A Method Of Dynamic Forecast

Fitting and forecast are two important application of analysis of regression, and the current research work aim to improve the accuracy of fitting, but it is less to research of forecast. For forecast, the traditional methods often get the model of regression according to current sample data, and use all kinds of methods to improve the fitted accuracy of current sample and forecast the new sample. This method don't consider the role of new sample, perhaps new sample don't change the basic model, for example, the model is still linear regression model, but it is most likely to change the estimate result of parameter in the model. In this case, it is obvious unsuitability to continue to use the model based on old data to make new forecast.In practical work, we can fit the empirical equation of regression according to least square method when we use the old data, and needs to make the Real-time treatment for new acquired data in the light of the equation, namely, we need combine new acquired data with the original data, then infer the new empirical equation of regression. If we use the equation of least square estimator directly, computing amount is often very great because course of computing need calculate the inverse of matrix and multiplication of matrix. This paper infer a series of recursive equation based on lease square estimation in order to reduce computing amount, include recurrence equation of regression coefficient, total dispersion square sum, residual square sum, regression square sum etc. on this basis, we can calculate determination coefficient and complex correlation coefficient, and do the test of Significance of regression equation. In the process of total recursive calculation, only the first step, namely calculating regression coefficient, need calculate invert matrix, other steps don't calculate it, which can reduce the computing amount greatly.According to the recursive formula above, the paper put forward a new method of dynamic forecast—modified method of dependent variable based on recursive regression. And the method considers the role of forecast sample adequately. The method divides theoriginal data into two parts in term of "close" degree between the original sample and forecast sample: one is initial sample, the other is training sample. Using lease square method, the initial empirical equation of regression is fitted via the initial sample, then, this equation is modified continually by the method that dependent variable of training sample make modification in turn, which makes this equation more suit to the situation of training sample. Because of the "close" relation between training sample and forecast sample, this equation improves not only the forecast accuracy of training sample, but also the forecast accuracy of forecast sample.In practical work, new sample data is often obtained continually, so these new data can be joined the empirical equation of regression by using recursive formula, and form a dynamic forecast system.