Parsimonious Modeling and Forecasting of Time Series drifted by Autoregressive Noise

Abstract

This paper addresses issue of modeling, analysis and forecasting of time series drifted by autoregressive noise and finding its optimal solution by extending a conventional linear growth model with an autoregressive component. This additional component is designed to take care of high frequencies of autoregressive noise drift without influencing the low frequencies of the linear trend and compromising on parsimonious nature of the model. The parameters of this model are then optimally estimated through the self updating recursive equations using Bayesian priors. For identification of autoregressive order of noise and estimation of its coefficients ATS procedure of Akram (2001) is employed. Further, for unknown variance of observations an on-line variance learning and estimation procedure is discussed. To demonstrate practical aspects of the model some examples are given and for generation of short, medium and long term forecasts in one go an appropriate forecast function is given.