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Statistical inference for time-varying ARCH processes. (English) Zbl 1113.62099

Summary: The class of \(\text{ARCH}(\infty)\) models is generalized to the nonstationary class of \(\text{ARCH}(\infty)\) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation “locally stationary \(\text{ARCH}(\infty)\) process”. The asymptotic properties of weighted quasi-likelihood estimators of time-varying \(\text{ARCH}(p)\) processes \((p<\infty)\) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62F10 Point estimation
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References:

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