Question: Trigg and Leach (1967) suggest the following adaptive response-rate exponential smoothing method. Along with smoothing the original series, also smooth the error |et| and the absolute error |et| according to the equations
The idea behind the approach is that when Et is close in magnitude to Mt, it suggests that the forecasts are biased. In that case, a larger value of the smoothing constant results that makes the exponential smoothing more responsive to sudden changes in the series.
a. Apply the Trigg-Leach method to the data. Using the MAD, compare the accuracy of these forecasts with the simple exponential smoothing forecasts obtained. Assume that E1 = e1 (the observed error in January) and M1 = e1. Use - = 1.
b. For what types of time series will the Trigg-Leach adaptive response rate give more accurate forecasts, and under what circumstances will it give less accurate forecasts? Comment on the advisability of using such a method for situations in which forecasts are not closely monitored.