A job-shop manufacturer that specializes in replacement parts has no forecasting system in place and manufactures products based on last month's sales. Twenty-four months of sales data are available and are given in Table P-16.

a. Plot the sales data as a time series. Are the data seasonal?
b. Use a naive model to generate monthly sales forecasts (e.g., the February 2005 forecast is given by the January 2005 value, and so forth). Compute the MAPE.
c. Use simple exponential smoothing with a smoothing constant of .5 and an initial smoothed value of 430 to generate sales forecasts for each month. Compute the MAPE.
d. Do you think either of the models in parts b and c is likely to generate accurate forecasts for future monthly sales? Explain.
e. Use Minitab and Winters' multiplicative smoothing method with smoothing constants α = β = γ = .5 to generate a forecast for January 2007. Save the residuals.
f. Refer to part e. Compare the MAPE for Winters' method from the computer printout with the MAPEs in parts b and c. Which of the three forecasting procedures do you prefer?
g. Refer to part e. Compute the autocorrelations (for six lags) for the residuals from Winters' multiplicative procedure. Do the residual autocorrelations suggest that Winters' procedure works well for these data? Explain.

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TABLE P 16 Month Sales Month Sales January 200s February March April May Junc July August September October November December 430 January 2006 442 420 February 436 March 452 April 477 May 420 June 449 458 472 463 431 400 8 July 50Auust 514 September 532 October 512 November 410 December 503 548 432