Robust Inference in Conditionally Heteroskedastic Autoregressions

We consider robust inference for an autoregressive parameter in a stationary autoregressive model with GARCH innovations when estimation is based on least squares estimation. As the innovations exhibit GARCH, they are by construction heavy-tailed with some tail index κ. The rate of consistency as well as the limiting distribution of the least squares estimator depend on κ. In the spirit of Ibragimov and Müller (“t-statistic based correlation and heterogeneity robust inference”, Journal of Business & Economic Statistics, 2010, vol. 28, pp. 453-468), we consider testing a hypothesis about a parameter based on a Student's t-statistic for a fixed number of subsamples of the original sample. The merit of this approach is that no knowledge about the value of κ nor about the rate of consistency and the limiting distribution of the least squares estimator is required. We verify that the one-sided t-test is asymptotically a level α test whenever α ≤ 5% uniformly over κ ≥ 2, which includes cases where the innovations have infinite variance. A simulation experiment suggests that the finite-sample properties of the test are quite good