Higher order approximations for autocovariances from linear processes with applications. (English) Zbl 0641.62055
Summary: We prove that the distribution of autocovariances from appropriate linear processes admit Edgeworth type expansions. As a result, Edgeworth expansions are valid for moment estimates in moving average processes and l.s.e. in autoregressive processes. Berry-Esseen bounds in all these situations is an incidental fall out.
MSC:
62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
62F12 | Asymptotic properties of parametric estimators |
62E20 | Asymptotic distribution theory in statistics |
Keywords:
Cramer’s condition; distribution of autocovariances; linear processes; Edgeworth type expansions; moment estimates; moving average processes; autoregressive processes; Berry-Esseen boundsReferences:
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