Business and Economic Forecasting Chapter 5 Demand Forecasting

Business and Economic Forecasting Chapter 5 Demand Forecasting is a critical managerial activity which comes in two forms: l Quantitative Forecasting Gives the precise amount or percentage l +2. 1047% Qualitative Forecasting Gives the expected direction Up, down, or about the same 2005 South-Western Publishing Slide 1

What Went Wrong With SUVs at Ford Motor Co? • Chrysler introduced the Minivan » in the 1980’s • Ford expanded its capacity to produce the Explorer, its popular SUV • Explorer’s price was raised substantially in 1995 at same time competitors expanded their offerings of SUVs. • Must consider response of rivals in pricing decisions Slide 2

Significance of Forecasting • Both public and private enterprises operate under conditions of uncertainty. • Management wishes to limit this uncertainty by predicting changes in cost, price, sales, and interest rates. • Accurate forecasting can help develop strategies to promote profitable trends and to avoid unprofitable ones. • A forecast is a prediction concerning the future. Good forecasting will reduce, but not eliminate, the uncertainty that all managers feel. Slide 3

Hierarchy of Forecasts • The selection of forecasting techniques depends in part on the level of economic aggregation involved. • The hierarchy of forecasting is: • National Economy (GDP, interest rates, inflation, etc. ) » sectors of the economy (durable goods) äindustry forecasts (all automobile manufacturers) > firm forecasts (Ford Motor Company) » Product forecasts (The Ford Focus) Slide 4

Forecasting Criteria The choice of a particular forecasting method depends on several criteria: 1. costs of the forecasting method compared with its gains 2. complexity of the relationships among variables 3. time period involved 4. accuracy needed in forecast 5. lead time between receiving information and the decision to be made Slide 5

Accuracy of Forecasting • The accuracy of a forecasting model is measured by how close the actual variable, Y, ends up to the ^ forecasting variable, Y. ^ • Forecast error is the difference. (Y - Y) • Models differ in accuracy, which is often based on the square root of the average squared forecast error over a series of N forecasts and actual figures • Called a root mean square error, RMSE. » RMSE = { (Y - ^ 2 Y) / N } Slide 6

Quantitative Forecasting • Deterministic Time Series » Looks For Patterns » Ordered by Time » No Underlying Structure Like technical security analysis • Econometric Models » Explains relationships » Supply & Demand » Regression Models Like fundamental security analysis Slide 7

Time Series Examine Patterns in the Past Dependent Variable Secular Trend Cyclical Variation X X X Forecasted Amounts To TIME The data may offer secular trends, cyclical variations, seasonal variations, and random fluctuations. Slide 8

Elementary Time Series Models for Economic Forecasting NO Trend 1. Naive Forecast ^ Yt+1 = Yt » Method best when there is no trend, only random error » Graphs of sales over time with and without trends » When trending down, the Naïve predicts too high time Trend time Slide 9

2. Naïve forecast with adjustments for secular trends ^ Yt+1 = Yt + (Yt - Yt-1 ) » This equation begins with last period’s forecast, Yt. » Plus an ‘adjustment’ for the change in the amount between periods Yt and Yt-1. » When the forecast is trending up, this adjustment works better than the pure naïve forecast method #1. Slide 10

3. Linear & 4. Constant rate of growth Linear Trend Growth • Used when trend has a constant AMOUNT of change Yt = a + b • T, where Yt are the actual observations and T is a numerical time variable Uses a Semi-log Regression • Used when trend is a constant PERCENTAGE rate Log Yt = a + b • T, where b is the continuously compounded growth rate Slide 11

More on Constant Rate of Growth Model a proof ^ • Suppose: Yt = Y 0( 1 + G) t where g is the annual growth rate • Take the natural log of both sides: ^ » Ln Yt = Ln Y 0 + t • Ln (1 + G) » but Ln ( 1 + G ) g, the equivalent continuously compounded growth rate » SO: Ln Yt = Ln Y 0 + t • g Ln Yt = a + b • t where b is the growth rate Slide 12

Numerical Examples: 6 observations MTB > Print c 1 -c 3. Sales Time Ln-sales 100. 0 109. 8 121. 6 133. 7 146. 2 164. 3 1 2 3 4 5 6 4. 60517 4. 69866 4. 80074 4. 89560 4. 98498 5. 10169 Using this sales data, estimate sales in period 7 using a linear and a semi-log functional form Slide 13

The regression equation is Sales = 85. 0 + 12. 7 Time Predictor Coef Constant 84. 987 Time 12. 6514 s = 2. 596 Stdev 2. 417 0. 6207 R-sq = 99. 0% t-ratio p 35. 16 0. 000 20. 38 0. 000 R-sq(adj) = 98. 8% The regression equation is Ln-sales = 4. 50 + 0. 0982 Time Predictor Coef Stdev Constant 4. 50416 0. 00642 Time 0. 098183 0. 001649 s = 0. 006899 R-sq = 99. 9% t-ratio p 701. 35 0. 000 59. 54 0. 000 R-sq(adj) = 99. 9% Slide 14

Forecasted Sales @ Time = 7 • Linear Model • Sales = 85. 0 + 12. 7 Time • Sales = 85. 0 + 12. 7 ( 7) • Sales = 173. 9 • Semi-Log Model • Ln-sales = 4. 50 + 0. 0982 Time • Ln-sales = 4. 50 + 0. 0982 ( 7 ) • Ln-sales = 5. 1874 • To anti-log: linear » e 5. 1874 = 179. 0 Slide 15

Sales Time Ln-sales 100. 0 1 4. 60517 109. 8 2 4. 69866 121. 6 3 4. 80074 133. 7 4 4. 89560 146. 2 5 4. 98498 164. 3 6 5. 10169 179. 07 semi-log 173. 97 linear Semi-log is exponential 7 Which prediction do you prefer? Slide 16

5. Declining Rate of Growth Trend • A number of marketing penetration models use a slight modification of the constant rate of growth model • In this form, the inverse of time is used Ln Yt = b 1 – b 2 ( 1/t ) • This form is good for patterns like the one to the right • It grows, but at continuously declining rate Y a time Slide 17

6. Seasonal Adjustments: The Ratio to Trend Method ü Take ratios of the actual to 12 quarters of data the forecasted values for past years. ü Find the average ratio. This is the seasonal adjustment Adjust by this percentage by multiply your forecast by the seasonal adjustment I II III IV I II IV » If average ratio is 1. 02, adjust forecast upward 2% Quarters designated with roman numerals. Slide 18

7. Seasonal Adjustments: Dummy Variables • Let D = 1, if 4 th quarter and 0 otherwise • Run a new regression: Yt = a + b • T + c • D » the “c” coefficient gives the amount of the adjustment for the fourth quarter. It is an Intercept Shifter. » With 4 quarters, there can be as many as three dummy variables; with 12 months, there can be as many as 11 dummy variables • EXAMPLE: Sales = 300 + 10 • T + 18 • D 12 Observations from the first quarter of 2002 to 2004 -IV. Forecast all of 2005. Sales(2005 -I) = 430; Sales(2005 -II) = 440; Sales(2005 -III) = 450; Sales(2005 -IV) = 478 Slide 19

Soothing Techniques 8. Moving Averages Dependent Variable • A smoothing forecast method for data that * * jumps around * • Best when there is no * trend • 3 -Period Moving Ave. Yt+1 = [Yt + Yt-1 + Yt-2]/3 * Forecast Line TIME Slide 20

Smoothing Techniques 9. First-Order Exponential Smoothing • A hybrid of the Naive • Each forecast is a function of all past observations and Moving Average methods • Can show that forecast is ^ ^ based on geometrically • Yt+1 = w • Yt +(1 -w)Yt declining weights. • A weighted average of past actual and past forecast. ^ Yt+1 = w. • Yt +(1 -w) • w • Yt-1 + ^ t-1 + … (1 -w)2 • w • Y Find lowest RMSE to pick the best alpha. Slide 21

First-Order Exponential Smoothing Example for w =. 50 1 2 3 4 5 Actual Sales 100 120 115 130 Forecast 100 initial seed required. 5(100) +. 5(100) = 100 ? Slide 22

First-Order Exponential Smoothing Example for w =. 50 1 2 3 4 5 Actual Sales 100 120 115 130 Forecast 100 initial seed required. 5(100) +. 5(100) = 100. 5(120) +. 5(100) = 110 ? Slide 23

First-Order Exponential Smoothing Example for w =. 50 1 2 3 4 5 Actual Sales 100 120 115 130 ? Forecast 100 initial seed required. 5(100) +. 5(100) = 100. 5(120) +. 5(100) = 110. 5(115) +. 5(110) = 112. 50. 5(130) +. 5(112. 50) = 121. 25 MSE = {(120 -100)2 + (110 -115)2 + (130 -112. 5)2}/3 = 243. 75 RMSE = 243. 75 = 15. 61 Period 5 Forecast Slide 24

1. Qualitative Forecasting 10. Barometric Techniques Direction of sales can be indicated by other variables. peak PEAK Motor Control Sales Index of Capital Goods TIME 4 Months Example: Index of Capital Goods is a “leading indicator” There also lagging indicators and coincident indicators Slide 25

Time given in months from change LEADING INDICATORS* COINCIDENT » M 2 money supply (-12. 4) INDICATORS » S&P 500 stock prices (-11. 1) » Nonagricultural payrolls » Building permits (-14. 4) (+. 8) » Initial unemployment claims » Index of industrial (-12. 9) production (-1. 1) » Contracts and orders for » Personal income less plant and equipment (-7. 4) transfer payment (-. 4) LAGGING INDICATORS *Survey of Current Business, 1994 See pages 206 -207 in textbook » Prime rate (+2. 0) » Change in labor cost per unit of output (+6. 4) Slide 26

Handling Multiple Indicators Diffusion Index: Index Wall Street With Louis Ruykeyser has eleven analysts. If 4 are negative about stocks and 7 are positive, the Diffusion Index is 7/11, or 63. 3%. • above 50% is a positive diffusion index Composite Index: One indicator rises 4% and another rises 6%. Therefore, the Composite Index is a 5% increase. • used for quantitative forecasting Slide 27

Qualitative Forecasting 11. Surveys and Opinion Polling Techniques Common Survey Problems New Products have no historical data -- Surveys can assess interest in new ideas. • Sample bias-» telephone, magazine • Biased questions-» advocacy surveys Survey Research Center of U. of Mich. does repeat surveys of households on Big Ticket items (Autos) • Ambiguous questions • Respondents may lie on questionnaires Slide 28

Qualitative Forecasting 12. Expert Opinion The average forecast from several experts is a Consensus Forecast. » Mean » Median » Mode » Truncated Mean » Proportion positive or negative Slide 29

EXAMPLES: • IBES, First Call, and Zacks Investment -earnings forecasts of stock analysts of companies • Conference Board – macroeconomic predictions • Livingston Surveys--macroeconomic forecasts of 50 -60 economists Individual economists tend to be less accurate over time than the ‘consensus forecast’. Slide 30

13. Econometric Models • Specify the variables in the model • Estimate the parameters » single equation or perhaps several stage methods » Qd = a + b • P + c • I + d • Ps + e • Pc • But forecasts require estimates for future prices, future income, etc. • Often combine econometric models with time series estimates of the independent variable. » Garbage in Garbage out Slide 31

example • Qd = 400 -. 5 • P + 2 • Y +. 2 • Ps » anticipate pricing the good at P = $20 » Income (Y) is growing over time, the estimate is: Ln Yt = 2. 4 +. 03 • T, and next period is T = 17. • Y = e 2. 910 = 18. 357 » The prices of substitutes are likely to be P = $18. • Find Qd by substituting in predictions for P, Y, and Ps • Hence Qd = 430. 31 Slide 32

14. Stochastic Time Series • A little more advanced methods incorporate into time series the fact that economic data tends to drift yt = a + byt-1 + et • In this series, if a is zero and b is 1, this is essentially the naïve model. When a is zero, the pattern is called a random walk. • When a is positive, the data drift. The Durbin-Watson statistic will generally show the presence of autocorrelation, or AR(1), integrated of order one. • One solution to variables that drift, is to use first differences. Slide 33

Cointegrated Time Series • Some econometric work includes several stochastic variable, each which exhibits random walk with drift » Suppose price data (P) has positive drift » Suppose GDP data (Y) has positive drift » Suppose the sales is a function of P & Y » Salest = a + b. Pt + c. Yt » It is likely that P and Y are cointegrated in that they exhibit comovement with one another. They are not independent. » The simplest solution is to change the form into first differences as in: DSalest = a + b. DPt + c. DYt Slide 34