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Abstract:
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A test of modality of the variance function for a modulated autoregressive model, i.e. autoregressive processes with errors whose variance depends on time, is presented. The test is based on the idea that, given two candidate modes, a function is bimodal if it is not monotonic between the two candidates. An estimate of a quantile q of the residuals is found, and the test statistic d(k,q) is the longest time span that contains at most k residuals which are larger than the estimate of q. Unimodality is rejected if d(k,q) is too large. The test is calibrated against the hypothesis that the function is flat on some interval between the two candidates. Under the null, should the errors and quantile be known, finding the p-value would amount to considering the distribution of the longest scan of type k.
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