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Alternative forms of fractional Brownian motion

Domenico Marinucci, +1 more
- 01 Aug 1999 - 
- Vol. 80, Iss: 1, pp 111-122
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TLDR
In this article, it is pointed out that two contradictory definitions of fractional Brownian motion are well-established, one prevailing in the probabilistic literature, the other in the econometric literature, each associated with a different definition of nonstationary fractional time series, arising in functional limit theorems based on such series.
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This article is published in Journal of Statistical Planning and Inference.The article was published on 1999-08-01 and is currently open access. It has received 301 citations till now. The article focuses on the topics: Fractional Brownian motion & Stochastic process.

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Journal ArticleDOI

Convergence of Probability Measures

J. F. C. Kingman
- 01 Nov 1969 - 
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Journal ArticleDOI

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Dave Applebaum
- 01 Nov 1995 - 
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Exact Local Whittle Estimation of Fractional Integration

Katsumi Shimotsu, +1 more
- 01 May 2002 - 
TL;DR: In this article, an exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter (d) that applies throughout the stationary and nonstationary regions of d and which does not rely on tapering or differencing prefilters.
Journal ArticleDOI

Exact local Whittle estimation of fractional integration

Katsumi Shimotsu, +1 more
- 01 Aug 2005 - 
TL;DR: In this article, an exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter (d) that applies throughout the stationary and nonstationary regions of d and which does not rely on tapering or differencing prefilters.
Journal ArticleDOI

Exact local whittle estimation of fractional integration with unknown mean and time trend

Katsumi Shimotsu
- 01 Apr 2010 - 
TL;DR: In this article, the exact local Whittle (ELW) estimator has been extended to accommodate an unknown mean and a polynomial time trend, and the two-step ELW estimator, which is based on a modified ELW objective function using a tapered local Whew estimator in the first stage, has an asymptotic distribution for (or when the data have a poynomial trend).
References
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Journal ArticleDOI

Handbook of Mathematical Functions

Milton Abramowitz, +2 more
- 01 Feb 1966 - 
Book

Convergence of Probability Measures

Patrick Billingsley
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.

Handbook of Mathematical Functions

Milton Abramowitz, +1 more
Journal ArticleDOI

Fractional Brownian Motions, Fractional Noises and Applications

Benoit B. Mandelbrot, +1 more
- 01 Oct 1968 - 
Journal ArticleDOI

Convergence of Probability Measures

J. F. C. Kingman
- 01 Nov 1969 - 
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.