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2020 Generalised cepstral models for the spectrum of vector time series
Maddalena Cavicchioli
Electron. J. Statist. 14(1): 605-631 (2020). DOI: 10.1214/19-EJS1672


The paper treats the modeling of stationary multivariate stochastic processes via a frequency domain model expressed in terms of cepstrum theory. The proposed model nests the vector exponential model of [20] as a special case, and extends the generalised cepstral model of [36] to the multivariate setting, answering a question raised by the last authors in their paper. Contemporarily, we extend the notion of generalised autocovariance function of [35] to vector time series. Then we derive explicit matrix formulas connecting generalised cepstral and autocovariance matrices of the process, and prove the consistency and asymptotic properties of the Whittle likelihood estimators of model parameters. Asymptotic theory for the special case of the vector exponential model is a significant addition to the paper of [20]. We also provide a mathematical machinery, based on matrix differentiation, and computational methods to derive our results, which differ significantly from those employed in the univariate case. The utility of the proposed model is illustrated through Monte Carlo simulation from a bivariate process characterized by a high dynamic range, and an empirical application on time varying minimum variance hedge ratios through the second moments of future and spot prices in the corn commodity market.


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Maddalena Cavicchioli. "Generalised cepstral models for the spectrum of vector time series." Electron. J. Statist. 14 (1) 605 - 631, 2020.


Received: 1 October 2019; Published: 2020
First available in Project Euclid: 28 January 2020

zbMATH: 07163268
MathSciNet: MR4056268
Digital Object Identifier: 10.1214/19-EJS1672

Primary: 62H12 , 62M10 , 62M15

Keywords: Box-Cox link , generalised spectrum models , spectral density matrix , spectral estimation , Stationary vector stochastic processes , Whittle likelihood , Wold coefficients


Vol.14 • No. 1 • 2020
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