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Whittle estimation of ARCH models. (English) Zbl 1051.62074

Summary: For a class of parametric ARCH models, Whittle estimation based on squared observations is shown to be \(\sqrt n\)-consistent and asymptotically normal. Our conditions require the squares to have short memory autocorrelation, by comparison with the work of P. Zaffaroni and B. d’Italia [J. Econom. 115, 199–258 (2003; Zbl 1027.62074)], who established the same properties on the basis of an alternative class of models with martingale difference levels and long memory autocorrelated squares.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators

Citations:

Zbl 1027.62074
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