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Identifier to cite or link to this item: https://hdl.handle.net/10086/19243

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Title
Distributions of Quadratic Functionals of the Fractional Brownian Motion Based on a Martingale Approximation
Creator
Creator Name
Tanaka, Katsuto Tanaka, Katsuto
田中, 勝人 田中, 勝人
Affiliation
Affiliation Name
Hitotsubashi University
Abstract (distribution restricted)
We discuss some computational problems associated with distributions of statistics arising from the fractional Brownian motion (fBm). In particular, we deal with (ratios of) its quadratic functionals. While it is easy in principle to deal with the standard Bm, the fBm is difficult to analyze because of its non-semimartingale nature. Here we suggest how to derive and compute the distributions of such functionals by using a martingale approximation. For this purpose we employ the Fredholm theory concerning the integral equations, illustrating how to compute the characteristic function via the Fredholm determinant. We also apply the present methodology to compute the fractional unit root distribution, and demonstrate some interesting moment properties.
Publisher
Graduate School of Economics, Hitotsubashi University
Issued Date
2011-06
Language
English(eng)
Resource Type
technical report
Version Type
VoR
Is Part OfRelation -
Related Title
Discussion papers ; No. 2011-06
Number of Pages
34
Appears in Collections
Discussion papers / Graduate School of Economics, Hitotsubashi University
URL
https://hdl.handle.net/10086/19243