Journal of Time Series Analysis

Some Results on Specification Search and Pre‐testing in an ARMA(1,1) Process

Journal Article

In this study we consider simple autoregressive moving‐average (ARMA) models of order at most 1. Pre‐testing, on the moving‐average coefficient θ, is used to choose between an ARMA(1,1) and an AR(1) in a Monte Carlo design. We find that the pre‐test estimator is not always dominated by the others, and that the bias and the mean square error of the estimate of the autoregressive coefficient φ very often depend on the sign of the autoregressive and moving‐average parameters of the ARMA(1,1) model in the data‐generating process. Further, we note that the degrees of size and power distortion of the t test on φ, after pre‐testing for θ, are generally associated with model misspecification.

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