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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
Date of revision:
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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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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References

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  1. 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.
  2. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824, October.
  3. Peter C.B. Phillips, 2003. "Laws and Limits of Econometrics," Cowles Foundation Discussion Papers 1397, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  6. 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.
  7. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  8. Werner Ploberger & Peter C. B. Phillips, 2003. "Empirical Limits for Time Series Econometric Models," Econometrica, Econometric Society, vol. 71(2), pages 627-673, March.
  9. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  10. 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.
  11. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  12. Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc.
  13. 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.
  14. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
  15. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics.
  16. Phillips, Peter C. B., 2002. "New unit root asymptotics in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 111(2), pages 323-353, December.
  17. 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.
  18. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
  19. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  20. 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.
  21. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
  22. 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.
  23. repec:cup:etheor:v:11:y:1995:i:4:p:736-49 is not listed on IDEAS
  24. Bai, Jushan, 1998. "A Note On Spurious Break," Econometric Theory, Cambridge University Press, vol. 14(05), pages 663-669, October.
  25. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
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Citations

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Cited by:
  1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
  2. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1466-1497, December.
  3. Peter C.B. Phillips & Donggyu Sul, 2005. "Economic Transition and Growth," Cowles Foundation Discussion Papers 1514, Cowles Foundation for Research in Economics, Yale University.
  4. Katsumi Shimotsu & Alex Maynard, 2004. "Covariance-based orthogonality tests for regressors with unknown persistence," Econometric Society 2004 North American Summer Meetings 536, Econometric Society.
  5. Peter C. B. Phillips & Donggyu Sul, 2007. "Transition Modeling and Econometric Convergence Tests," Econometrica, Econometric Society, vol. 75(6), pages 1771-1855, November.
  6. David Greasley & Les Oxley, 2010. "Cliometrics And Time Series Econometrics: Some Theory And Applications," Journal of Economic Surveys, Wiley Blackwell, vol. 24(5), pages 970-1042, December.
  7. Yonghui Zhang & Liangjun Su & Peter C.B. Phillips, 2011. "Testing for Common Trends in Semiparametric Panel Data Models with Fixed Effects," Cowles Foundation Discussion Papers 1832, Cowles Foundation for Research in Economics, Yale University.
  8. Guillaume Chevillon, 2004. "`Weak` trends for inference and forecasting in finite samples," Economics Series Working Papers 210, University of Oxford, Department of Economics.
  9. Ulrich Fritsche & Vladimir Kuzin, 2008. "Analysing Convergence in Europe Using a Non-linear Single Factor Model," Macroeconomics and Finance Series 200802, Hamburg University, Department Wirtschaft und Politik.
  10. Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
  11. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2012. "Unit roots, nonlinearities and structural breaks," CREATES Research Papers 2012-14, School of Economics and Management, University of Aarhus.
  12. repec:rdg:wpaper:em-dp2013-03 is not listed on IDEAS
  13. Ulrich Fritsche & Vladimir Kuzin, 2011. "Analysing convergence in Europe using the non-linear single factor model," Empirical Economics, Springer, vol. 41(2), pages 343-369, October.
  14. David O'Toole, 2009. "Exchange Rate Forecasts and Stochastic Trend Breaks," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 7.

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