An Extended Yule-Walker Method for Estimating a Vector Autoregressive Model With Mixed-Frequencey Data

Chen, Baoline; Zadrozny, Peter A.

doi:10.1108/s0731-9053(1999)0000013005

Cited by 25 publications

(27 citation statements)

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“…The techniques we use in the paper draw heavily from Chen and Zadrozny (1998) and Zamani (2012) and the approach given for blocking is related to Ghysels (2012). The paper is organized as follows: In Section 2 the setting and the problem are described.…”

Section: Introductionmentioning

confidence: 99%

“…Given the frequent occurrence of MF data and the desire to use as much as possible or indeed all the information contained in these data, it is not surprising that a number of different approaches to MF problems such as parameter estimation have been developed (see e.g. Harvey and Pierse, 1984;Nijman, 1985;Kohn and Ansley, 1986;Zadrozny, 1990b;Bernanke, Gertler, Watson, Sims, and Friedman, 1997;Chen and Zadrozny, 1998;Marcellino, 1998;Mariano and Murasawa, 2003;Aruoba, Diebold, and Scotti, 2007;Wohlrabe, 2008;Ghysels and Wright, 2009;Marcellino and Schumacher, 2010;Ghysels, 2012). These approaches differ as far as their final aims, the model classes considered and the estimation procedures developed are concerned.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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“…Although the paper is not directly concerned with parameter estimation, the extended XYW method becomes a consistent method for estimating VARMA parameters simply by replacing population covariances with consistent sample covariances. However, experience with the XYW method (Chen and Zadrozny, 1998) suggests that such a consistent estimation method is unlikely to be accurate in small samples but that a generalized method of moments (GMM) extension of the method could be accurate in small samples. However, a GMM extension of the extended XYW method is beyond the scope of this paper and is left for the future.…”

Section: Introductionmentioning

confidence: 99%

“…If the covariance inputs are true population covariances and the outputs are unique, then, the outputs are the true model parameters and the VAR model is identified; if the covariance inputs are consistent sample estimates and the outputs are unique, then, the outputs are consistent parameter estimates. 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: 99%

“…In response, Chen and Zadrozny (1998) developed the linear extended Yule-Walker (XYW) method for determining the parameters of a VAR model, which uses available covariances of MFD and has the computational simplicity of least squares, and illustrated XYW's accuracy relative to MLE. The XYW method overcomes the computational problem of not being able to evaluate standard Yule-Walker equations because autocovariances at high-frequency lags of variables observed at low frequencies are unavailable.…”

Section: Introductionmentioning

confidence: 99%

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Extended Yule–Walker identification of VARMA models with single- or mixed-frequency data

Zadrozny

2016

Journal of Econometrics

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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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Forecasting Quarterly German GDP at Monthly Intervals Using Monthly Ifo Business Conditions Data

Mittnik

Zadrozny

Ifo Survey Data in Business Cycle and Monetary Policy Analysis

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. The paper illustrates and evaluates a Kalman filtering method for forecasting German real GDP at monthly intervals. German real GDP is produced at quarterly intervals but analysts and decision makers often want monthly GDP forecasts. Quarterly GDP could be regressed on monthly indicators, which would pick up monthly feedbacks from the indicators to GDP, but would not pick up implicit monthly feedbacks from GDP onto itself or the indicators. An efficient forecasting model which aims to incorporate all significant correlations in monthlyquarterly data should include all significant monthly feedbacks. We do this with estimated VAR(2) models of quarterly GDP and up to three monthly indicator variables, estimated using a Kalman-filtering-based maximum-likelihood estimation method. Following the method, we estimate monthly and quarterly VAR(2) models of quarterly GDP, monthly industrial production, and monthly, current and expected, business conditions. The business conditions variables are produced by the Ifo Institute from its own surveys. We use early insample data to estimate models and later out-of-sample data to produce and evaluate forecasts. The monthly maximum-likelihood-estimated models produce monthly GDP forecasts. The Kalman filter is used to compute the likelihood in estimation and to produce forecasts. Generally, the monthly German GDP forecasts from 3 to 24 months ahead are competitive with quarterly German GDP forecasts for the same time-span ahead, produced using the same method and the same data in purely quarterly form. However, the present mixed-frequency method produces monthly GDP forecasts for the first two months of a quarter ahead which are more accurate than one-quarter-ahead GDP forecasts based on the purely-quarterly data. Moreover, quarterly models based on purely-quarterly data generally cannot be transformed into monthly models which produce equally accurate intra-quarterly monthly forecasts. Terms of use: Documents inJEL classification: E37, C32.

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An Extended Yule-Walker Method for Estimating a Vector Autoregressive Model With Mixed-Frequencey Data

Cited by 25 publications

References 9 publications

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

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

Extended Yule–Walker identification of VARMA models with single- or mixed-frequency data

Forecasting Quarterly German GDP at Monthly Intervals Using Monthly Ifo Business Conditions Data

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