Internal Seminar: Lorenzo Trapani (Economics)

[Statistics & Probability Seminar]

Testing for randomness and for strict stationarity in a Random Coefficient Autoregression

We propose two tests to study the causal solutions of a Random Coefficient Autoregressive model.

The first test is designed 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. 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.

The second test is for the null hypothesis of (strict) stationarity, 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 presence of infinite variance, and in general requires minimal assumptions on the existence of moments.