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Frequency domain gaussian estimation of temporally aggregated cointegrated systems

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Author Info
Chambers, M.J.
McCrorie, J.R. (Tilburg University, Center for Economic Research)

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Abstract

This paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time. The model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows. We derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form, which acts as the basis for frequency domain Gaussian estimation of the unknown parameters using discrete time data. We formally establish the order of consistency and the asymptotic sampling properties of such an estimator. The function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution, while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution.

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Publisher Info
Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 40.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:200440

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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  1. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Blackwell Publishing, vol. 53(4), pages 473-95, August. [Downloadable!] (restricted)
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  2. Lawrence J. Christiano & Martin S. Eichenbaum, 1986. "Temporal Aggregation and Structural Inference in Macroeconomics," NBER Technical Working Papers 0060, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Chambers, Marcus J., 2003. "The Asymptotic Efficiency Of Cointegration Estimators Under Temporal Aggregation," Econometric Theory, Cambridge University Press, vol. 19(01), pages 49-77, February. [Downloadable!]
  6. Stock], James H., 1987. "Temporal aggregation and structural inference in macroeconomics a comment," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 26(1), pages 131-139, January. [Downloadable!] (restricted)
  7. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November. [Downloadable!] (restricted)
  8. Saikkonen, Pentti, 2001. "Statistical Inference In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 17(02), pages 327-356, April. [Downloadable!]
  9. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May. [Downloadable!] (restricted)
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  10. Pesaran,H.M. & Shin,Y., 1995. "Long-Run Structural Modelling," Cambridge Working Papers in Economics 9419, Faculty of Economics, University of Cambridge.
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  11. 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 377-87, March. [Downloadable!] (restricted)
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  12. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
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  13. Saikkonen, Pentti, 1995. "Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 11(05), pages 888-911, October. [Downloadable!]
  14. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation, Yale University. [Downloadable!]
  15. Peter C.B. Phillips, 1988. "Error Correction and Long Run Equilibrium in Continuous Time," Cowles Foundation Discussion Papers 882R, Cowles Foundation, Yale University, revised Jul 1989. [Downloadable!]
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  16. repec:cup:etheor:v:11:y:1995:i:5:p:888-911 is not listed on IDEAS
  17. Chambers, Marcus J., 1998. "The estimation of systems of joint differential-difference equations," Journal of Econometrics, Elsevier, vol. 85(1), pages 1-31, July. [Downloadable!] (restricted)
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