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Statistical inference for time-varying ARCH processes
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DOI：10.1214/009053606000000227.png)
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In this paper the class of ARCH(infinity) models is generalized to the nonstationary class of ARCH(infinity) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation locally stationary ARCH(infinity) process. The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p < infinity) 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.
Keyword:
derivative process
locally stationary
quasi-likelihood estimates
timevarying
ARCH process
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