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Challenges of Trending Time Series Econometrics

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Abstract

We discuss some challenges presented by trending data in time series econometrics. To the empirical economist there is little guidance from theory about the source of trend behavior and even less guidance about practical formulations. Moreover, recent proximity theorems reveal that trends are more elusive to model empirically than stationary processes, with the upshot that optimal forecasts are also harder to estimate when the data involve trends. These limitations are implicitly acknowledged in much practical modeling and forecasting work, where adaptive methods are often used to help keep models on track as trends evolve. The paper discusses these broader issues and limitations of econometrics and o.ers some thoughts on new practical possibilities for data analysis in the absence of good theory models for trends. In particular, a new concept of coordinate cointegration is introduced and some new econometric methodology is suggested for analyzing trends and comovement and for producing forecasts in a general way that is agnostic about the specific nature of the trend process. Some simulation exercises are conducted and some long historical series on prices and yields on long securities are used to illustrate the methods.

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File URL: http://cowles.econ.yale.edu/P/cd/d14b/d1472.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1472.

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Length: 20 pages
Date of creation: Jul 2004
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Publication status: Published in Mathematics and Computers in Simulation (2005), 68: 401-416
Handle: RePEc:cwl:cwldpp:1472

Note: CFP 1151.
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Keywords: Coordinate instrumental variables; coordinate reduced rank regression; coordinate trend functions; limitations of econometrics; nonstationarity; trend;

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  1. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  2. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
  3. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  4. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824.
  5. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  6. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
  7. Dean Corbae & Sam Ouliaris & Peter C.B. Phillips, 1997. "Band Spectral Regression with Trending Data," Cowles Foundation Discussion Papers 1163, Cowles Foundation for Research in Economics, Yale University.
  8. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation for Research in Economics, Yale University, revised Sep 2003.
  9. Peter C.B. Phillips & Werner Ploberger, 1999. "Empirical Limits for Time Series Econometric Models," Cowles Foundation Discussion Papers 1220, Cowles Foundation for Research in Economics, Yale University.
  10. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  11. Peter C.B. Phillips, 1998. "New Unit Root Asymptotics in the Presence of Deterministic Trends," Cowles Foundation Discussion Papers 1196, Cowles Foundation for Research in Economics, Yale University.
  12. Tsay, Wen-Jen & Chung, Ching-Fan, 2000. "The spurious regression of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 155-182, May.
  13. Shiller, Robert J & Siegel, Jeremy J, 1977. "The Gibson Paradox and Historical Movements in Real Interest Rates," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 891-907, October.
  14. Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
  15. Peter C.B. Phillips, 2003. "Laws and Limits of Econometrics," Cowles Foundation Discussion Papers 1397, Cowles Foundation for Research in Economics, Yale University.
  16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  17. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Cowles Foundation Discussion Papers 1367, Cowles Foundation for Research in Economics, Yale University, revised Jul 2004.
  18. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  19. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
  20. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
  21. 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.
  22. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
  23. Bai, Jushan, 1998. "A Note On Spurious Break," Econometric Theory, Cambridge University Press, vol. 14(05), pages 663-669, October.
  24. Marmol, Francesc, 1996. "Nonsense Regressions between Integrated Processes of Different Orders," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 525-36, August.
  25. repec:cup:etheor:v:11:y:1995:i:4:p:736-49 is not listed on IDEAS
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