Stochastic integral convergence: A white noise calculus approach

Chi Tim Ng; Ngai Hang Chan

doi:10.1214/15-EJS1070

Stochastic integral convergence: A white noise calculus approach

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

By virtue of long-memory time series, it is illustrated in this paper that white noise calculus can be used to handle subtle issues of stochastic integral convergence that often arise in the asymptotic theory of time series. A main difficulty of such an issue is that the limiting stochastic integral cannot be defined path-wise in general. As a result, continuous mapping theorem cannot be directly applied to deduce the convergence of stochastic integrals ∫¹₀ Hn(s) dZ_n(s) to ∫¹₀H(s) dZ(s) based on the convergence of (H_n, Z_n) to (H,Z) in distribution. The white noise calculus, in particular the technique of S-transform, allows one to establish the asymptotic results directly.

Original language	English
Pages (from-to)	2035-2057
Journal	Electronic Journal of Statistics
Volume	9
Issue number	2
DOIs	https://doi.org/10.1214/15-EJS1070
Publication status	Published - 29 Sept 2015
Externally published	Yes

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Convergence
Fractional dickey-fuller statistic
S-transform
Stochastic integral
White noise calculus

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title = "Stochastic integral convergence: A white noise calculus approach",

abstract = "By virtue of long-memory time series, it is illustrated in this paper that white noise calculus can be used to handle subtle issues of stochastic integral convergence that often arise in the asymptotic theory of time series. A main difficulty of such an issue is that the limiting stochastic integral cannot be defined path-wise in general. As a result, continuous mapping theorem cannot be directly applied to deduce the convergence of stochastic integrals ∫10 Hn(s) dZn(s) to ∫10H(s) dZ(s) based on the convergence of (Hn, Zn) to (H,Z) in distribution. The white noise calculus, in particular the technique of S-transform, allows one to establish the asymptotic results directly.",

keywords = "Convergence, Fractional dickey-fuller statistic, S-transform, Stochastic integral, White noise calculus",

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T1 - Stochastic integral convergence

T2 - A white noise calculus approach

AU - Ng, Chi Tim

AU - Chan, Ngai Hang

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2015/9/29

Y1 - 2015/9/29

N2 - By virtue of long-memory time series, it is illustrated in this paper that white noise calculus can be used to handle subtle issues of stochastic integral convergence that often arise in the asymptotic theory of time series. A main difficulty of such an issue is that the limiting stochastic integral cannot be defined path-wise in general. As a result, continuous mapping theorem cannot be directly applied to deduce the convergence of stochastic integrals ∫10 Hn(s) dZn(s) to ∫10H(s) dZ(s) based on the convergence of (Hn, Zn) to (H,Z) in distribution. The white noise calculus, in particular the technique of S-transform, allows one to establish the asymptotic results directly.

AB - By virtue of long-memory time series, it is illustrated in this paper that white noise calculus can be used to handle subtle issues of stochastic integral convergence that often arise in the asymptotic theory of time series. A main difficulty of such an issue is that the limiting stochastic integral cannot be defined path-wise in general. As a result, continuous mapping theorem cannot be directly applied to deduce the convergence of stochastic integrals ∫10 Hn(s) dZn(s) to ∫10H(s) dZ(s) based on the convergence of (Hn, Zn) to (H,Z) in distribution. The white noise calculus, in particular the technique of S-transform, allows one to establish the asymptotic results directly.

KW - Convergence

KW - Fractional dickey-fuller statistic

KW - S-transform

KW - Stochastic integral

KW - White noise calculus

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DO - 10.1214/15-EJS1070

M3 - RGC 21 - Publication in refereed journal

SN - 1935-7524

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SP - 2035

EP - 2057

JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

IS - 2

ER -

Stochastic integral convergence: A white noise calculus approach

Abstract

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Research Keywords

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