ISSN:
1531-5851
Keywords:
Fractional ARIMA
;
midpoint displacement technique
;
fractional Gaussian noise
;
fractional derivative
;
generalized functions
;
self-similarity
;
Primary 60G18
;
secondary 41A58
;
60F15.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We provide an almost sure convergent expansion of fractional Brownian motion in wavelets which decorrelates the high frequencies. Our approach generalizes Lévy's midpoint displacement technique which is used to generate Brownian motion. The low-frequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series. The wavelets fill in the gaps and provide the necessary high frequency corrections. We also obtain a way of constructing an arbitrary number of non-Gaussian continuous time processes whose second order properties are the same as those of fractional Brownian motion.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01261639
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