IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_5884.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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, 2016. "Extended Yule-Walker Identification of Varma Models with Single- or Mixed-Frequency Data," CESifo Working Paper Series 5884, CESifo.
    • Handle: RePEc:ces:ceswps:_5884
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp5884.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Eric Ghysels & Arthur Sinko & Rossen Valkanov, 2007. "MIDAS Regressions: Further Results and New Directions," Econometric Reviews, Taylor & Francis Journals, vol. 26(1), pages 53-90.
    2. Hannan, E J, 1976. "The Identification and Parameterization of ARMAX and State Space Forms," Econometrica, Econometric Society, vol. 44(4), pages 713-723, July.
    3. Zadrozny, Peter A, 1997. "An Econometric Analysis of Polish Inflation Dynamics with Learning about Rational Expectations," Economic Change and Restructuring, Springer, vol. 30(2-3), pages 221-238.
    4. Peter A. Zadrozny, 1990. "Forecasting U.S. GNP at monthly intervals with an estimated bivariate time series model," Economic Review, Federal Reserve Bank of Atlanta, issue Nov, pages 2-15.
    5. Andrzej Kocięcki & Marcin Kolasa, 2018. "Global identification of linearized DSGE models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1243-1263, November.
    6. Ivana Komunjer & Serena Ng, 2011. "Dynamic Identification of Dynamic Stochastic General Equilibrium Models," Econometrica, Econometric Society, vol. 79(6), pages 1995-2032, November.
    7. Milton Friedman, 1962. "Introduction to "The Interpolation of Time Series by Related Series"," NBER Chapters, in: The Interpolation of Time Series by Related Series, pages 1-3, National Bureau of Economic Research, Inc.
    8. Hansen, Lars Peter & Sargent, Thomas J, 1983. "The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities," Econometrica, Econometric Society, vol. 51(2), pages 377-387, March.
    9. Bjørn Eraker & Ching Wai (Jeremy) Chiu & Andrew T. Foerster & Tae Bong Kim & Hernán D. Seoane, 2015. "Bayesian Mixed Frequency VARs," Journal of Financial Econometrics, Oxford University Press, vol. 13(3), pages 698-721.
    10. Milton Friedman, 1962. "The Interpolation of Time Series by Related Series," NBER Books, National Bureau of Economic Research, Inc, number frie62-1, March.
    11. Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
    12. Daniel M. Chin & Preston J. Miller, 1996. "Using monthly data to improve quarterly model forecasts," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 20(Spr), pages 16-33.
    13. Baoline Chen & Peter Zadrozny, 2013. "Further model-based estimates of US total manufacturing production capital and technology, 1949–2005," Journal of Productivity Analysis, Springer, vol. 39(1), pages 61-73, February.
    14. Zadrozny, Peter, 1988. "Gaussian Likelihood of Continuous-Time ARMAX Models When Data Are Stocks and Flows at Different Frequencies," Econometric Theory, Cambridge University Press, vol. 4(1), pages 108-124, April.
    15. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
    16. Zadrozny, Peter A., 1998. "An eigenvalue method of undetermined coefficients for solving linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1353-1373, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Peter A. Zadrozny, 2022. "Linear Identification of Linear Rational-Expectations Models by Exogenous Variables Reconciles Lucas and Sims," CESifo Working Paper Series 10078, CESifo.
    5. Morris, Stephen D., 2017. "DSGE pileups," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 56-86.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter A. Zadrozny, 2022. "Linear Identification of Linear Rational-Expectations Models by Exogenous Variables Reconciles Lucas and Sims," CESifo Working Paper Series 10078, CESifo.
    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. Claudia Foroni & Massimiliano Marcellino, 2013. "A survey of econometric methods for mixed-frequency data," Economics Working Papers ECO2013/02, European University Institute.
    4. Peter Fuleky & Carl S. Bonham, 2013. "Forecasting with Mixed Frequency Samples: The Case of Common Trends," Working Papers 201316, University of Hawaii at Manoa, Department of Economics.
    5. Eric Ghysels & J. Isaac Miller, 2015. "Testing for Cointegration with Temporally Aggregated and Mixed-Frequency Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 797-816, November.
    6. Paccagnini, Alessia, 2017. "Dealing with Misspecification in DSGE Models: A Survey," MPRA Paper 82914, University Library of Munich, Germany.
    7. Qian, Hang, 2013. "Vector Autoregression with Mixed Frequency Data," MPRA Paper 47856, University Library of Munich, Germany.
    8. Foroni, Claudia & Guérin, Pierre & Marcellino, Massimiliano, 2015. "Markov-switching mixed-frequency VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 692-711.
    9. Bjørn Eraker & Ching Wai (Jeremy) Chiu & Andrew T. Foerster & Tae Bong Kim & Hernán D. Seoane, 2015. "Bayesian Mixed Frequency VARs," Journal of Financial Econometrics, Oxford University Press, vol. 13(3), pages 698-721.
    10. Peter Fuleky & Carl Bonham, 2010. "Forecasting Based on Common Trends in Mixed Frequency Samples," Working Papers 2010-17R1, University of Hawaii Economic Research Organization, University of Hawaii at Manoa, revised Jul 2013.
    11. Peter Zadrozny, 1997. "An Econometric Analysis of Polish Inflation Dynamics with Learning about Rational Expectations," Economic Change and Restructuring, Springer, vol. 30(2), pages 221-238, May.
    12. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.
    13. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.
    14. Qian, Hang, 2016. "A computationally efficient method for vector autoregression with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 433-437.
    15. Vicky Fasen-Hartmann & Celeste Mayer, 2022. "Whittle estimation for continuous-time stationary state space models with finite second moments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 233-270, April.
    16. Ghysels, Eric & Hill, Jonathan B. & Motegi, Kaiji, 2016. "Testing for Granger causality with mixed frequency data," Journal of Econometrics, Elsevier, vol. 192(1), pages 207-230.
    17. Ivashchenko, Sergey & Mutschler, Willi, 2020. "The effect of observables, functional specifications, model features and shocks on identification in linearized DSGE models," Economic Modelling, Elsevier, vol. 88(C), pages 280-292.
    18. Qian, Hang, 2012. "Essays on statistical inference with imperfectly observed data," ISU General Staff Papers 201201010800003618, Iowa State University, Department of Economics.
    19. Schumacher, Christian & Breitung, Jörg, 2008. "Real-time forecasting of German GDP based on a large factor model with monthly and quarterly data," International Journal of Forecasting, Elsevier, vol. 24(3), pages 386-398.
    20. Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report 75, Federal Reserve Bank of Minneapolis.

    More about this item

    Keywords

    block-Vandermonde eigenvectors of block-companion state-transition matrix of state-space representation; matrix spectral factorization;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ces:ceswps:_5884. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.