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Vector autoregression with varied frequency data

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  • Qian, Hang

Abstract

The Vector Autoregression (VAR) model has been extensively applied in macroeconomics. A typical VAR requires its component variables being sampled at a uniformed frequency, regardless of the fact that some macro data are available monthly and some are only quarterly. Practitioners invariably align variables to the same frequency either by aggregation or imputation, regardless of information loss or noises gain. We study a VAR model with varied frequency data in a Bayesian context. Lower frequency (aggregated) data are essentially a linear combination of higher frequency (disaggregated) data. The observed aggregated data impose linear constraints on the autocorrelation structure of the latent disaggregated data. The perception of a constrained multivariate normal distribution is crucial to our Gibbs sampler. Furthermore, the Markov property of the VAR series enables a block Gibbs sampler, which performs faster for evenly aggregated data. Lastly, our approach is applied to two classic structural VAR analyses, one with long-run and the other with short-run identification constraints. These applications demonstrate that it is both feasible and sensible to use data of different frequencies in a new VAR model, the one that keeps the branding of the economic ideas underlying the structural VAR model but only makes minimum modification from a technical perspective.

Suggested Citation

  • Qian, Hang, 2010. "Vector autoregression with varied frequency data," MPRA Paper 34682, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:34682
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    References listed on IDEAS

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    1. Michael P. Clements & Ana Beatriz Galvao, 2009. "Forecasting US output growth using leading indicators: an appraisal using MIDAS models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1187-1206.
    2. 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.
    3. Sims, Christopher A., 1992. "Interpreting the macroeconomic time series facts : The effects of monetary policy," European Economic Review, Elsevier, vol. 36(5), pages 975-1000, June.
    4. Andreou, Elena & Ghysels, Eric & Kourtellos, Andros, 2010. "Regression models with mixed sampling frequencies," Journal of Econometrics, Elsevier, vol. 158(2), pages 246-261, October.
    5. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    6. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    7. Clements, Michael P & Galvão, Ana Beatriz, 2008. "Macroeconomic Forecasting With Mixed-Frequency Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 546-554.
    8. Michael P. Clements & Ana Beatriz Galvão, 2007. "Macroeconomic Forecasting with Mixed Frequency Data: Forecasting US Output Growth," Working Papers 616, Queen Mary University of London, School of Economics and Finance.
    9. 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.
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    Cited by:

    1. Franco, Ray John Gabriel & Mapa, Dennis S., 2014. "The Dynamics of Inflation and GDP Growth: A Mixed Frequency Model Approach," MPRA Paper 55858, University Library of Munich, Germany.
    2. Trujillo-Barrera, Andres & Pennings, Joost M.E., 2013. "Energy and Food Commodity Prices Linkage: An Examination with Mixed-Frequency Data," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150465, Agricultural and Applied Economics Association.

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    More about this item

    Keywords

    Vector Autoregression; Bayesian; Temporal aggregation;
    All these keywords.

    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
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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