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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.

Suggested Citation

  • Werner Ploberger & Peter C.B. Phillips, 1998. "Rissanen's Theorem and Econometric Time Series," Cowles Foundation Discussion Papers 1197, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1197
    Note: CFP 1037.

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    References listed on IDEAS

    1. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-469, December.
    2. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
    3. 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.
    4. 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 1057-1072, June.
    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. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. 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.
    8. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
    9. 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.
    10. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    11. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    12. repec:cup:etheor:v:10:y:1994:i:3-4:p:774-808 is not listed on IDEAS
    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.
    14. 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.
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    Cited by:

    1. Patrick Marsh, "undated". "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, Springer;Society for Computational Economics, vol. 25(3), pages 207-228, June.

    More about this item


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

    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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