Convergence in distribution for the sup-norm of a kernel density estimator for GARCH innovations. (English) Zbl 1136.62369
Summary: The estimation and identification of the GARCH innovation density is an important task, leading to efficient parameter estimation. We derive the asymptotic distribution for the sup-norm of a kernel density estimator, and presents a goodness-of-fit test for the innovation density.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62G07 | Density estimation |
| 60F05 | Central limit and other weak theorems |
| 62E20 | Asymptotic distribution theory in statistics |
| 62G20 | Asymptotic properties of nonparametric inference |
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