Business and Economic Forecasting Chapter 5 Business and Economic 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 2008 Thomson * South-Western 1

Managerial Challenge Excess Fiber Optic Capacity High-speed data installation grew exponentially But adoption follows a typical S-curve pattern, similar to the adoption rate of TV Access grew too fast, leading to excess capacity around the time of the tech bubble in 2001 The challenge is to predict demand properly 100% Color TVs Internet Access 1940 1960 1980 2000 2020

The 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. 2

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) 3

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 time period involved lead time between receiving information and the decision to be made accuracy needed in forecast 4

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 } ^ ^ ^ 5

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 20

Time Series Examine Patterns in the Past Dependent Variable X X X Forecasted Amounts TIME To The data may offer secular trends, cyclical variations, seasonal variations, and random fluctuations. 21

Time Series Examine Patterns in the Past Dependent Variable Secular Trend X X X Forecasted Amounts TIME To The data may offer secular trends, cyclical variations, seasonal variations, and random fluctuations. 21

Time Series Examine 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. 21

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 23

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.

3. Linear Trend & 4. Constant rate of growth Linear Trend Growth Uses a Semi-log Regression 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 26

More on Constant Rate of Growth Model a proof ^ Suppose: Yt = Y0( 1 + G) t where 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 ^ 27

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 28

The linear 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 semi-log 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% 29

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: e5.1874 = 179.0 linear   30

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 Semi-log is exponential 7 Which prediction do you prefer? 31

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

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. 32

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 2005 to 2007-IV. Forecast all of 2008. Sales(2008-I) = 430; Sales(2008-II) = 440; Sales(2008-III) = 450; Sales(2008-IV) = 478 33

Soothing Techniques 8. Moving Averages A smoothing forecast method for data that jumps around Best when there is no trend 3-Period Moving Ave is: Yt+1 = [Yt + Yt-1 + Yt-2]/3 For more periods, add them up and take the average Dependent Variable * * * Forecast Line is Smoother * * TIME 24

Smoothing Techniques 9. First-Order Exponential Smoothing 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, with a weight of w 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 w. ^ ^ ^ ^ 25

First-Order Exponential Smoothing Example for w = .50 Actual Sales Forecast 100 100 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 100 100 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 100 100 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 Forecasting 10. Barometric Techniques Direction of sales can be indicated by other variables. PEAK Motor Control Sales 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 15

Time given in months from change LEADING INDICATORS* M2 money supply (-14.4) S&P 500 stock prices (-11.1) Building permits (-15.4) Initial unemployment claims (-12.9) Contracts and orders for plant and equipment (-7.3) COINCIDENT INDICATORS Nonagricultural payrolls (+.8) Index of industrial production (-1.1) Personal income less transfer payment (-.4) LAGGING INDICATORS Prime rate (+17.9) Change in labor cost per unit of output (+6.4) *Survey of Current Business, 1995 See pages 182-183 in the textbook 16

Handling Multiple Indicators Diffusion Index: Suppose 11 forecasters predict stock prices in 6 months, up or down. If 4 predict down and seven predict up, 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 18

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 Ambiguous questions Respondents may lie on questionnaires Survey Research Center of U. of Mich. does repeat surveys of households on Big Ticket items (Autos) 14

Qualitative Forecasting 12. Expert Opinion The average forecast from several experts is a Consensus Forecast. Mean Median Mode Truncated Mean Proportion positive or negative 11

Conference Board – macroeconomic predictions 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’. 12

Qd = a + b•P + c•I + d•Ps + e•Pc 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 35

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 36

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