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Common factors in conditional distributions for Bivariate time series

  • Timo Terasvirta
  • Clive W.J Granger
  • Andrew Patton


A definition for a common factor for bivariate time series is suggested by considering the decomposition of the conditional density into the product of the marginals and the copula,�with the conditioning variable being a common factor if it does not directly enter the copula.� The links of this definition with a common factor being a dominant feature in standard linear representations is shown. An application using a business cycle indicator as the common factor in the relationship between U.S. income and consumption found that both series held the factor� in their marginals but not in the copula.

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Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp455.

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Date of creation: Jun 2003
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Handle: RePEc:fmg:fmgdps:dp455
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  1. White,Halbert, 1994. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521252805, October.
  2. Issler, Joao Victor & Vahid, Farshid, 2001. "Common cycles and the importance of transitory shocks to macroeconomic aggregates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 449-475, June.
  3. Granger, C. W. J., 1987. "Implications of Aggregation with Common Factors," Econometric Theory, Cambridge University Press, vol. 3(02), pages 208-222, April.
  4. Patton, Andrew J, 2001. "Estimation of Copula Models for Time Series of Possibly Different Length," University of California at San Diego, Economics Working Paper Series qt3fc1c8hw, Department of Economics, UC San Diego.
  5. Wallis, Kenneth F., 2003. "Chi-squared tests of interval and density forecasts, and the Bank of England's fan charts," International Journal of Forecasting, Elsevier, vol. 19(2), pages 165-175.
  6. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
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