Question

The following timeplot charts the value (in millions of dollars) of inventories held by Dell, Incorporated (the computer maker). This time series is quarterly. The scatterplot on the next page graphs the value of inventories on its lag.
(a) Two outliers are evident in the timeplot (high-lighted with ×€™s). These occur for the quarters ending January 31, 2003 and January 31, 2004. Why might inventories have been so high at the end of these quarters?

(b) Why do two outliers in the timeplot produce the four outliers seen in the scatterplot of Yt on Yt -1?
(c) What is the effect of the outliers on the estimated dependence of inventory levels: Do the outliers create the impression of more or less dependence?
(d) How do you recommend treating these outliers when forecasting future levels of inventory at Dell?

Answer 1

(a)        The outliers may be due to Dell having anticipated a better holiday selling season than materialized. Manufacturers often ramp up production and inventory levels in preparation for anticipated increases in sales. Evidently, that did not happen during these quarters.

 

(b)        First each outlier shows up as the y coordinate in the pairing (x, y), then the outlier shows up in the next pair as the x-coordinate. For example, inventories at Dell at the end of October 2002 were $307 million, and then rose to $729 million at the end of January 2003, and fell back to $264 million at the end of April. For plotting on the lagged value, these 3 consecutive observations produce the (x, y) pairs (307,729) and (729,264).

 

(c)        Less dependence, which makes sense because it is harder to anticipate the level of inventories with these large, unanticipated changes.

 

(d)       Since the outliers have not occurred in the more recent data, we would exclude them when building a model for the trend.

 Then when forecasting inventories at the end of the next January, we would be sure to mention that our estimates could dramatically under-predict inventories if these events were to occur again.