Identifiability of regular and singular multivariate autoregressive models from mixed frequency data

Anderson, Brian D. O.; Deistler, Manfred; Felsenstein, Elisabeth; Funovits, Bernd; Zadrozny, Peter A.; Eichler, Michael; Chen, Weitian; Zamani, Mohsen

doi:10.1109/cdc.2012.6426713

Cited by 16 publications

(28 citation statements)

References 7 publications

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“…2.1.4), i.e., a set of (multivariate) polynomial zeros where in addition inequalities are imposed, and so we conclude that for generic parameter values identifiability is obtained. This case has been described in detail in Anderson et al (2012).…”

Section: Identifiability For Ar(1) Systemsmentioning

confidence: 95%

“…A proof of this theorem has been given in Anderson et al (2012) and a more elegant proof is presented in the appendix.…”

Section: G-identifiability Of System and Noise Parametersmentioning

confidence: 99%

“…In addition to the assumptions of Theorem 7 we assume (a) that the pair I n f 0 ··· 0 , A is observable, which is generic, see Anderson et al (2012), and (b) that the eigenvalues of A are distinct, which also is generic, as is easy to see, since the eigenvalues are the inverse of the zeros of det a(z).…”

Section: Remarkmentioning

confidence: 99%

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Multivariate Ar Systems and Mixed Frequency Data: G-Identifiability and Estimation

et al. 2015

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This paper is concerned with the problem of identifiability of the parameters of a high frequency multivariate autoregressive model from mixed frequency time series data. We demonstrate identifiability for generic parameter values using the population second moments of the observations. In addition we display a constructive algorithm for the parameter values and establish the continuity of the mapping attaching the high frequency parameters to these population second moments. These structural results are obtained using two alternative tools viz. extended Yule Walker equations and blocking of the output process. The cases of stock and flow variables, as well as of general linear transformations of high frequency data, are treated. Finally, we briefly discuss how our constructive identifiability results can be used for parameter estimation based on the sample second moments.The authors want to thank Hans Havlicek, Vienna University of Technology, and Benedikt Pötscher, University of Vienna, for valuable suggestions concerning the proof of Theorem 2. In addition we thank Peter Phillips, several anonymous referees and handling co-editors for valuable comments.

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Section: Identifiability For Ar(1) Systemsmentioning

confidence: 95%

“…A proof of this theorem has been given in Anderson et al (2012) and a more elegant proof is presented in the appendix.…”

Section: G-identifiability Of System and Noise Parametersmentioning

confidence: 99%

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Multivariate Ar Systems and Mixed Frequency Data: G-Identifiability and Estimation

et al. 2015

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“…monthly data only, the authors in [7] have shown when the generalized dynamic factor model is zero-free then the latent variables can be modeled as a singular autoregressive process whose parameters can be easily identified using Yule-Walker equations. These results were subsequently extended to multirate systems type-1 [1] and [13]. The authors in [13] have demonstrated that the blocked system associated with multirate systems type-1 has no finite nonzero zeros in a generic setting i.e.…”

Section: Introductionmentioning

confidence: 94%

On the properties of linear multirate systems with coprime output rates

Zamani

Bottegal²,

Anderson

2013

52nd IEEE Conference on Decision and Control

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This paper studies discrete-time linear systems with multirate outputs, assuming that two measured output streams are available at coprime rates. In the literature this type of system, which can be considered as periodic timevarying, is commonly studied in its blocked version, since the well-known techniques of analysis developed for linear timeinvariant systems can be used. In particular, we focus on some structural properties of the blocked systems and we prove that, under a generic setting i.e. for a generic choice of parameter matrices, the blocked systems are minimal when the underlying multirate system is defined using a minimal dimension system. Moreover, we focus on zeros of tall blocked systems i.e. blocked systems with more outputs than inputs. In particular, we study those cases where the associated system matrix attains fullcolumn rank. We exhibit situations where they generically have no finite nonzero zeros.

QC 20131216

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“…Chen and Zadrozny (1998) introduced XYW as an estimation method with sample covariances but did not prove, under certain conditions, that XYW is feasible (computationally implementable) or that XYW determines unique AR parameter outputs for true-population or consistent-sample covariance inputs. Anderson et al (2012) proved this for a general VAR model and a particular MFD case, but only for a "generic" set of parameters.…”

Section: Introductionmentioning

confidence: 94%

Extended Yule-Walker Identification of Varma Models with Single- or Mixed Frequency Data

Zadrozny

2015

SSRN Journal

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Chen and Zadrozny (1998) developed the linear extended Yule-Walker (XYW) method for determining the parameters of a vector autoregressive (VAR) model with available covariances of mixed-frequency observations on the variables of the model. If the parameters are determined uniquely for available population covariances, then, the VAR model is identified. The present paper extends the original XYW method to an extended XYW method for determining all ARMA parameters of a vector autoregressive moving-average (VARMA) model with available covariances of single-or mixed-frequency observations on the variables of the model. The paper proves that under conditions of stationarity, regularity, miniphaseness, controllability, observability, and diagonalizability on the parameters of the model, the parameters are determined uniquely with available population covariances of single-or mixed-frequency observations on the variables of the model, so that the VARMA model is identified with the single-or mixed-frequency covariances.

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Identifiability of regular and singular multivariate autoregressive models from mixed frequency data

Cited by 16 publications

References 7 publications

Multivariate Ar Systems and Mixed Frequency Data: G-Identifiability and Estimation

Multivariate Ar Systems and Mixed Frequency Data: G-Identifiability and Estimation

On the properties of linear multirate systems with coprime output rates

Extended Yule-Walker Identification of Varma Models with Single- or Mixed Frequency Data

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