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Simulating a class of stationary Gaussian processes using the Davies–Harte algorithm, with application to long memory processes

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  • PETER F. CRAIGMILE

Abstract

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).

Suggested Citation

  • Peter F. Craigmile, 2003. "Simulating a class of stationary Gaussian processes using the Davies–Harte algorithm, with application to long memory processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 505-511, September.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:5:p:505-511
    DOI: 10.1111/1467-9892.00318
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    1. Gneiting, Tilmann, 1998. "Simple tests for the validity of correlation function models on the circle," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 119-122, August.
    2. Caccia, David C. & Percival, Donald & Cannon, Michael J. & Raymond, Gary & Bassingthwaighte, James B., 1997. "Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 609-632.
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    Cited by:

    1. Neuenkirch, Andreas, 2008. "Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2294-2333, December.
    2. Aït-Sahalia, Yacine & Mancini, Loriano, 2008. "Out of sample forecasts of quadratic variation," Journal of Econometrics, Elsevier, vol. 147(1), pages 17-33, November.
    3. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.
    4. Sun, Qi & Xu, Weijun & Xiao, Weilin, 2013. "An empirical estimation for mean-reverting coal prices with long memory," Economic Modelling, Elsevier, vol. 33(C), pages 174-181.

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