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Log periodogram regression of two-dimensional intrinsic stationary random fields

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  • Yoshihiro Yajima
  • Yasumasa Matsuda

Abstract

We propose a new estimator for a semiparametric two-dimensional intrinsic stationary random model observed on a regular grid and derive its asymptotic properties. This random field is nonstationary and includes a fractional Brownian field, which is a Gaussian random field and is used to model many physical processes in space. First we calculate tapered bivariate discrete Fourier transforms and periodograms of data observed on a grid and next apply a log-periodogram regression, which is originally proposed to estimate a long-memory parameter of semiparametric models for time series data. We prove that for a nonstationary two-dimensional random field, the estimator is still consistent and has the limiting normal distribution as the sample size goes to infinity. We conduct a computational simulation to compare the performance of it with those of different estimators proposed by other authors.

Suggested Citation

  • Yoshihiro Yajima & Yasumasa Matsuda, 2018. "Log periodogram regression of two-dimensional intrinsic stationary random fields," DSSR Discussion Papers 85, Graduate School of Economics and Management, Tohoku University.
  • Handle: RePEc:toh:dssraa:85
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    File URL: http://hdl.handle.net/10097/00122644
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