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August 2016 Estimation of inverse autocovariance matrices for long memory processes
Ching-Kang Ing, Hai-Tang Chiou, Meihui Guo
Bernoulli 22(3): 1301-1330 (August 2016). DOI: 10.3150/14-BEJ692


This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this goal. The spectral norm consistency of the proposed estimate is established. We then extend this result to linear regression models with long-memory time series errors. In particular, we show that when the objective is to consistently estimate the inverse autocovariance matrix of the error process, the same approach still works well if the estimated (by least squares) errors are used in place of the unobservable ones. Applications of this result to estimating unknown parameters in the aforementioned regression model are also given. Finally, a simulation study is performed to illustrate our theoretical findings.


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Ching-Kang Ing. Hai-Tang Chiou. Meihui Guo. "Estimation of inverse autocovariance matrices for long memory processes." Bernoulli 22 (3) 1301 - 1330, August 2016.


Received: 1 December 2013; Revised: 1 November 2014; Published: August 2016
First available in Project Euclid: 16 March 2016

zbMATH: 06579698
MathSciNet: MR3474817
Digital Object Identifier: 10.3150/14-BEJ692

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability


Vol.22 • No. 3 • August 2016
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