining weights.

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1

3

2

211-t

....2

2

1

)1(

...)1()1(Y

OR

1.0Where

)1()1(

ttt

ttt

tttt

YXY

XXX

XXXY

If is close to 1, then Xt is given heavy weight & the resulting serieswill also be unsmooth. The smaller the value of, smoother Yt willbe. In exponential smoothing, only one observation is lost whereasin moving average, (m-1) observations are lost.

Exponential smoothing is also useful when adjusting forecasts toallow for prediction errors made in the recent past !

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EVALUATING FORECAST ACCURACY

In general, it is the standard error of the equation that is used to measurethe accuracy of any given equation.

However, when we move beyond the sample period, the relevantmeasure is the Root Mean Square Error or RMS Forecast Error

Symbolically, RMSE =

Where Ytf

are forecast values of Y and Yta

are actual values.

Comparable results are also obtained by a somewhat similar measurecalled Absolute Average Error (AAE) which is the actual error

ignoring the sign.

N

YYtatf

2

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An equation generating forecasts with continuing bias maystill be useful if we can adjust for that bias:

e.g., if all recent residuals have been 5 or 10% above (orbelow) the actual figures, that 5 or 10% factor can beincorporated in the forecast.

Or it may be that the parameters need to be re-estimated;or it is also likely that there has been a structural shift inrecent years (periods) that is noticeable in the residuals.

But has not occurred for a long enough time to warrant theinclusion of an additional variable.

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IMPLICATIONS:

If the predicted values are below the actual values,the firms may lose some sales.

Alternatively, if predicted values are higher thanthe actuals, the firms may run the risk of goingbankrupt.

Again, in financial markets, forecasting thedirection in which a particular market will move is

as important as forecasting the magnitude of thatmove!

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IMPLICATIONS (Contd.)

Surely, in all these cases, smaller forecast errors are

preferred to larger ones; and attention should be focussedon the sources of the errors:

Errors that occur from the random nature of the

forecasting process

Errors due to the shift in the data generation function

as a subset this includes influences (exogenous) that

have not previously occurred.

Errors that occur because the actual values of theindependent variables are not known at the time of

forecast.

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Hence, estimates and forecasts are not

always robust and often cannot be

precisely quantified. A lot of trial &

error, combining with qualitativeforecasts, judgments, collaborative/

consensus forecasts, scenario analysisetc. become relevant.

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GRANGER CAUSALITY

Often, one is tempted to infer on causation whileinterpreting regression results. A good fit/significance ofthe coefts. need not necessarily mean causation. One needsto go deeper and look at the Granger causation.

Direction of casuality F-Value Decision Criterion

Y X 3 Do not rejectthe Ho

X Y 0.7 Reject Ho

Great caution has to be exercised, as the Granger test issensitive to the lags involved in the model.

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NON-PARAMETRIC METHODS OF

LONG-TERM FORECASTING

Oftentimes, especially when a new product or service isbeing introduced, or new technology is being unveiled,companies/corporate planners have no prior data to go by.Also in situations where a firm plans to go for expansion,

it notices how other firms have fared, but has no data ofits own.

Further, when unprecedented events take place like the

first oil crisis, the fall of the Soviet Union/Berlin wall,deregulation, stringent environmental regulations onpolluting vehicles/plants/technologies/products/processeschange the way business is done.

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Although guess work plays a major role in such

contexts of forecasting, the challenge is to comeup with superior guesses. This is done by taking

recourse to:

Survey Methods

Analogy & Precursor Methods

Scenario Analysis Delphi Analysis

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A BRIEF RECAP & GENERAL CHECKLIST

Estimating regression equations for time series with

strong trends often gives rise to

Multi Collinearity and Autocorrelation

Even when based on economic theory whether they are:

Demand Functions Supply Functions Production Functions

Stock Prices. Although a number of different factors may be

responsible, more often than not it is the strong common

trend which is responsible.

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CHECKLIST:

No cook book recipe for econometric forecasting equations.

However, if different forms of the regression equationroutinely result in R2 greater than 0.99 it indicatesthat one is only measuring a common trend and is should beremoved.

If the Durbin-Watson (DW) statistic is smaller than R2we should use percentage changes or first-

differences of logarithms rather than the absolute values.

If monthly or quarterly data are involved in similarconditions try annual percentage changes i.e., say aparticular month or quarter over the same month or quarter ayear ago.

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SOME USEFUL TIPS:

RETAIN THE INTERCEPT (CONSTANT) TERM EVENWHEN IT MAY APPEAR OTHERWISE THEORETICALLY

.

AVOID INTERPRETING THE ESTIMATES OF THE

INTERCEPT TERM.

THE UNDERLYING ECONOMIC THEORY SHOULD

GUIDE THE CHOICE OF THE FUNCTIONAL FORM IN

GENERAL. HOWEVER, A FUNCTION WHICH IS LINEAR

IN THE VARIABLES MAY BE RESORTED TO UNLESS

OTHERWISE INDICATED BY A PARTICULARHYPOTHESIS.

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SOME USEFUL TIPS: (contd..)

MULTICOLLINEARITY IS HIGH WHEN R-2

IS HIGHWITH INSIGNIFICANT t-VALUES AND/OR WHEN

SIMPLE CORRELATION COEFTS. BETWEEN THE

EXPLANATORY VARIABLES IS HIGH. IT CAN BE A

THEORETICAL PHENOMENON AND ALSO BE A

SAMPLE PHENOMENON.

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ONE WAY IS TO IGNORE THE PROBLEM

ESPECIALLY IF THE t-VALUE ARE NOT REDUCEDTO INSIGNIFICANCE.

ANOTHER WAY IS TO DROP SOME

MULTICOLLINEAR (OR REDUNDANT) VARIABLES.

WE MAY ALSO INCREASE THE SAMPLE SIZE.

TRANSFORM THE MULTICOLLINEAR VARIABLES.

AUTOCORRELATION IS GENERALLY PRESENT(+VE) IN ECONOMIC/BUSINESS SITUATIONS.

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DURBIN-WATSON d-STATISTIC OF VALUE O

SUGGESTS EXTREME +VE AUTOCORRELATION

AND 4 INDICATES EXTREME VE

AUTOCORRELATION. A d-VALUE OF 2 SUGGESTS

NO SUCH CORRELATION. THE SAFE RANGE IS

BETWEEN 1.8 TO 2.2.

HERE, ONE SHOULD CHECK FOR POSSIBLE

SPECIFICATION ERRORS.

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HETEROSCEDASTICITY IS OFTEN SEEN IN CROSS-

SECTIONAL DATA.

SPECIFICATION ERROR SUCH AS AN OMITTEDVARIABLE MAY HAVE CAUSED IT OR IT MAY EVEN

BE A FUNCTION OF THE ERROR TERM OF THE

CORRECTLY SPECIFIED REGRESSION EQUATION.

HERE, ONE MAY CHECK FOR THE OMMITTEDVARIABLE.

ALSO, HAVE A RELOOK AT THE UNDERLYING

THEORY AND REFORMULATE THE VARIABLES,

CONVERT THEM TO PER CAPITA BASIS, ADJUSTING

THEM TO SIZE DIFFERENCES ETC.

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LAG STRUCTURE OF DISTRIBUTED LAGS

IN CROSS SECTION DATA, LAGS ARE NOTCONSIDERED IN GENERAL.

IN TIME-SERIES DATA, LAGGED VALUES DO PLAY AROLE.

WHETHER MACROECONOMIC RELATIONS LIKEWAGES, INTEREST RATES, PRICES, CONSUMPTION,

INVESTMENT AND EXPORTS.ORMICROECONOMIC RELATIONS LIKE CHANCES INNEW ORDERS, SHIPMENTS AND INVENTORIESDEPEND ON THE PAST AS WELL AS CURRENT

HAPPENINGS. THEORETICALLY, THERE IS NOTHING TO TELL US

WHETHER MOST OF THE REACTION WILL TAKEPLACE IN THE FIRST TIME PERIOD OR IT WILL

SPREAD OVER SEVERAL PERIODS