Log periodogram regression of two-dimensional intrinsic stationary random fields

Yoshihiro Yajima and Yasumasa Matsuda

No 85, DSSR Discussion Papers from Graduate School of Economics and Management, Tohoku University

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.

Pages: 21 pages
Date: 2018-05
New Economics Papers: this item is included in nep-ecm and nep-ets
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Persistent link: https://EconPapers.repec.org/RePEc:toh:dssraa:85

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