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Simulating a class of stationary Gaussian processes using the Davies–Harte algorithm, with application to long memory processes
Author(s) -
CRAIGMILE PETER F.
Publication year - 2003
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00318
Subject(s) - autocovariance , fractional brownian motion , mathematics , long memory , gaussian , gaussian process , class (philosophy) , algorithm , zero (linguistics) , brownian motion , sequence (biology) , statistical physics , mathematical analysis , computer science , artificial intelligence , statistics , econometrics , volatility (finance) , linguistics , physics , philosophy , genetics , fourier transform , quantum mechanics , biology
We demonstrate that the fast and exact Davies–Harte algorithm is valid for simulating a certain class of stationary Gaussian processes – those with a negative autocovariance sequence for all non‐zero lags. The result applies to well known classes of long memory processes: Gaussian fractionally differenced (FD) processes, fractional Gaussian noise (fGn) and the nonstationary fractional Brownian Motion (fBm).