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Testing for strict stationarity in a random coefficient autoregressive model and Testing for randomness in a random coefficient autoregression model

Thursday 15 February 2018, 3.15PM to 4.30pm

Speaker(s): Lorenzo Trapani (Nottingham)



We propose a test for the null hypothesis of (strict) stationarity in the context of a Random Coefficient AutoRegression (RCA), versus the alternative of non-stationarity. The test is based on randomising a diagnostic which diverges to positive infinity under the null, and drifts to zero under the alternative, and it can be applied under very general circumstances: albeit developed for an RCA\ model, it can be used in the case of a standard AR(1) model, without requiring any modifications or prior knowledge. Also, the test works (again with no modification or prior knowledge being required) in the presence of infinite variance, and in general requires minimal assumptions on the existence of moments.



We propose a test to discern between an ordinary autoregressive model, and a random coefficient one. To this end, we develop a full-fledged 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.

Location: Economics Staff Room A/EC202

Admission: All welcome