A New Method for Defining Parameters to SETAR(2;k ₁,k ₂)-models

Abstract

This paper describes a new numerical method for defining the threshold and delay parameters of k-order self-exciting threshold autoregressive (SETAR) models. The idea of the method is to divide a time series into ascending and descending parts. This division can especially be exploited in building prediction models: it is a considerably easier task to predict the ascending and descending parts separately than to try to predict both of them at the same time.

Another issue of this paper is to build the prediction model with only the most significant predictor variables. This is achieved with the help of evolutionary optimizing. In the first step we generate a number of models (networks) with different predictor variables, then we train each of the networks and the fittest ones are used for reproduction. In the beginning we also set the possible number of predictor variables to some constant. In the next step we reduce the number of predictor variables by leaving out the ones not chosen by the algorithm in the first step. Then we repeat the training and dropping procedure until the genetic algorithm does not drop any predictors anymore.

I have shown in this paper that the division procedure works very well, that building separate prediction models increases the accuracy of the predictions noticeably, and that using evolutionary optimization is succesful in dropping out the irrelevant predictors.