The time plot in Figure 17.18 describes actual quarterly sales for a department store over a 6-year period (data are available in Department Store Sales.xls, data courtesy of Chris Albright).

a. The forecaster decided that there is an exponential trend in the series. In order to fit a regression-based model that accounts for this trend, which of the following operations must be performed?
- Take \(\log\) of quarter index.
- Take \(\log\) of sales.
- Take an exponent of sales.
- Take an exponent of quarter index.

b. Fit a regression model with an exponential trend and seasonality, using the first 20 quarters as the training data (remember to first partition the series into training and validation series).

c. A partial output is shown in Figure 17.19. From the output, after adjusting for trend, are Q2 average sales higher, lower, or approximately equal to the average Q1 sales?

d. Use this model to forecast sales in quarters 21 and 22.

e. The plots in Figure 17.20 describe the fit (top) and forecast errors (bottom) from this regression model.

i. Recreate these plots.

ii. Based on these plots, what can you say about your forecasts for quarters 21 and 22? Are they likely to over-forecast, under-forecast or be reasonably close to the real sales values?

f. From the forecast errors plot, which of the following statements appear true?
- Seasonality is not captured well.
- The regression model fits the data well.
- The trend in the data is not captured well by the model.
g. Which of the following solutions is adequate and a parsimonious solution for improving model fit?
- - Fit a quadratic trend model to the residuals (with Quarter and Quarter \({ }^{2}\) ).
- Fit an AR model to the residuals.
- Fit a quadratic trend model to Sales (with Quarter and Quarter²).

Transcribed Image Text:

120000 100000 80000 60000 40000 20000 0 Quarter FIGURE 17.18 DEPARTMENT STORE QUARTERLY SALES SERIES