Forecasting Techniques: Naïve Methods

1. Forecasting Techniques: Naïve Methods Su, Chapter 10, sections I-II

2. Forecasting Exercises: Data • Table 10.2 in Su • Annual New Car Sales (in thousands) and a New Automobile Price Index (1982-1984=100) for 1971-1991

4. Forecasting Exercises • First, read the file table10-2.dat into excel • This file contains three columns, containing dates (Col. A), New Car Sales (Col. B) and the New Car Price Index (Col. C) • Extend the date column through 1999 • Label Columns D-H: No Change, Same Change, Same Ratio, MA, Partial Adjustment

5. No Change Model • Simplest Naïve Model • Often used without even realizing it • Requires only one period of historical data • Anticipated level of the variable this period is the same as last period X*t = Xt-1 X*t: Forecast value

6. Same Change Model • No change model in first differences DX*t = DXt-1 X*t - Xt-1 = Xt-1 - Xt-2 • Requires only 2 periods of past data

7. Same Ratio Model • Same change model in multiplicative form (X*t / Xt-1) = (Xt-1 / Xt-2) X*t = Xt-1 (Xt-1/Xt-2 )

8. Three Naïve Forecasts

9. Evaluating these Forecasts • What are the underlying assumptions? • How much historical data were used by each • How accurate are they? • Over how long a period should these forecasts be evaluated?

10. Defining and Measuring Accuracy • Reading: Su, Chapter 16, section I-II • The criteria that should be used to measure forecast accuracy are open to debate; we’ll look at the main competing methods • Assessment of forecast accuracy is a very important component of forecast evaluation

11. Definitions: Forecast Errors • Forecast Error in Levels FEt in level = Ft - At FEt: Forecasting Error in period t Ft: Forecast in period t At: Actual (or Realized) value in period t • Forecast error measured in same units as variable • FEt > 0 Overestimate FEt < 0 Underestimate

12. Summary Statistics • Must avoid problems associated with signs of forecast errors - can’t simply add them up! • Two ways to correct for this: • Absolute Value • Squaring

13. Three Summary Statistics • Mean Absolute Error (MAE) MAE = S |FEt| / n = S |Ft - At| / n • Mean Square error (MSE) MSE = S (FEt)2 / n = S (Ft - At)2 / n • Root Mean Square Error (RMSE) RMSE = SQRT[S (FEt)2 / n = S (Ft - At)2 / n]

14. Naïve Forecasts: In-Sample Measurement of Accuracy • Use these definitions to evaluate the accuracy of these three naïve methods • We’ll use “In-Sample” evaluation, as we have a lot of historical data but require very little to make these forecasts • Step 1: Copy Table to a new sheet • Step 2: Calculate in-sample forecasts • Step 3: Calculate forecast error • Step 4: Calculate Summary Statistics

15. Summary Statistics • No Change MAE = 812.3 MSE = 1077729.1 RMSE = 1038.1 • Same Change MAE = 1561.4MSE = 6080819.2 RMSE = 2465.9 • Same Ratio MAE = 1561.9 MSE = 6015850.2 RMSE = 2452.7

16. Conclusions From Summary Statistics • Which is the “best” at one-period ahead forecasts?

17. Moving Average Methods • Provides more efficient mechanical projections of short-term movements • Has advantage of flexibility and presents a more realistic picture of long-run movements • Data are not forced into any particular patterns MA: X*t = (1/n)Sni=1Xt-i =(1/n)[Xt-1 +Xt-2 +Xt-3 + ...+Xt-n] • Note this is not a centered moving average • Must only decide on n • Can be applied to first differences or % changes

18. Moving Average Example • Start with an MA(4) forecast • For ease of coding, copy the car sales values to the MA column, then the out of sample MA forecast can be easily written and copied • Compute the within sample, one period ahead MAE, MSE, RMSE

19. Naïve Forecasts and MA(4)

20. Changing the Order of an MA Forecast • Economists refer to MA forecasts by the number of periods they use, which is called the “order” of the moving average • MA(2): Two period moving average • MA(3): Three period moving average • etc. • The forecast depends on the MA order

21. Effect of Changing Order