◆ SpookStack

For the recursive form of this filter, where each datum is weighted by its position in the chronological sequence, the recursive filter factor for the nth point is given by n 2n 2 a=-=---=-- (16) n f i n·(n+l) n+l i=l Using Eq. (12), (17) The "memory'' (i.e., importance) of older data in this filter fades at a rate dictated by the filter. In this case, the 50th value is 50 times more important than the first, and the 100th value is twice as important as the 50th and 100 times more important than the first. The exponentially-weighted filter provides the analyst with more flexibility. This filter uses F as a weighting factor, where the filter-control constant F is a value chosen between zero and one, and i is the "age-count" of the ith data point. For this filter, i = 0 now designates the current -or latest data point, i =1 designates the immediately preceding or next-to-last data point, etc., so the data points are indexed in reverse chronological order starting with zero. The weighted least-squares solution is (18) Using F =0.9 and the same example as before, X3 = Fox3 + F1x2 + F2x1 po +Fl +F2 (.9)0(7) +(.9)1(5) +(.9)2(6) (19) = 0 1 2 (.9) +(.9) +(.9) = 7 + 4.5 +4.86 =- 16.36 = 6.04 2.71 2.71 The weighting of each data point for sample sizes up to 300 is sqown in Figure 35 for values of F from 0.8 to 1.0. For F = 1, all points in the sample are weighted equally. For 9/10/96 92 RTI