The Statistical Theory of Linear Systems

Hannan, E. J.; Deistler, Manfred

doi:10.1137/1.9781611972191

Cited by 106 publications

(86 citation statements)

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“…As discussed in Brockwell and Davis (1991), and at more length in Hannan and Deistler (2012), a VARMA does not have this property. In practice, additional conditions on coefficients -that are quite subtle to enforce -must be levied in order to obtain a stable and invertible fit to data.…”

Section: The Vexp Processmentioning

confidence: 98%

The Cepstral Model for Multivariate Time Series: The Vector Exponential Model

Holan¹,

McElroy²,

Wu³

2017

STAT SINICA

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Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to work with a stable, or at least stationary, representation. To fit such models, one must impose restrictions on the coefficient matrices to ensure that certain determinants are nonzero; which, except in special cases, may prove burdensome. To circumvent these difficulties, we propose a flexible frequency domain model expressed in terms of the spectral density matrix. Specifically, this paper treats the modeling of covariance stationary vector-valued (i.e., multivariate) time series via an extension of the exponential model for the spectrum of a scalar time series. We discuss the modeling advantages of the vector exponential model and its computational facets, such as how to obtain Wold coefficients from given cepstral coefficients. Finally, we demonstrate the utility of our approach through simulation as well as two illustrative data examples focusing on multi-step ahead forecasting and estimation of squared coherence.

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Section: The Vexp Processmentioning

confidence: 98%

The Cepstral Model for Multivariate Time Series: The Vector Exponential Model

Holan¹,

McElroy²,

Wu³

2017

STAT SINICA

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“…Furthermore, while it would be possible to analyze some interesting properties of Hankel matrices given by [26] or [27] inter alia, there are some numerical algorithms, like [28], or [29] for polynomial regressions, that work with a Hankel matrix. That said, we are not interested in computing the exact inverse, but rather, using cases with k = 1, 2, 3, .…”

Section: B Proof Of Theoremmentioning

confidence: 99%

Polynomial Regressions and Nonsense Inference

Ventosa‐Santaulària

Rodríguez-Caballero

2013

Econometrics

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Polynomial specifications are widely used, not only in applied economics, but also in epidemiology, physics, political analysis and psychology, just to mention a few examples. In many cases, the data employed to estimate such specifications are time series that may exhibit stochastic nonstationary behavior. We extend Phillips' results (Phillips, P. Understanding spurious regressions in econometrics. J. Econom. 1986, 33, 311-340.) by proving that an inference drawn from polynomial specifications, under stochastic nonstationarity, is misleading unless the variables cointegrate. We use a generalized polynomial specification as a vehicle to study its asymptotic and finite-sample properties. Our results, therefore, lead to a call to be cautious whenever practitioners estimate polynomial regressions.

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“…E. J. Hannan and Deistler (1988) showed that, for linear ARMA processes and for ≤ (log n) α , α < ∞, the infinity norm ofΓ n, − Γ n is O n −1/2 √ log log n . Wu and Pourahmadi (2009) proved the consistency of (3) for the class of non-linear short-range dependent processes considered by Wu (2005), and obtained an explicit upper bound for the operator norm ofΓ n, −Γ n See Appendix A for a review of the different matrix norms.…”

Section: Introductionmentioning

confidence: 99%

A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices

Proietti

Giovannelli

2017

SSRN Journal

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We consider the problem of estimating the high-dimensional autocovariance matrix of a stationary random process, with the purpose of out of sample prediction and feature extraction. This problem has received several solutions. In the nonparametric framework, the literature has concentrated on banding and tapering the sample autocovariance matrix. This paper proposes and evaluates an alternative approach, based on regularizing the sample partial autocorrelation function, via a modified Durbin-Levinson algorithm that receives as input the banded and tapered partial autocorrelations and returns a sample autocovariance sequence which is positive definite. We show that the regularized estimator of the autocovariance matrix is consistent and its convergence rates is established. We then focus on constructing the optimal linear predictor and we assess its properties. The computational complexity of the estimator is of the order of the square of the banding parameter, which renders our method scalable for high-dimensional time series. The performance of the autocovariance estimator and the corresponding linear predictor is evaluated by simulation and empirical applications.

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The Statistical Theory of Linear Systems

Cited by 106 publications

References 0 publications

The Cepstral Model for Multivariate Time Series: The Vector Exponential Model

The Cepstral Model for Multivariate Time Series: The Vector Exponential Model

Polynomial Regressions and Nonsense Inference

A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices

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