GC 18/03: Testing for randomness in a random coefficient autoregression model

Summary

We propose a test to discern between an ordinary autoregressive model, and a random coefficient one. To this end, we develop a full- edged estimation theory for the variances of the idiosyncratic innovation and of the random coefficient, based on a two-stage WLS approach. Our results hold irrespective of whether the series is stationary or nonstationary, and, as an immediate result, they afford the construction of a test for "relevant" randomness. Further, building on these results, we develop 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.

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Authors 

Lajos Horváth and Lorenzo Trapani

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