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Can One Use the Durbin–Levinson Algorithm to Generate Infinite Variance Fractional ARIMA Time Series?
Author(s) -
Kokoszka Piotr S.,
Taqqu Murad S.
Publication year - 2001
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 - 10.1111/1467-9892.00226
Subject(s) - autoregressive integrated moving average , mathematics , gaussian , series (stratigraphy) , covariance , variance (accounting) , algorithm , range (aeronautics) , time series , statistics , paleontology , physics , accounting , quantum mechanics , business , biology , materials science , composite material
The Durbin–Levinson algorithm is used to generate Gaussian time series with a given covariance structure. This is the most efficient way, for example, to simulate a Gaussian fractional ARIMA (FARIMA) time series, a linear sequence with i.i.d. Gaussian innovations which exhibits long‐range dependence. The paper studies the applicability of the Durbin–Levinson algorithm to the simulation of infinite variance FARIMA sequences including an α‐stable FARIMA.