Open Access
May 2018 Baxter’s inequality for finite predictor coefficients of multivariate long-memory stationary processes
Akihiko Inoue, Yukio Kasahara, Mohsen Pourahmadi
Bernoulli 24(2): 1202-1232 (May 2018). DOI: 10.3150/16-BEJ897


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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Akihiko Inoue. Yukio Kasahara. Mohsen Pourahmadi. "Baxter’s inequality for finite predictor coefficients of multivariate long-memory stationary processes." Bernoulli 24 (2) 1202 - 1232, May 2018.


Received: 1 January 2016; Revised: 1 May 2016; Published: May 2018
First available in Project Euclid: 21 September 2017

zbMATH: 06778363
MathSciNet: MR3706792
Digital Object Identifier: 10.3150/16-BEJ897

Keywords: Baxter’s inequality , long memory , multivariate stationary processes , partial autocorrelation functions , phase functions , Predictor coefficients

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 2 • May 2018
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