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Estimation Of Autocovariance Matrices For Infinite Dimensional Vector Linear Process

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  • Monika Bhattacharjee
  • Arup Bose

Abstract

type="main" xml:id="jtsa12063-abs-0001"> Consider an infinite dimensional vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite-dimensional vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large dimensional variance–covariance matrix has the same convergence rate as that in case of i.i.d. samples.

Suggested Citation

  • Monika Bhattacharjee & Arup Bose, 2014. "Estimation Of Autocovariance Matrices For Infinite Dimensional Vector Linear Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 262-281, May.
    • Handle: RePEc:bla:jtsera:v:35:y:2014:i:3:p:262-281
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    File URL: http://hdl.handle.net/10.1111/jtsa.12063
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    References listed on IDEAS

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    1. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April.
    2. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    3. Chudik, Alexander & Pesaran, M. Hashem, 2011. "Infinite-dimensional VARs and factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 4-22, July.
    4. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
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    1. Bose, Arup & Hachem, Walid, 2020. "Smallest singular value and limit eigenvalue distribution of a class of non-Hermitian random matrices with statistical application," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    2. Zhang, Qihu & Chung, Jongik & Park, Cheolwoo, 2025. "Joint estimation of precision matrices for long-memory time series," Computational Statistics & Data Analysis, Elsevier, vol. 212(C).
    3. Monika Bhattacharjee & Nilanjan Chakraborty & Hira L. Koul, 2023. "Weighted l1‐Penalized Corrected Quantile Regression for High‐Dimensional Temporally Dependent Measurement Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(5-6), pages 442-473, September.

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