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Cointegration Analysis with Mixed-Frequency Data

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Author Info
Byeongchan Seong ()
Sung K. Ahn ()
Peter A. Zadrozny ()

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Abstract

We develop a method for directly modeling cointegrated multivariate time series that are observed in mixed frequencies. We regard lower-frequency data as regularly (or irregularly) missing and treat them with higher-frequency data by adopting a state-space model. This utilizes the structure of multivariate data as well as the available sample information more fully than the methods of transformation to a single frequency, and enables us to estimate parameters including cointegrating vectors and the missing observations of low-frequency data and to construct forecasts for future values. For the maximum likelihood estimation of the parameters in the model, we use an expectation maximization algorithm based on the state-space representation of the error correction model. The statistical efficiency of the developed method is investigated through a Monte Carlo study. We apply the method to a mixed-frequency data set that consists of the quarterly real gross domestic product and the monthly consumer price index.

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Publisher Info
Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number CESifo Working Paper No. 1939.

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Date of creation: 2007
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Handle: RePEc:ces:ceswps:_1939

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Related research
Keywords: missing data; Kalman filter; expectation maximization algorithm; forecasting; error correction model; smoothing; maximum likelihood estimation;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Chow, Gregory C & Lin, An-loh, 1971. "Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series," The Review of Economics and Statistics, MIT Press, vol. 53(4), pages 372-75, November. [Downloadable!] (restricted)
  2. Granger, C. W. J. & Siklos, Pierre L., 1995. "Systematic sampling, temporal aggregation, seasonal adjustment, and cointegration theory and evidence," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 357-369. [Downloadable!] (restricted)
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  3. Roberto S. Mariano & Yasutomo Murasawa, 2003. "A new coincident index of business cycles based on monthly and quarterly series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 427-443. [Downloadable!]
  4. Liu, H & Hall, Stephen G, 2001. "Creating High-Frequency National Accounts with State-Space Modelling: A Monte Carlo Experiment," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(6), pages 441-49, September.
  5. Haug, Alfred A, 2002. " Temporal Aggregation and the Power of Cointegration Tests: A Monte Carlo Study," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(4), pages 399-412, September. [Downloadable!] (restricted)
  6. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  7. Nicolas A. Cuche & Martin K. Hess, 1999. "Estimating Monthly GDP In A General Kalman Filter Framework: Evidence From Switzerland," Working Papers 99.02, Swiss National Bank, Study Center Gerzensee. [Downloadable!]
  8. Bernanke, Ben S. & Gertler, Mark & Waston, Mark, 1997. "Systematic Monetary Policy and the Effects of Oil Price Shocks," Working Papers 97-25, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  9. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-36, January.
  10. Pons, Gabriel & Sans , Andreu, 2005. "Estimation Of Cointegrating Vectors With Time Series Measured At Different Periodicity," Econometric Theory, Cambridge University Press, vol. 21(04), pages 735-756, August. [Downloadable!]
  11. Stefan Mittnik & Peter Zadrozny, 2004. "Forecasting Quarterly German GDP at Monthly Intervals Using Monthly IFO Business Conditions Data," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  12. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
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