1. After this analysis was completed, the figure for sales in 1961 became available: $1,426. What is the model's forecast for 1961? If this year were added to the testing data set, what would the revised MAPE and MAD be?
2. There is some evidence that the Lydia Pinkham data may be nonstationary. For example, the sample autocorrelations tend to be large (persist) for several lags. Difference the data. Construct a time series plot of the differences. Using Minitab or a similar program, fit an ARIMA(1, 1, 0) model to annual sales for 1907 to 1948. Generate one-step-ahead forecasts for the years 1949 to 1960. Which model, AR(2) or ARIMA(1,1,0), do you think is better for the Lydia Pinkham data?
3. The Lydia Pinkham data are interesting due to the unique (unchanging) nature of the product and marketing for the 54-year period represented. What factors might affect annual sales data for automobiles and copper over this same period? Why?
The Lydia E. Pinkham Medicine Company was a family-owned concern whose income was derived largely from the sale of Lydia Pinkham's Vegetable Compound. Perhaps students today could use some of the compound to relieve stress; unfortunately, it is no longer sold. Lydia Pinkham's picture was on the label, and the compound was marketed to women.