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Analyzing the effects of level shifts and temporary changes on the identification of ARIMA models

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  • F. Javier Trivez
  • Javier Nievas

Abstract

The presence of outliers in time series gives rise to important effects on the sample autocorrelation coefficients. In the case where these outliers are not adequately treated, their presence causes errors in the identification of the stochastic process generator of the time series under study. In this respect, Chan has demonstrated that, independent of the underlying process of the outlier-free series, a level shift (LS) at the limit (i.e. asymptotically and considering an LS of a sufficiently large size) will lead to the identification of non-stationary processes; with respect to a temporary change (TC), this will lead, again at the limit, to the identification of an AR(1) autoregressive process with a coefficient equal to the dampening factor that defines this TC. The objective of this paper is to analyze, by way of a simulation exercise, how large the LS and TC present in the time series must be for the limiting result to be relevant, in the sense of seriously affecting the instruments used at the identification stage of the ARIMA models, i.e. the sample autocorrelation function and the sample partial autocorrelation function.

Suggested Citation

  • F. Javier Trivez & Javier Nievas, 1998. "Analyzing the effects of level shifts and temporary changes on the identification of ARIMA models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(3), pages 409-424.
  • Handle: RePEc:taf:japsta:v:25:y:1998:i:3:p:409-424
    DOI: 10.1080/02664769823133
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    References listed on IDEAS

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    1. Ledolter, Johannes, 1989. "The effect of additive outliers on the forecasts from ARIMA models," International Journal of Forecasting, Elsevier, vol. 5(2), pages 231-240.
    2. Wai-Sum Chan, 1995. "Understanding the effect of time series outliers on sample autocorrelations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 179-186, June.
    3. Chen, Chung & Tiao, George C, 1990. "Random Level-Shift Time Series Models, ARIMA Approximations, and Level-Shift Detection," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 83-97, January.
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