1. Slide 1 Business and Economic Forecasting Chapter 5 Demand Forecasting is a critical managerial activity which comes in two forms: lQuantitative Forecasting +2.1047% lQuantitative Forecasting +2.1047% Gives the precise amount or percentage Qualitative Forecasting Qualitative Forecasting Gives the expected direction Up, down, or about the same  2005 South-Western Publishing

2. Slide 2 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

3. Slide 3 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.

4. Slide 4 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) ä industry forecasts (all automobile manufacturers) > firm forecasts (Ford Motor Company) » Product forecasts (The Ford Focus)

5. Slide 5 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

6. Slide 6 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 - Y) 2 / N } ^ ^ ^

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

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

9. Slide 9 Elementary Time Series Models for Economic Forecasting 1.Naive Forecast Y t+1 = Y t »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 NO Trend Trend          ^ time

10. Slide 10 2. Naïve forecast with adjustments for secular trends Y t+1 = Y t + (Y t - Y t-1 ) »This equation begins with last period’s forecast, Y t. »Plus an ‘adjustment’ for the change in the amount between periods Y t and Y t-1. »When the forecast is trending up, this adjustment works better than the pure naïve forecast method #1. ^

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

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

13. Slide 13 Numerical Examples: 6 observations MTB > Print c1-c3. 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 Using this sales data, estimate sales in period 7 using a linear and a semi-log functional form

14. Slide 14 The regression equation is Sales = 85.0 + 12.7 Time Predictor Coef Stdev t-ratio p Constant 84.987 2.417 35.16 0.000 Time 12.6514 0.6207 20.38 0.000 s = 2.596 R-sq = 99.0% R-sq(adj) = 98.8% The regression equation is Ln-sales = 4.50 + 0.0982 Time Predictor Coef Stdev t-ratio p Constant 4.50416 0.00642 701.35 0.000 Time 0.098183 0.001649 59.54 0.000 s = 0.006899 R-sq = 99.9% R-sq(adj) = 99.9%

15. Slide 15 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: »e 5.1874 = 179.0  linear 

16. Slide 16 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 Which prediction do you prefer? Semi-log is exponential 7

17. Slide 17 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 Y t =  1 –  2 ( 1/t ) This form is good for patterns like the one to the right It grows, but at continuously a declining rate time Y

18. Slide 18 6. Seasonal Adjustments: The Ratio to Trend Method Take ratios of the actual to the forecasted values for past years. Find the average ratio. This is the seasonal adjustment Adjust by this percentage by multiply your forecast by the seasonal adjustment »If average ratio is 1.02, adjust forecast upward 2% 12 quarters of data I II III IV I II III IV I II III IV             Quarters designated with roman numerals.

19. Slide 19 Let D = 1, if 4th quarter and 0 otherwise Run a new regression: Y t = a + bT + cD »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 + 10T + 18D 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 7. Seasonal Adjustments: Dummy Variables

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

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

22. Slide 22 First-Order Exponential Smoothing Example for  =.50 Actual SalesForecast 100100initial seed required 120.5(100) +.5(100) = 100 115 130 ? 1234512345

23. Slide 23 First-Order Exponential Smoothing Example for  =.50 Actual SalesForecast 100100initial seed required 120.5(100) +.5(100) = 100 115.5(120) +.5(100) = 110 130 ? 1234512345

24. Slide 24 First-Order Exponential Smoothing Example for  =.50 Actual SalesForecast 100100initial seed required 120.5(100) +.5(100) = 100 115.5(120) +.5(100) = 110 130.5(115) +.5(110) = 112.50 ?.5(130) +.5(112.50) = 121.25 Period 5 Forecast MSE = {(120-100) 2 + (110-115) 2 + (130-112.5) 2 }/3 = 243.75 RMSE =  243.75 = 15.61 1234512345

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

26. Slide 26 LEADING INDICATORS* »M2 money supply (-12.4) »S&P 500 stock prices (-11.1) »Building permits (-14.4) »Initial unemployment claims (-12.9) »Contracts and orders for plant and equipment (-7.4) COINCIDENT INDICATORS »Nonagricultural payrolls (+.8) »Index of industrial production (-1.1) »Personal income less transfer payment (-.4) LAGGING INDICATORS »Prime rate (+2.0) »Change in labor cost per unit of output (+6.4) *Survey of Current Business, 1994 See pages 206-207 in textbook Time given in months from change

27. Slide 27 Handling Multiple Indicators Diffusion Index Diffusion 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 Composite Index : One indicator rises 4% and another rises 6%. Therefore, the Composite Index is a 5% increase. used for quantitative forecasting

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

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

30. Slide 30 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’.

31. Slide 31 13. Econometric Models Specify the variables in the model Estimate the parameters »single equation or perhaps several stage methods »Q d = a + bP + cI + dP s + eP c 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

32. Slide 32 Q d = 400 -.5P + 2Y +.2P s »anticipate pricing the good at P = $20 »Income (Y) is growing over time, the estimate is: Ln Y t = 2.4 +.03T, and next period is T = 17. Y = e 2.910 = 18.357 »The prices of substitutes are likely to be P = $18. Find Q d by substituting in predictions for P, Y, and P s Hence Q d = 430.31

33. Slide 33 14. Stochastic Time Series A little more advanced methods incorporate into time series the fact that economic data tends to drift y t =  +  y t-1 +  t In this series, if  is zero and  is 1, this is essentially the naïve model. When  is zero, the pattern is called a random walk. When  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.

34. Slide 34 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 » Sales t = a + bP t + cY t »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:  Sales t = a + b  P t + c  Y t