Modeling the Effects of Outliers on the Estimation of Linear Stochastic Time Series Model

Abstract

This study investigates the effects of outliers on the estimates of ARIMA model parameters with particular attention given to the performance of two outlier detection and modeling methods targeted at achieving more accurate estimates of the parameters. The two methods considered are: an iterative outlier detection aimed at obtaining the joint estimates of model parameters and outlier effects, and an iterative outlier detection with the effects of outliers removed to obtain an outlier free series, after which a successful ARIMA model is entertained. We explored the daily closing share price returns of Fidelity bank, Union bank of Nigeria, and Unity bank from 03/01/2006 to 24/11/2016, with each series consisting of 2690 observations from the Nigerian Stock Exchange. ARIMA (1, 1, 0) models were selected based on the minimum values of Akaike information criteria which fitted well to the outlier contaminated series of the respective banks. Our findings revealed that ARIMA (1, 1, 0) models which fitted adequately to the outlier free series outperformed those of the parameter-outlier effects joint- estimated model. Furthermore, we discovered that outliers biased the estimates of the model parameters by reducing the estimated values of the parameters. The implication is that, in order to achieve more accurate estimates of ARIMA model parameters, it is needful to account for the presence of significant outliers and preference should be given to the approach of cleaning the series of outliers before subsequent entertainment of adequate linear time series models.