Diagnostic tests for non-causal time series with infinite variance

Goodness-of-fit testing for non-causal autoregressive time series with non-Gaussian stable noise is studied. To model time series exhibiting sharp spikes or occasional bursts of outlying observations, the exponent of the stable errors is assumed to be less than two. Under such a condition, the innovation variables have no finite second moment. We prove that the sample autocorrelation functions of the trimmed residuals are asymptotically normal. Nonparametric tests are also investigated. An assortment of test statistics is suggested for model assessment.