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Ch 3: Forecasting:Techniques and Routes

IntroductionForecasting is the establishment of future expectations by the analysis of past data, or the formation of opinions.

Forecasting is an essential element of capital budgeting.

Capital budgeting requires the commitment of significant funds today in the hope of long term benefits. The role of forecasting is the estimation of these benefits.

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Forecasting Techniques and Routes

Techniques

Routes

Top-down routeBottom-up route

Quantitative

Qualitative

Simple regressionsMultiple regressionsTime trendsMoving averages

Delphi methodNominal group techniqueJury of executive opinionScenario projection

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Quantitative Forecasting Quantitative: Regression with related variable

Data set of ‘Sales’ as related to both time and the number of households.

YEAR HOUSEHOLDS SALES1991 815 21091992 927 25301993 1020 22871994 987 31941995 1213 37851996 1149 33721997 1027 36981998 1324 39081999 1400 37252000 1295 41292001 1348 45322002 1422 4487

HISTORICAL DATA

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Quantitative ForecastingQuantitative: Sales plotted related to households.

SalesUnits Related to Number of Households

0

1000

2000

3000

4000

5000

0 500 1000 1500

Number of Households

Sa

les

Un

its

Sales

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Quantitative ForecastingQuantitative: Sales regressed on households.

Edited output from the Excel regression.SUMMARY OUTPUT SALES REGRESSED AS A FUNCTION

OF HOUSEHOLDSRegression Statistics

Multiple R 0.824389811R Square 0.67961856Adjusted R Square 0.644020623 <== "Strength" of the regressionStandard Error 429.2094572Observations 11

Coefficients Standard Error t Stat P-valueY Axis Intercept -348.218 913.798 -0.381 0.712Number of Households 3.316 0.759 4.369 0.002

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Quantitative ForecastingQuantitative: Sales regressed on households.

Predicting with the regression output.Regression equation is:Sales(for year) = -348.218 + ( 3.316 x households).

Assuming that a separate data set forecasts the number of households at 1795 for the year 2006, then:

Sales(year 2006) = -348.218 + ( 3.316 x 1795)

= 5,604 units.

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Quantitative Forecasting Quantitative: Multiple RegressionSales as a function of both time and the number of households.

YEAR HOUSEHOLDS SALES1991 815 21091992 927 25301993 1020 22871994 987 31941995 1213 37851996 1149 33721997 1027 36981998 1324 39081999 1400 37252000 1295 41292001 1348 45322002 1422 4487

HISTORICAL DATA

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Quantitative Forecasting: Multiple Regression Line InformationFrom the Excel spreadsheet.

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.9216R Square 0.8494Adjusted R Square 0.8118 <== "Strength" of regression.Standard Error 312.1217Observations 11

Coefficients Standard Error t Stat P-value Lower 95%Y Axis Intercept -382643.9164 127299.584 -3.006 0.017 -676197.474Calendar Year 193.3326 64.376 3.003 0.017 44.880Households 0.1368 1.194 0.115 0.912 -2.616

MULTIPLE REGRESSION:SALES ON YEARS and HOUSEHOLDS

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Quantitative Forecasting: Using Multiple Regression Multiple regression equation is:Sales in year = -382643.91 +(193.33 x Year) + (0.1368 x Households)

Forecast of sales for the year 2005 is:Sales in year 2005 = -382643.91 + (193.33 x 2005)

+ (0.1368 x 1586) = 5200 Units

(Note: the sales forecast relies upon a separate forecast of the number of households, given as 1 586, for 2005.)

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Quantitative Forecasting Quantitative: Time Series RegressionSales plotted as a function of time.

Plot of Past Sales Units By Year

0

1000

2000

3000

4000

5000

1990 1995 2000 2005

Year

Sa

les

Un

its

Sales

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Quantitative Forecasting: Fitted Regression Line

Sales Regression: Line Fit Plot

0

1000

2000

3000

4000

5000

1990 1995 2000 2005

Year

Sale

s Actual

Predicted

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Quantitative Forecasting: Regression Line Information

EDITED SUMMARY OUTPUT REGRESSION OF SALES ON YEARS

Regression StatisticsMultiple R 0.9215R Square 0.8492Adjusted R Square 0.8324 <== "Strength" of regression.Standard Error 294.5125Observations 11

Coefficients Standard Error t Stat P-valueY axis intercept -395541.56 56077.1544 -7.0535 0.0001Slope of line 199.87 28.0807 7.1178 0.0001

From the Excel spreadsheet.

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Quantitative Forecasting: Regression Line UseEquation for the regression line is:Sales in year = -395541.56 + (199.87 x Year)

Forecast of sales for the year 2005 is:

Sales in 2005 = -395541.56 + (199.87 x 2005)

= 5198 Units (Note: the large negative Y axis intercept results from using the actual calendar years as the X axis scale.)

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Quantitative Forecasting:Regression: Auto Forecast by Excel.

Sales by Year, With Automatic Three Year Prediction

0

1000

2000

3000

4000

5000

6000

1990 1995 2000 2005 2010

Year

Sale

s

SALES

Simple LinearRegression,Forecast Out toYear 2005

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Quantitative Forecasting:Moving Average- Auto Plot

Sales Units Per Year With Fitted Two Year Moving Average

0

1000

2000

3000

4000

5000

1990 1995 2000 2005

Years

Sa

les

Un

its

SALES

2 per. Mov.Avg.(SALES)

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Quantitative Forecasting:Notes on Excel Auto Plot.

Excel will plot, and automatically forecast, a data series which has a functional relationship. For example, a regression trend line.

The auto plot is driven through the ‘Chart’ menu as ‘Add Trendline’. A particular forecast is specified via the dialog box.

Non-functional relationships, such as a moving average, can be plotted, but cannot be automatically forecast.

Future point data values cannot be read from the automated trendline.

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Forecasting Routes

Top-Down where international and national

events affect the future behaviour of local variables.

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Forecasting Routes

Bottom-Up

Where local events affect the future behaviour of local variables.

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Forecasting: Summary Sophisticated forecasting is essential for

capital budgeting decisions Quantitative forecasting uses historical

data to establish relationships and trends which can be projected into the future

Qualitative forecasting uses experience and judgment to establish future behaviours

Forecasts can be made by either the‘top down’ or ‘bottom up’ routes.

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