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 Et  et  (1  )Et1, Mt  et  (1  )Mt1 and define the smoothing constant to be used in forecasting the series in period t as The forecast made in period t for period t  1 is obtained by the usual exponential smoothing equation, using t as the smoothing constant. That is, Ft1  tDt  (1  t)Ft.

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 in Problem