International Journal of Statistics and Reliability Engineering

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Vol 10, No 2:

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Effect of a Seasonal Level Shift Outlier on Residuals of SAR(1) and SMA(1) Models

Abstract

The existence of outliers in time series data is very common and its occurrence can be attributed to wars, economic or political changes, etc. Unlike in regression analysis, there are many types of outliers encountered in time series and one such outlier is the Seasonal Level Shift (SLS) outlier. In the present study, we explore analytically, the deleterious effect of the presence of SLS outlier on the residuals of the seasonal autoregressive model of order one (SAR(1)) and seasonal moving average model of order one (SMA(1)). To gain more insight, we have carried out a simulation study. We have found that the outlier not only affects the residuals at its time of incidence but also the subsequent seasons in both models. Further, the extent of the effect depends on the magnitude of the outlier and the parameter of the underlying model

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References

1. A.J. Fox; Outliers in Time Series. Journal of Royal Statistical Society, Series B (Methodological), 34(3), 350-363 (1972).
2. C. Chen and L.M. Liu; Joint Estimation of Model Parameters and Outlier Effects in Time Series. Journal of American Statistical Association, 88(421), 284-297 (1993).
3. I. Chang; G.C. Tiao and C. Chen; Estimation of Time Series Parameters in the Presence of Outliers. Technometrics, 30(2), 193-204 (1988).
4. J.V. Janhavi and R. Suresh; Role of Structural Coefficients in the Study of the Influence of an Additive Outlier on the Residuals in ARMA(1,1), AR(1) and MA(1) Models. Journal of Statistics, 18, 67-83 (2011).
5. R. Kaiser and A. Maravall; Seasonal Outliers in Time Series. Estadistica, 53 (2001). URL: https://www.inec.gob.pa/IASI/publi_journal.html
6. R.S. Tsay; Outliers, Level Shifts, and Variance Changes in Time Series. Journal of Forecasting, 7(1), 1-20 (1988).
7. Z. Asghar and A. Urooj; Analysis of Seasonal Level Shift (SLS) Detection in SARIMA Models. Communications in Statistics - Simulation and Computation, 46(9), 7264-7318 (2017).

ISSN(P) 2350-0174

ISSN(O) 2456-2378

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