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A model for long memory conditional heteroscedasticity. (English) Zbl 1084.62516

For a particular conditionally heteroscedastic nonlinear (ARCH) process for which the conditional variance of the observable sequence \(r_t\) is the square of an inhomogeneous linear combination of \(r_s, s < t\), we give conditions under which, for integers \(l \geq 2, r_t^l\) has long memory autocorrelation and normalized partial sums of \(r_t^l\) converge to fractional Brownian motion.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60F05 Central limit and other weak theorems
60J65 Brownian motion
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