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

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  • Peter A. Zadrozny

Abstract

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.

Suggested Citation

  • Peter A. Zadrozny, 2015. "Extended Yule-Walker Identification of Varma Models with Single- or Mixed- Frequency Data," Economic Working Papers 485, Bureau of Labor Statistics.
    • Handle: RePEc:bls:wpaper:485
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    File URL: https://www.bls.gov/osmr/research-papers/2015/pdf/ec150070.pdf
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    2. Zadrozny, Peter A., 2022. "Linear identification of linear rational-expectations models by exogenous variables reconciles Lucas and Sims," CFS Working Paper Series 682, Center for Financial Studies (CFS).
    3. Thornton, Michael A. & Chambers, Marcus J., 2017. "Continuous time ARMA processes: Discrete time representation and likelihood evaluation," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 48-65.
    4. Morris, Stephen D., 2017. "DSGE pileups," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 56-86.
    5. Deistler, Manfred & Koelbl, Lukas & Anderson, Brian D.O., 2017. "Non-identifiability of VMA and VARMA systems in the mixed frequency case," Econometrics and Statistics, Elsevier, vol. 4(C), pages 31-38.
    6. Celina Pestano-Gabino & Concepción González-Concepción & María Candelaria Gil-Fariña, 2024. "VARMA Models with Single- or Mixed-Frequency Data: New Conditions for Extended Yule–Walker Identification," Mathematics, MDPI, vol. 12(2), pages 1-15, January.
    7. Thomas B. Götz & Alain W. Hecq, 2019. "Granger Causality Testing in Mixed‐Frequency VARs with Possibly (Co)Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(6), pages 914-935, November.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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