A model for long memory conditional heteroscedasticity

Giraitis, L., Robinson, P. M. & Surgailis, D. (2000). A model for long memory conditional heteroscedasticity. Annals of Applied Probability, 10(3), 1002-1024.
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For a particular conditionally heteroscedastic nonlinear (ARCH) process for which the conditional variance of the observable sequence rt is the square of an inhomogeneous linear combination of rs, s < t, we give conditions under which, for integers 1 > 2, r' has long memory autocorrelation and normalized partial sums of ri converge to fractional Brownian motion.

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