TY  - JOUR
T1  - The Cepstral Model for Multivariate Time Series: The Vector Exponential Model
JF  - Statistica Sinica
Y1  - 2017
A1  - Holan, S.H.
A1  - McElroy, T.S.
A1  - Wu, G.
KW  - Autocovariance matrix
KW  - Bayesian estimation
KW  - Cepstral
KW  - Coherence
KW  - Spectral density matrix
KW  - stochastic search variable selection
KW  - Wold coefficients.
AB  - 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.
VL  - 27
UR  - http://www3.stat.sinica.edu.tw/statistica/J27N1/J27N12/J27N12.html
ER  - 

TY  - JOUR
T1  - Computation of the Autocovariances for Time Series with Multiple Long-Range Persistencies
JF  - Computational Statistics and Data Analysis
Y1  - 2016
A1  - McElroy, T.S.
A1  - Holan, S.H.
AB  - Gegenbauer processes allow for flexible and convenient modeling of time series data with multiple spectral peaks, where the qualitative description of these peaks is via the concept of cyclical long-range dependence. The Gegenbauer class is extensive, including ARFIMA, seasonal ARFIMA, and GARMA processes as special cases. Model estimation is challenging for Gegenbauer processes when multiple zeros and poles occur in the spectral density, because the autocovariance function is laborious to compute. The method of splitting–essentially computing autocovariances by convolving long memory and short memory dynamics–is only tractable when a single long memory pole exists. An additive decomposition of the spectrum into a sum of spectra is proposed, where each summand has a single singularity, so that a computationally efficient splitting method can be applied to each term and then aggregated. This approach differs from handling all the poles in the spectral density at once, via an analysis of truncation error. The proposed technique allows for fast estimation of time series with multiple long-range dependences, which is illustrated numerically and through several case-studies.
UR  - http://www.sciencedirect.com/science/article/pii/S0167947316300202
ER  - 

TY  - RPRT
T1  - The Cepstral Model for Multivariate Time Series: The Vector Exponential Model.
Y1  - 2014
A1  - Holan, S.H.
A1  - McElroy, T.S.
A1  - Wu, G.
AB  - <p><span>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.</span></p>
PB  - arXiv
UR  - http://arxiv.org/abs/1406.0801
ER  - 

TY  - CONF
T1  - Fast Estimation of Time Series with Multiple Long-Range Persistencies
T2  - ASA Proceedings of the Joint Statistical Meetings
Y1  - 2014
A1  - McElroy, T.S.
A1  - Holan, S.H.
JF  - ASA Proceedings of the Joint Statistical Meetings
PB  - American Statistical Association
CY  - Alexandria, VA
ER  - 

TY  - RPRT
T1  - Asymptotic Theory of Cepstral Random Fields
Y1  - 2012
A1  - McElroy, T.S.
A1  - Holan, S.H.
AB  - Asymptotic Theory of Cepstral Random Fields McElroy, T.S.; Holan, S.H. Random fields play a central role in the analysis of spatially correlated data and, as a result,have a significant impact on a broad array of scientific applications. Given the importance of this topic, there has been a substantial amount of research devoted to this area. However, the cepstral random field model remains largely underdeveloped outside the engineering literature. We provide a comprehensive treatment of the asymptotic theory for two-dimensional random field models. In particular, we provide recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the necessary autocovariance matrix. Additionally, we establish asymptotic consistency results for Bayesian, maximum likelihood, and quasi-maximum likelihood estimation of random field parameters and regression parameters. Further, in both the maximum and quasi-maximum likelihood frameworks, we derive the asymptotic distribution of our estimator. The theoretical results are presented generally and are of independent interest,pertaining to a wide class of random field models. The results for the cepstral model facilitate model-building: because the cepstral coefficients are unconstrained in practice, numerical optimization is greatly simplified, and we are always guaranteed a positive definite covariance matrix. We show that inference for individual coefficients is possible, and one can refine models in a disciplined manner. Finally, our results are illustrated through simulation and the analysis of straw yield data in an agricultural field experiment. http://arxiv.org/pdf/1112.1977.pdf
PB  - University of Missouri
UR  - http://hdl.handle.net/1813/34461
ER  -