• Bernoulli
  • Volume 24, Number 2 (2018), 1202-1232.

Baxter’s inequality for finite predictor coefficients of multivariate long-memory stationary processes

Akihiko Inoue, Yukio Kasahara, and Mohsen Pourahmadi

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For a multivariate stationary process, we develop explicit representations for the finite predictor coefficient matrices, the finite prediction error covariance matrices and the partial autocorrelation function (PACF) in terms of the Fourier coefficients of its phase function in the spectral domain. The derivation is based on a novel alternating projection technique and the use of the forward and backward innovations corresponding to predictions based on the infinite past and future, respectively. We show that such representations are ideal for studying the rates of convergence of the finite predictor coefficients, prediction error covariances, and the PACF as well as for proving a multivariate version of Baxter’s inequality for a multivariate FARIMA process with a common fractional differencing order for all components of the process.

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Bernoulli, Volume 24, Number 2 (2018), 1202-1232.

Received: January 2016
Revised: May 2016
First available in Project Euclid: 21 September 2017

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Baxter’s inequality long memory multivariate stationary processes partial autocorrelation functions phase functions predictor coefficients


Inoue, Akihiko; Kasahara, Yukio; Pourahmadi, Mohsen. Baxter’s inequality for finite predictor coefficients of multivariate long-memory stationary processes. Bernoulli 24 (2018), no. 2, 1202--1232. doi:10.3150/16-BEJ897.

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