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

2015/07/10 by Akihiko Inoue, Inoue, Akihiko, Yukio Kasahara +3
Economics, Econometrics and Finance · Mathematics · #60M10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary 60G25 #Probability (math.PR) #Random Matrices and Applications #Secondary 62M20 #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1507.02848

openalex publication_date 2015/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 the 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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