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Rissanen's Theorem and Econometric Time Series

In a typical empirical modeling context, the data generating process (DGP) of a time series is assumed to be known up to a finite-dimensional parameter. In such cases, Rissanen's (1986) theorem provides a lower bound for the empirically achievable distance between all possible data-based models and the true DGP. This distance depends only on the dimension of the parameter space. The present paper examines the empirical relevance of this notion to econometric time series and discusses a new version of the theorem that allows for nonstationary DGP's. Nonstationarity is relevant in many economic applications and it is shown that the form of nonstationarity affects, and indeed increases, the empirically achievable distance to the true DGP.

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File URL: http://cowles.econ.yale.edu/P/cd/d11b/d1197.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1197.

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Length: 14 pages
Date of creation: Oct 1998
Date of revision:
Publication status: Published in Arnold Zellner, Hugo A. Keuzenkamp and Michael McAleer, eds., Simplicity, Inference and Modelling, Cambridge University Press, 2001, pp. 165-180
Handle: RePEc:cwl:cwldpp:1197
Note: CFP 1037.
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  1. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  3. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  4. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
  5. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  6. repec:cup:etheor:v:10:y:1994:i:3-4:p:774-808 is not listed on IDEAS
  7. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
  8. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  9. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  10. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
  11. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  12. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
  13. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
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