Application of generally weighted moving average method to tracking signal state space model. Issue 5 (29th August 2012) - Lin, Cheng‐Yi; Sheu, Shey‐Huei; Hsu, Tsung‐Shin; Chen, Yan‐Chun
Abstract In predicting time series, if a trend includes a structural break, then a state space model can be applied to revise the predictive method. Some scholars suggest that restricted damped trend models yield excellent prediction results by automatically revising unforeseen structural break factors in the prediction process. Restricted damped trend models add a smoothed error statistic to a local‐level model and use the exponentially weighted moving average (EWMA) method to make corrections. This paper applies the generally weighted moving average (GWMA) concept and method to a restricted damped trend model that changes the smoothed error statistic from the EWMA form to the GWMA form and adds the correction parameter λ, which distinguishes three situations <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg3x88c324" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />λ<1</alternatives>, <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg3x88c35s" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />λ=1</alternatives>, and <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg3x88c2v9" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />λ>1</alternatives>. The original restricted damped trend model applies only to <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg3x88c2zz" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />λ=1</alternatives>, enabling the model to capture situations in which <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg3x88c3c3" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />λ<1</alternatives> and <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg3x88c3gr" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />λ>1</alternatives> increases its generality. This paper also compares the effect of various parameter values on the predictive model and finds the range of parameter settings that optimize the model.