The influence of anomalous observations on the least squares estimate of the parameter of the autoregressive equation with random coefficient

The study tested robustness properties of the least squares estimate of the parameter of the autoregressive equations with random coefficients in the presence of additive or replacement outliers in the observations. We investigated the following parameters: the relation of the functional of the least squares estimate with the autoregression parameter; the variance of the autoregressive coefficient; the variance of the innovation process and parameters of the observations process. Moreover, we calculated the gross-error sensitivity of the least squares estimate and investigated the conditions for its boundedness. The findings of the research illustrate that the estimate is always biased except in the degenerate case of zero autoregressive parameter.

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