Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations. (English) Zbl 1254.91679
Summary: A general method is proposed for the construction of valid simultaneous confidence sets in the context of stationary GARCH models. The proposed method proceeds by numerically inverting the conventional likelihood ratio test. In order to hedge against the risk of a spurious rejection, candidate points that are rejected by the conventional test undergo a finite-sample parametric bootstrap test. A projection technique is then exploited to produce conservative confidence sets for general functions of the parameters. A simulation study illustrates the performance of the parametric bootstrap approach in the context of a GARCH model with heavy-tailed and skewed innovations. That model is then used in an empirical application to construct simultaneous confidence intervals for multi-step ahead volatility forecasts for the returns on a major stock market index.
MSC:
| 91B84 | Economic time series analysis |
| 62F40 | Bootstrap, jackknife and other resampling methods |
| 91B82 | Statistical methods; economic indices and measures |
| 62F25 | Parametric tolerance and confidence regions |
| 62G32 | Statistics of extreme values; tail inference |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
conditional heteroskedasticity; heavy tails; weak identification; parametric bootstrap; Monte Carlo \(p\)-value; projection techniqueReferences:
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