The law of the iterated logarithm for self-similar processes represented by multiple wiener integrals

Mōri, Toshio; Oodaira, Hiroshi

doi:10.1007/bf01000212

Cited by 28 publications

(42 citation statements)

References 22 publications

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“…Our ®rst result generalizes previous consistency results for I(0) data, such as those of Bai (1994) and Nunes et al (1995).…”

Section: Resultssupporting

confidence: 90%

“…Consequently, for I(d) data with 0 , d , 0X5, the least-squares estimator for ô 0 would suggest a spurious change point between zero and one, even when there is no change. Our result indicates that stationary data (with long memory) may still result in a spurious change, in contrast with the result of Nunes et al (1995). This spurious-change phenomenon is apparently due to strong positive serial correlations of data.…”

Section: Resultsmentioning

confidence: 63%

“…It also includes Theorem 3.1(b) of Nunes et al (1995) as a special case. For 0 , d , 0X5, the law of the iterated logarithm (4) now ensures that…”

Section: Resultsmentioning

confidence: 99%

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Change‐Point Estimation of Fractionally Integrated Processes

Kuan

Hsu

1998

Journal Time Series Analysis

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In this paper we analyze the least-squares estimator of the change point for fractionally integrated processes with fractionally differencing parameter À0X5 , d , 0X5. When there is a one-time change, we show that the least-squares estimator is consistent and that the rate of convergence depends on d. When there is no change, we ®nd that the least-squares estimator converges in probability to the set f0, 1g for À0X5 , d < 0 but is likely to suggest a spurious change for 0 , d , 0X5. Simulations are also used to illustrate the asymptotic analysis.

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“…Our ®rst result generalizes previous consistency results for I(0) data, such as those of Bai (1994) and Nunes et al (1995).…”

Section: Resultssupporting

confidence: 90%

Section: Resultsmentioning

confidence: 63%

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Change‐Point Estimation of Fractionally Integrated Processes

Kuan

Hsu

1998

Journal Time Series Analysis

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“…The technique utilizes the pathwise representation of multiple subfractional integrals as multiple Wiener-Itoˆintegral via an operator of fractional type (Proposition 3.1) and a maximal inequality for multiple Stratonovich integral process driven by the Brownian motion as obtained in [18].…”

Section: Introductionmentioning

confidence: 99%

Multiple sub-fractional integrals and some approximations

Tudor

2008

Applicable Analysis

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We study multiple fractional integrals with respect to the even fractional Brownian motion (also called sub-fractional Brownian motion). The multiple integrals are introduced by using a representation formula for the even fractional Brownian motion as a Wiener integral with respect to a Brownian motion defined on the same probability space and a transfer principle. Then, Riemann-Stieltjes integral approximations to multiple Stratonovich fractional integrals are also considered. For two standard approximations (Wong-Zakai and mollifier approximations) and continuous integrands, the mean square convergence in the uniform norm of these approximations to the multiple Stratonovich sub-fractional integral is shown.

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“…In [6] a functional law of the iterated logarithm has been proved for a class of selfsimilar processes X with stationary increments, which are represented in the form ~(t) = S...S Qt (ul,..., u,,)cle (ul)...cm (u,,), t > O, (1.1) Rm where the right-hand side is an m-pie Wiener integral with respect to standard Brownian motion {B(u), u E R}. The purpose of this paper is to extend the above result in [6] to a certain class of processes converging weakly to the processes X of the form (1.1) with appropriate normalization.…”

Section: Introductionmentioning

confidence: 99%

The functional iterated logarithm law for stochastic processes represented by multiple Wiener integrals

Mōri

Oodaira

1987

Probab. Th. Rel. Fields

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In a previous paper the authors obtained a functional law of the iterated logarithm for a class of self-similar processes X with stationary increments, which are represented by multiple Wiener integrals. This result is extended to a certain class of processes represented by multiple Wiener integrals which converge to X with an appropriate normalization. As an application a functional log log law for nonlinear functionals of some stationary Gaussian processes is given.

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The law of the iterated logarithm for self-similar processes represented by multiple wiener integrals

Cited by 28 publications

References 22 publications

Change‐Point Estimation of Fractionally Integrated Processes

Change‐Point Estimation of Fractionally Integrated Processes

Multiple sub-fractional integrals and some approximations

The functional iterated logarithm law for stochastic processes represented by multiple Wiener integrals

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