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Rissanen's Theorem and Econometric Time Series

Abstract

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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Keywords: Complexity; data generating process; Fisher information; model selection; optimal prediction; parsimony; trends;

Find related papers by JEL classification:

  • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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  1. 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.
  2. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
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  4. 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.
  5. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  6. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  7. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
  8. 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.
  9. repec:cup:etheor:v:10:y:1994:i:3-4:p:774-808 is not listed on IDEAS
  10. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  11. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
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  13. 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.
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Cited by:

  1. Patrick Marsh, . "The Available Information for Invariant Tests of a Unit Root," Discussion Papers 05/03, Department of Economics, University of York.
  2. Kelvin Balcombe, 2005. "Model Selection Using Information Criteria and Genetic Algorithms," Computational Economics, Society for Computational Economics, vol. 25(3), pages 207-228, June.

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