Moment estimation for a class of moving averages driven by Brownian motions

HE Wei-ping; ZHANG Shi-bin

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HE Wei-ping, ZHANG Shi-bin. Moment estimation for a class of moving averages driven by Brownian motions[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 18-25.

Citation:

HE Wei-ping, ZHANG Shi-bin. Moment estimation for a class of moving averages driven by Brownian motions[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 18-25.

HE Wei-ping, ZHANG Shi-bin. Moment estimation for a class of moving averages driven by Brownian motions[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 18-25.

Citation:

HE Wei-ping, ZHANG Shi-bin. Moment estimation for a class of moving averages driven by Brownian motions[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 18-25.

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Moment estimation for a class of moving averages driven by Brownian motions

HE Wei-ping¹,
ZHANG Shi-bin²

1.
Department of Mathematics, Inner Mongolia University, Hohhot} 010021, China;
2.
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China

Received Date: 2013-09-01
Rev Recd Date: 2013-12-01
Publish Date: 2014-07-25

Abstract

Abstract

This paper was concerned with moment estimation for a class of moving averages driven by Brownian motions, whose autocorrelation functions take on both periodic and regressive properties. Based on investigation of the relationship between the parameter and auto-covariance function, the moment estimator of the parameter was constructed. By analyzing the spectral density of the discretely sampled trajectory, the properties of the mixing coefficient were captured. Further, the consistency and asymptotic normality of the estimator were proved. A simulation study showed that the estimator achieves good performance even in the small-sample circumstances. The real data analysis evidences that the model can be used to depict the ship hull stress data.
- moving average,
- consistency,
- asymptotic normality,
- spectral density,
- \alpha-mixing

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References(1)

References

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