Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (4): 18-25.

• Article • Previous Articles     Next Articles

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

HE Wei-ping1, ZHANG Shi-bin2   

  1. 1. Department of Mathematics, Inner Mongolia University, Hohhot} 010021, China; 2. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
  • Received:2013-09-01 Revised:2013-12-01 Online:2014-07-25 Published:2014-07-25

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.

Key words: moving average, consistency, asymptotic normality, spectral density, \alpha-mixing

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