Joint Estimation of Model Parameters and Outlier Effects in Time Series

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Abstract
Time series data are often subject to uncontrolled or unexpected interventions, from which various types of outlying observations are produced. Outliers in time series, depending on their nature, may have a moderate to significant impact on the effectiveness of the standard methodology for time series analysis with respect to model identification, estimation, and forecasting. In this article we use an iterative outlier detection and adjustment procedure to obtain joint estimates of model parameters and outlier effects. Four types of outliers are considered, and the issues of spurious and masking effects are discussed. The major differences between this procedure and those proposed in earlier literature include (a) the types and effects of outliers are obtained based on less contaminated estimates of model parameters, (b) the outlier effects are estimated simultaneously using multiple regression, and (c) the model parameters and the outlier effects are estimated jointly. The sampling behavior of the test statistics for cases of small to large sample sizes is investigated through a simulation study. The performance of the procedure is examined over a representative set of outlier cases. We find that the proposed procedure performs well in terms of detecting outliers and obtaining unbiased parameter estimates. An example is used to illustrate the application of the proposed procedure. It is demonstrated that this procedure performs effectively in avoiding spurious outliers and masking effects. The model parameter estimates obtained from the proposed procedure are typically very close to those estimated by the exact maximum likelihood method using an intervention model to incorporate the outliers.

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