New procedure for determining order of subset autoregressive integrated moving average (ARIMA) based on over-fitting concept

Abstract

One of the most popular models that usually be used to predict time series data is Autoregressive Integrated Moving Average (ARIMA) model. The most crucial steps in ARIMA modeling are identification and selection the best model based on available data. These steps require a good understanding about the characteristics of the process in terms of their theoretical autocorrelation function (ACF) and partial autocorrelation function (PACF). In identification step, the goal is to match the patterns of the sample ACF and PACF with the patterns of theoretical ACF and PACF for determining an appropriate order of ARIMA, including order of subset ARIMA. In this paper, we propose the new procedure for determining the order of ARIMA based on over-fitting concept. The process is started from the simplest ARIMA model that all of parameters are statistically significant and determination of an additional order AR or MA is based on over-fitting concept, i.e. based on ACF of the residual model. This new proposed procedure is applied for constructing a subset ARIMA model of Indonesia's inflation data. The results show that the proposed procedure yields an appropriate order of subset ARIMA model for Indonesia's inflation data.