The m-delay Autoregressive Model with Application

Abstract

The classical autoregressive (AR) model has been widely applied to predict future data using m past observations over five decades. As the classical AR model required m unknown parameters, this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model. We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique. The performance of the m-delay AR model was tested by comparing with the classical AR model. The results, obtained from Monte Carlo simulation using the monthly mean minimum temperature in Perth Western Australia from the Bureau of Meteorology, are no significant difference compared to those obtained from the classical AR model. This confirms that the m-delay AR model is an effective model for time series analysis.