3-1 Forecasting

CHAPTER3

Forecasting

Homework Problems: # 2,3,4,8(a),22,23,25,27 on pp. 121-128.

3-2 Forecasting

Forecast – a statement about the future value of a variable of interest We make forecasts about such things as

weather, demand, and resource availability Forecasts are an important element in making

informed decisions

ForecastForecast

3-3 Forecasting

Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads

Product/service design New products and services

Uses of ForecastsUses of Forecasts

3-4 ForecastingTwo Important Aspects of Two Important Aspects of

ForecastsForecasts

Expected level of demand The level of demand may be a function of some

structural variation such as trend or seasonal variation

Accuracy Related to the potential size of forecast error

3-5 Forecasting

I see that you willget an A this semester.

Features Common to All ForecastsFeatures Common to All Forecasts

1. Techniques assume some underlying causal system that existed in the past will persist into the future

2. Forecasts are not perfect3. Forecasts for groups of items are more accurate

than those for individual items4. Forecast accuracy decreases as the forecasting

horizon increases

3-6 Forecasting

Elements of a Good ForecastElements of a Good Forecast

The forecast should be timely should be accurate should be reliable should be expressed in meaningful units should be in writing technique should be simple to understand and use should be cost effective

3-7 Forecasting

Steps in the Forecasting ProcessSteps in the Forecasting Process

1. Determine the purpose of the forecast

2. Establish a time horizon

3. Select a forecasting technique

4. Obtain, clean, and analyze appropriate data

5. Make the forecast

6. Monitor the forecast

3-8 Forecasting

Types of ForecastsTypes of Forecasts

Judgmental - uses subjective inputs

Time series - uses historical data assuming the future will be like the past

Associative models - uses explanatory variables to predict the future

3-9 Forecasting

Forecast Accuracy and ControlForecast Accuracy and Control

Forecasters want to minimize forecast errors It is nearly impossible to correctly forecast real-

world variable values on a regular basis So, it is important to provide an indication of

the extent to which the forecast might deviate from the value of the variable that actually occurs

Forecast accuracy should be an important forecasting technique selection criterion

3-10 Forecasting

Forecast Accuracy and Control (contd.)Forecast Accuracy and Control (contd.)

Forecast errors should be monitored Error = Actual – Forecast If errors fall beyond acceptable bounds,

corrective action may be necessary

3-11 Forecasting

Forecast Accuracy MetricsForecast Accuracy Metrics

n

tt ForecastActualMAD

2

tt

1

ForecastActualMSE

n

n

100

Actual

ForecastActual

MAPE t

tt

MAD weights all errors evenly

MSE weights errors according to their squared values

MAPE weights errors according to relative error

3-12 Forecasting

Forecast Error CalculationForecast Error CalculationPeriod

Actual

(A)

Forecast

(F)(A-F) Error |Error| Error2 [|Error|/Actual]x100

1 107 110 -3 3 9 2.80%

2 125 121 4 4 16 3.20%

3 115 112 3 3 9 2.61%

4 118 120 -2 2 4 1.69%

5 108 109 1 1 1 0.93%

Sum 13 39 11.23%

n = 5 n-1 = 4 n = 5

MAD MSE MAPE

= 2.6 = 9.75 = 2.25%

3-13 Forecasting

Forecasting ApproachesForecasting Approaches

Qualitative Forecasting Qualitative techniques permit the inclusion of soft information such

as: Human factors Personal opinions Hunches

These factors are difficult, or impossible, to quantify Quantitative Forecasting

Quantitative techniques involve either the projection of historical data or the development of associative methods that attempt to use causal variables to make a forecast

These techniques rely on hard data

3-14 Forecasting

Judgmental ForecastsJudgmental Forecasts

Forecasts that use subjective inputs such as opinions from consumer surveys, sales staff, managers, executives, and experts Executive opinions Sales force opinions Consumer surveys Delphi method

3-15 Forecasting

Time Series ForecastsTime Series Forecasts

Forecasts that project patterns identified in recent time-series observations Time-series - a time-ordered sequence of

observations taken at regular time intervals Assume that future values of the time-series

can be estimated from past values of the time-series

3-16 Forecasting

Time Series ForecastsTime Series Forecasts

Trend - long-term movement in data Seasonality - short-term regular variations in

data Cycle – wavelike variations of more than one

year’s duration Irregular variations - caused by unusual

circumstances Random variations - caused by chance

3-17 Forecasting

Forecast VariationsForecast Variations

Trend

Irregularvariation

Seasonal variations

908988

Figure 3.1

Cycles

3-18 Forecasting

Naive ForecastsNaive Forecasts

Naïve Forecast Uses a single previous value of a time series as

the basis for a forecast The forecast for a time period is equal to the

previous time period’s value Can be used when

The time series is stable There is a trend There is seasonality

3-19 Forecasting

Time-Series Forecasting-- AveragingTime-Series Forecasting-- Averaging

These Techniques work best when a series tends to vary about an average Averaging techniques smooth variations in the

data They can handle step changes or gradual

changes in the level of a series Techniques

Moving average Weighted moving average Exponential smoothing

3-20 Forecasting

Moving AveragesMoving Averages

Technique that averages a number of the most recent actual values in generating a forecast

average moving in the periods ofNumber

1 periodin valueActual

average moving period MA

period for timeForecast

where

MA

1

1t

n

tA

n

tF

n

AF

t

t

t

n

iit

t

3-21 Forecasting

Moving AveragesMoving Averages

As new data become available, the forecast is updated by adding the newest value and dropping the oldest and then recomputing the average

The number of data points included in the average determines the model’s sensitivity Fewer data points used-- more responsive More data points used-- less responsive

3-22 Forecasting

Weighted Moving AveragesWeighted Moving Averages

The most recent values in a time series are given more weight in computing a forecast The choice of weights, w, is somewhat arbitrary

and involves some trial and error

Ft wn At n wn 1At (n 1) ... w1At 1

where

wt weight for period t, wt 1 weight for period t 1, etc.

At the actual value for period t, At 1 the actual value for period t 1, etc.

3-23 Forecasting

Moving Averages ExampleMoving Averages Example

Given the following data: Period # of complaints

1 60

2 65

3 55

4 58

5 64

A). Prepare the forecasts for period 6 using a 3-period, 5-period moving average.

B). Prepare a weighted moving average forecast for period 6 using weights of 0.3, 0.2, and 0.1.

3-24 Forecasting

Simple Moving AverageSimple Moving Average

35

37

39

41

43

45

47

1 2 3 4 5 6 7 8 9 10 11 12

Actual

MA3

MA5

Q. What n to use? Large or small?

3-25 Forecasting

Exponential SmoothingExponential Smoothing

• Premise--The most recent observations might have the highest predictive value.

Therefore, we should give more weight to the more recent time periods when forecasting.

Ft = Ft-1 + (At-1 - Ft-1)

3-26 Forecasting

Exponential SmoothingExponential Smoothing

Weighted averaging method based on previous forecast plus a percentage of the forecast error

A-F is the error term, is the % feedback

Ft = Ft-1 + (At-1 - Ft-1)

3-27 Forecasting

Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92

Example - Exponential SmoothingExample - Exponential Smoothing

3-28 Forecasting

Picking a Smoothing ConstantPicking a Smoothing Constant

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12

Period

Dem

and .1

.4

Actual

3-29 Forecasting

Other Forecasting Methods - Other Forecasting Methods - FocusFocus

Focus Forecasting Some companies use forecasts based on a “best

current performance” basis Apply several forecasting methods to the last

several periods of historical data The method with the highest accuracy is used to

make the forecast for the following period This process is repeated each month

3-30 Forecasting

Other Forecasting Methods - DiffusionOther Forecasting Methods - Diffusion

Diffusion Models Historical data on which to base a forecast are

not available for new products Predictions are based on rates of product

adoption and usage spread from other established products

Take into account facts such as Market potential Attention from mass media Word-of-mouth

3-31 Forecasting

Technique for TrendTechnique for Trend

Linear trend equation Non-linear trends

Parabolic trend equation Exponential trend equation Growth curve trend equation

3-32 Forecasting

Linear Trend EquationLinear Trend Equation

A simple data plot can reveal the existence and nature of a trend

Linear trend equation

Ft a bt

where

Ft Forecast for period t

a Value of Ft at t 0

b Slope of the line

t Specified number of time periods from t 0

3-33 Forecasting

Estimating slope and interceptEstimating slope and intercept

Slope and intercept can be estimated from historical data

b n ty t yn t 2 t

2

a y b t

n or y bt

where

n Number of periods

y Value of the time series

3-34 Forecasting

Linear Trend Equation ExampleLinear Trend Equation Example

t yW e e k t 2 S a l e s t y

1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5

t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5

3-35 Forecasting

Linear Trend CalculationLinear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)

5 =

b = 5 (2499) - 15(812)

5(55) - 225 =

12495-12180

275 -225 = 6.3

143.5

3-36 Forecasting

Associative ForecastingAssociative Forecasting

Home values may be related to such factors as home and property size, location, number of bedrooms, and number of bathrooms Associative techniques are based on the

development of an equation that summarizes the effects of predictor variables

Predictor variables - variables that can be used to predict values of the variable of interest

3-37 Forecasting

Simple Linear RegressionSimple Linear Regression

Regression - a technique for fitting a line to a set of data points Simple linear regression - the simplest form of

regression that involves a linear relationship between two variables The object of simple linear regression is to

obtain an equation of a straight line that minimizes the sum of squared vertical deviations from the line (i.e., the least squares criterion)

3-38 Forecasting

Least Squares LineLeast Squares Line

yc a bx

where

yc Predicted (dependent) variable

x Predicted (independent) variable

b Slope of the line

a Value of yc when x 0 (i.e., the height of the line at the y intercept)

and

b n xy x yn x 2 x

2

a y b x

n or y bx

where

n Number of paired observations

Predictor

3-39 Forecasting

Standard ErrorStandard Error Standard error of estimate

A measure of the scatter of points around a regression line

If the standard error is relatively small, the predictions using the linear equation will tend to be more accurate than if the standard error is larger

points data ofnumber

point dataeach of valuethe

estimate oferror standard

where2

2

n

y

S

n

yyS

e

ce

3-40 Forecasting

Linear Model Seems ReasonableLinear Model Seems Reasonable

A straight line is fitted to a set of sample points.

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 15

14 2515 2716 2412 2014 2720 4415 347 17

Computedrelationship

3-41 Forecasting

Correlation CoefficientCorrelation Coefficient

Correlation A measure of the strength and direction of relationship

between two variables Ranges between -1.00 and +1.00

r2, square of the correlation coefficient A measure of the percentage of variability in the values of y

that is “explained” by the independent variable Ranges between 0 and 1.00

r2 n xy x y

n x 2 x 2n y 2 y 2

3-42 Forecasting

Regression and Correlation ExampleRegression and Correlation Example Given the following values of X and Y, (a) obtain a linear regression line for the

data, and (2) what percentage of the variation is explained by the regression line? x y xy x2 y2 15.00 74.00 1110.0 225.0 5476.0 25.00 80.00 2000.0 625.0 6400.0 40.00 84.00 3360.0 1600.0 7056.0 32.00 81.00 2592.0 1024.0 6561.0 51.00 96.00 4896.0 2601.0 9216.0 47.00 95.00 4465.0 2209.0 9025.0 30.00 83.00 2490.0 900.0 6889.0 18.00 78.00 1404.0 324.0 6084.0 14.00 70.00 980.0 196.0 4900.0 15.00 72.00 1080.0 225.0 5184.0 22.00 85.00 1870.0 484.0 7225.0 24.00 88.00 2112.0 576.0 7744.0 33.00 90.00 2970.0 1089.0 8100.0

3-43 Forecasting

Simple Linear Regression Simple Linear Regression AssumptionsAssumptions

1. Variations around the line are random

2. Deviations around the average value (the line) should be normally distributed

3. Predictions are made only within the range of observed values

3-44 Forecasting

Issues to considerIssues to consider

Always plot the line to verify that a linear relationships is appropriate

The data may be time-dependent. If they are

use analysis of time series use time as an independent variable in a multiple

regression analysis A small correlation may indicate that other

variables are important

3-45 Forecasting

Controlling the ForecastControlling the Forecast

Control chart A visual tool for monitoring forecast errors Used to detect non-randomness in errors

Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are

present

3-46 Forecasting

Sources of Forecast errorsSources of Forecast errors

Model may be inadequate Irregular variations Incorrect use of forecasting technique

3-47 Forecasting

Choosing a Forecasting TechniqueChoosing a Forecasting Technique

No single technique works in every situation Two most important factors

Cost Accuracy

Other factors include the availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon

3-48 Forecasting

Using Forecast InformationUsing Forecast Information

Reactive approach View forecasts as probable future demand React to meet that demand

Proactive approach Seeks to actively influence demand

Advertising Pricing Product/service modifications

Generally requires either and explanatory model or a subjective assessment of the influence on demand