Filtering Economic Time Series
Terence C. Mills · Palgrave Macmillan UK eBooks · 2003
In Chapter 2, section 2 we considered using moving averages to estimate a trend component. We now wish to take the analysis further and investigate the statistical implications of applying a moving average to an observed series. Thus, suppose we transform the observed series y t to a new series y* t by using an MA (2n + 1) filter (4.1) yt*=∑j=−nnajyt−j=a(B)yt $$y_t^* = \sum olimits_{j = - n}^n {{a_j}{y_{t - j}}} = a\left( B \right){y_t}$$