Testing for randomness in a Random Coefficient AutoRegression model

Lajos Horvath and Lorenzo Trapani

Autoregressive models are frequently employed in virtually all applied sciences, from economics to engineering. Despite their simplicity, several variants and extensions of the basic autoregressive models can be proposed. This paper studies a popular extension of the basic autoregressive model, where the autoregressive coefficients may be random and thus time-varying. This set-up clearly enhances the flexibility of the autoregressive specification, allowing for different dynamics in the evolution of the relevant series over time. However, it comes at a cost, as the model becomes more complex. It is therefore important to make sure whether considering random coefficients, as opposed to fixed, constant ones, is really necessary or not.

In this Nottingham School of Economics working paper, published in the Journal of Econometrics, Lajos Horvath and Lorenzo Trapani propose a test to discern between an ordinary autoregressive model, and a random coefficient one. To this end, a full-fledged estimation theory is developed, based on a two-stage Weighted Least Squares approach. The results in the paper hold irrespective of whether the series is stationary or nonstationary, thus ensuring robustness. Further, the paper deals in an innovative way with the issue of testing when the null hypothesis (in this case, that one variance is zero) is on the boundary of the parameter space. Specifically, the paper is based on a randomised test statistic for the null that the coefficient is non-random, as opposed to the alternative of a standard RCA(1) model. Monte Carlo evidence shows that the test has the correct size and very good power for all cases considered.

Journal of Econometrics, “Testing for randomness in a Random Coefficient AutoRegression model”, by Lajos Horvath and Lorenzo Trapani. https://doi.org/10.1016/j.jeconom.2019.01.005

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