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Temporal Aggregation and Ordinary Least Squares Estimation of Cointegrating Regressions

  • Gabriel Pons Rotger

    (University of Barcelona)

The paper derives the asymptotic distribution of the ordinary least squares estimator of cointegrating vectors with temporally aggregated time series. It is shown, that temporal aggregation reduces the bias and variance of the estimator for average sampling (temporal aggregation of flow series) and does not affect the limiting distribution for systematic sampling (temporal aggregation of stock series). A Monte Carlo experiment shows the consistency of the finite sample results with the asymptotic theory.

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File URL: http://fmwww.bc.edu/RePEc/es2000/1317.pdf
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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1317.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1317
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  1. Pierre Perron & Robert J. Shiller, 1984. "Testing the Random Walk Hypothesis: Power Versus Frequency of Observation," Cowles Foundation Discussion Papers 732, Cowles Foundation for Research in Economics, Yale University.
  2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  3. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
  4. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  5. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
  6. Granger, C.W.J. & Siklos, P.L., 1993. "Systematic Sampling, Temporal Aggregation, Seasonal Adjustment, and Cointegration: Theory and Evidence," Working Papers 93001, Wilfrid Laurier University, Department of Economics.
  7. Engle, R.F. & Yoo, B.S., 1989. "Cointegrated Economic Time Series: A Survey With New Results," Papers 8-89-13, Pennsylvania State - Department of Economics.
  8. Peter C.B. Phillips, 1988. "Error Correction and Long Run Equilibrium in Continuous Time," Cowles Foundation Discussion Papers 882R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  9. Gregory, A.W. & Hansen, B.E., 1992. "Residual-Based Tests for Cointegration in Models with Regime Shifts," RCER Working Papers 335, University of Rochester - Center for Economic Research (RCER).
  10. repec:cup:etheor:v:7:y:1991:i:3:p:341-68 is not listed on IDEAS
  11. Brewer, K. R. W., 1973. "Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models," Journal of Econometrics, Elsevier, vol. 1(2), pages 133-154, June.
  12. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  13. Clive W. J. Granger, 1988. "Aggregation of time series variables-a survey," Discussion Paper / Institute for Empirical Macroeconomics 1, Federal Reserve Bank of Minneapolis.
  14. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
  15. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-77, August.
  16. 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.
  17. Gonzalo, Jesus & Pitarakis, Jean-Yves, 1998. "On the Exact Moments of Asymptotic Distributions in an Unstable AR(1) with Dependent Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(1), pages 71-88, February.
  18. 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.
  19. Abadir, Karim & Paruolo, P., 1994. "The Marginal Density of Bivariate Cointegration Estimators," Discussion Papers 9405, Exeter University, Department of Economics.
  20. Perron, Pierre, 1991. "Test Consistency with Varying Sampling Frequency," Econometric Theory, Cambridge University Press, vol. 7(03), pages 341-368, September.
  21. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
  22. repec:ner:tilbur:urn:nbn:nl:ui:12-153273 is not listed on IDEAS
  23. Gonzalo, Jesus, 1994. "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233.
  24. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  25. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
  26. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
  27. Perron,P., 1988. "Testing For A Random Walk: A Simulation Experiment Of Power When The Simpling Interval Is Varied," Papers 336, Princeton, Department of Economics - Econometric Research Program.
  28. 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.
  29. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  30. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  31. Lahiri, Kajal & Mamingi, Nlandu, 1995. "Testing for cointegration: Power versus frequency of observation -- another view," Economics Letters, Elsevier, vol. 49(2), pages 121-124, August.
  32. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  33. In Choi & Bhum Suk Chung, 1995. "Sampling frequency and the power of tests for a unit root: A simulation study," Economics Letters, Elsevier, vol. 49(2), pages 131-136, August.
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