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## Business and Economic Forecasting Chapter 5

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**Business and Economic ForecastingChapter 5**• Demand Forecasting is a critical managerial activity which comes in two forms: • Quantitative Forecasting +2.1047% Gives the precise amount or percentage • Qualitative Forecasting • Gives the expected direction • Up, down, or about the same 2005 South-Western Publishing**What Went Wrong WithSUVs 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**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.**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) • industry forecasts(all automobile manufacturers) • firm forecasts (Ford Motor Company) • Product forecasts (The Ford Focus)**Forecasting Criteria**The choice of a particular forecasting method depends on several criteria: • costs of the forecasting method compared with its gains • complexity of the relationships among variables • timeperiod involved • accuracyneeded in forecast • lead time between receiving information and the decision to be made**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 } ^ ^ ^**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**Time SeriesExamine Patterns in the Past**Dependent Variable Secular Trend Cyclical Variation X X X Forecasted Amounts TIME To The data may offer secular trends, cyclical variations, seasonal variations, and random fluctuations.**Elementary Time Series Models for Economic Forecasting**NO Trend • 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**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.**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 Used when trend is a constant PERCENTAGE rate Log Yt = a + b•T, where b is the continuously compounded growth rate 3. Linear & 4. Constant rate of growth Linear Trend Growth Uses a Semi-log Regression**More on Constant Rate of Growth Modela proof**^ • Suppose: Yt = Y0( 1 + G) twhere g is the annual growth rate • Take the natural log of both sides: • Ln Yt = Ln Y0 + t • Ln (1 + G) • but Ln ( 1 + G ) g, the equivalent continuously compounded growth rate • SO: Ln Yt = Ln Y0 + t • g Ln Yt = a+ b • t where b is the growth rate ^**Numerical Examples: 6 observations**Using this sales data, estimate sales in period 7 using a linear and a semi-log functional form 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**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%**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: e5.1874 = 179.0 Forecasted Sales @ Time = 7 linear **Semi-log is**exponential 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 179.0 7 semi-log 173.9 7 linear 7 Which prediction do you prefer?**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 = b1 – b2 ( 1/t ) • This form is good for patterns like the one to the right • It grows, but at continuously a declining rate Y time**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% 6. Seasonal Adjustments:The Ratio to Trend Method 12 quarters of data I II III IV I II III IV I II III IV Quarters designated with roman numerals.**7.Seasonal Adjustments:Dummy Variables**• Let D = 1, if 4th 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**Soothing Techniques8. Moving Averages**• 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 Dependent Variable * * * Forecast Line * * TIME**A hybrid of the Naive and Moving Average methods**Yt+1 = w•Yt +(1-w)Yt 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. Yt+1 = w .•Yt +(1-w)•w•Yt-1 + (1-w)2•w•Yt-1 + … Find lowest RMSE to pick the best alpha. Smoothing Techniques9. First-Order Exponential Smoothing ^ ^ ^ ^**First-Order Exponential Smoothing Example for w = .50**Actual Sales Forecast 100100 initial seed required 120 .5(100) + .5(100) = 100 115 130 ? 1 2 3 4 5**First-Order Exponential Smoothing Example for w = .50**Actual Sales Forecast 100100 initial seed required 120 .5(100) + .5(100) = 100 115 .5(120) + .5(100) = 110 130 ? 1 2 3 4 5**First-Order Exponential Smoothing Example for w = .50**Actual Sales Forecast 100100 initial 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 1 2 3 4 5 MSE = {(120-100)2 + (110-115)2 + (130-112.5)2}/3 = 243.75 RMSE = 243.75 = 15.61 Period 5 Forecast**Qualitative Forecasting10. Barometric Techniques**Direction of sales can be indicated by other variables. Motor Control Sales PEAK peak Index of Capital Goods TIME 4 Months Example: Index of Capital Goods is a “leading indicator” There are also lagging indicators and coincident indicators**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) Time given in months from change *Survey of Current Business, 1994 See pages 206-207 in textbook**Handling Multiple Indicators**• 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: One indicator rises 4% and another rises 6%. Therefore, the Composite Index is a 5% increase. • used for quantitative forecasting**Qualitative Forecasting11. Surveys and Opinion Polling**Techniques Common Survey Problems • 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)**Qualitative Forecasting12. Expert Opinion**The average forecast from several experts is a Consensus Forecast. • Mean • Median • Mode • Truncated Mean • Proportion positive or negative**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’.**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**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 = e2.910 = 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**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.**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 + bPt + cYt • 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 + bDPt + cDYt