Influence of Seasonal Level Shift Outlier on the Residuals of SARMA(1, 1) Model

Abstract

Time series often contain discrepant observations which are called outliers. Seasonal Level Shift (SLS) outlier is one such which occurs in seasonal time series. And the importance of residuals in time series model building is well known. Thus in this paper, through analytical expressions, we establish the effect of the presence of an SLS outlier on the residuals of the Seasonal Autoregressive Moving Average model of order (1, 1) (SARMA(1, 1)), followed by a simulation study. One of the principle conclusions of this paper is that the SLS outlier not only affects the residuals at its time of incidence but also at the subsequent seasons. And, the extent of the effect depends on the magnitude of the outlier and parameters of the underlying model.. KEYWORDS :Time series, Seasonal level shift, Residuals, Seasonal autoregressive moving average.