Naslov
Regular variation of GARCH processes

Autori
Basrak, Bojan ; Davis, Richard A. ; Mikosch, Thomas

Izvornik
Stochastic processes and their applications (0304-4149) 99 (2002), 1; 95-115

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
point process ; vague convergence ; multivariate regular variation ; mixing condition ; stationary process ; heavy tail ; sample autocovariance ; sample autocorrelation ; GARCH ; finance ; Markov chain

Sažetak
We show that the finite-dimensional distributions of a GARCH process are regularly varying, i.e., the tails of these distributions are Pareto-like and hence heavy-tailed. Regular variation of the joint distributions provides insight into the moment properties of the process as well as the dependence structure between neighboring observations when both are large. Regular variation also plays a vital role in establishing the large sample behavior of a variety of statistics from a GARCH process including the sample mean and the sample autocovariance and autocorrelation functions. In particular, if the 4th moment of the process does not exist, the rate of convergence of the sample autocorrelations becomes extremely slow, and if the second moment does not exist, the sample autocorrelations have non-degenerate limit distributions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA