3 Table 27 gives the following data for monthly U.S.

housing sales (in thousands of houses) for 1965–1972.

a Use the years 1965–1966 to initialize the parameters for Winter’s method. Then find values of

a, b, and g that yield a MAD (for 1967–1972) of less than 3.5. (Hint: It may be necessary to use a 0.5.)

b We would expect 68% of our forecasts to be accurate within _____ and 95% of our forecasts to be accurate within _____.

c Check to see whether the data are consistent with the answer to part (b).

d Although we have not discussed autocorrelation for smoothing methods, good forecasts derived from smoothing methods should exhibit no autocorrelation.

Do the forecast errors for this problem exhibit autocorrelation?

e It has been stated that if only trend and seasonality are important factors, then a should be at most 0.5. Explain why this problem required a 0.5.

f At the end of December 1972, what is the forecast for housing sales during the first three months of 1973?

Note: This assignment is a snap on a spreadsheet.

The spreadsheet might be set up as in Table 28. In B14, enter A$3*A14/D2(1-A$3)*(B13C13). Insert analogous formulas in C14, D14, E14. Remember that the forecast must be made before “seeing” A14. In F14, enter A14-E14. In G14, enter ABS(F14). Copy from B14:G14 to ??. To compute MAD, average the absolute errors for each month (rows 14–85).

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TABLE 27 Year Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 1965 38 44 53 49 54 57 51 58 1966 42 43 53 49 49 40 40 36 29 1967 29 32 41 44 49 47 46 47 424 48 44 42 37 31 26 23 43 45 34 31 1968 35 43 46 46 43 41 44 47 41 40 32 32 1969 34 40 43 42 43 44 39 40 33 32 31 28 1970 34 29 36 42 43 44 44 48 45 44 40 37 1971 45 49 62 62 58 59 64 62 50 52 50 44 1972 51 56 60 65 64 63 63 72 61 65 51 47