How to implement the bootstrap in static or stable dynamic regression models: test statistic versus confidence region approach. (English) Zbl 1020.62015
Summary: By combining two alternative formulations of a test statistic with two alternative resampling schemes we obtain four different bootstrap tests. In the context of static linear regression models two of these are shown to have serious size and power problems, whereas the remaining two are adequate and in fact equivalent. The equivalence between the two valid implementations is shown to break down in dynamic regression models. Then, the procedure based on the test statistic approach performs best, at least in the AR(1)-model. Similar finite-sample phenomena are illustrated in the ARMA(1,1)-model through a small-scale Monte Carlo study and an empirical example.
MSC:
| 62F03 | Parametric hypothesis testing |
| 62F40 | Bootstrap, jackknife and other resampling methods |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62F25 | Parametric tolerance and confidence regions |
| 62J05 | Linear regression; mixed models |
Keywords:
asymptotic rejection probabilities; autoregressive models; bootstrap; hypothesis testing; resampling schemesReferences:
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