An improved self-adaptive filter forecasting method

This paper improved the selfadaptive filter-forecasting model that is one of deterministic constant parameter forecasting models. An attenuation/gain function is drawn into a direct iteration search method that belongs to the multi-variables extreme value research based on the optimization theory, so that it combines the quantitative methods with the qualitative analysis by the experts and increases the explanatory ability and simulation level of the original model. As an empirical study, the authors applied the improved method to the forecasting of the middle-term demand for cellular phones in China. The mechanism of the improved selfadaptive model First, determine P, the order of the model, then suppose a set of original weight values as …1† it , and substitute them into the model to obtain ŷ …1† t , compare the actual value of yt with ŷ …1† it , suppose the error e …1† t ˆ yt ÿ ŷ…1† t . Adjust the original weight value …1† it into …1† i…t‡1†, according to the error e …1† t and certain rules. …1† i…t‡1†should be determined by the following formula: …1† i…t‡1† ˆ …1† it ‡ …1† i…t‡1† …3† where, as adjusting value of ̂it; ̂ …1† i…t‡1† should be related to error e …1† t and ytÿ1. If the forecasting result is on the low side, i.e. e …1† t > 0, the reason is that …1† it is low, so all weights need to be adjusted higher in accordance with their corresponding independent variables, respectively. In general, the larger the ith variable to which the ith parameter corresponds, the larger value should be adjusted, and vice versa. If the forecasting result is on the high side, e …1† t < 0, the reason is that the …1† it is high, so all weights need to be adjusted lower in proportion to their corresponding independent variables, respectively, i.e. …1† i…t‡1† ˆ he…1† t ytÿi i ˆ 1; 2; . . . ;p …4† in which, h > 0 is adjusting proportion. After adjusting …1† it into …1† i…t‡1†, estimate ŷ …1† t‡1 by putting …1† i…t‡1† into the model, then compare yt‡1 with ŷ …1† t‡1 to obtain error e …1† t‡1, finally adjust …1† i…t‡1† into …1† i…t‡2† according to the above reasons. Keep on doing this following the above process until the weight is adjusted at the end of the first iteration. After that, repeat the above process with …1† i…n‡1† as the original value …2† it of the second iterations. After several iterations, suppose d iterations, …d† i…n‡1† makes Xn