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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.

Suggested Citation

  • Peter C.B. Phillips, 2004. "Challenges of Trending Time Series Econometrics," Cowles Foundation Discussion Papers 1472, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1472
    Note: CFP 1151.
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    1. 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 525-536, August.
    2. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May.
    3. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
    4. repec:bla:restud:v:57:y:1990:i:1:p:99-125 is not listed on IDEAS
    5. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    6. 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.
    7. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
    8. 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.
    9. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    10. 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.
    11. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    12. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    13. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    14. Francesc Marmol, 1995. "SPURIOUS REGRESSIONS BETWEEN I(d) PROCESSES," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(3), pages 313-321, May.
    15. repec:cup:etheor:v:11:y:1995:i:4:p:736-49 is not listed on IDEAS
    16. Shimotsu, Katsumi & Phillips, Peter C B, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 8838, University of Essex, Department of Economics.
    17. Werner Ploberger & Peter C. B. Phillips, 2003. "Empirical Limits for Time Series Econometric Models," Econometrica, Econometric Society, vol. 71(2), pages 627-673, March.
    18. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
    19. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    20. 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.
    21. Bai, Jushan, 1998. "A Note On Spurious Break," Econometric Theory, Cambridge University Press, vol. 14(05), pages 663-669, October.
    22. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    23. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    24. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    25. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
    26. 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.
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    Cited by:

    1. 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, january-d.
    2. 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.
    3. Gonzalo, Jesús & Gadea Rivas, María Dolores, 2017. "Trends in distributional characteristics : Existence of global warming," UC3M Working papers. Economics 24121, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Guillaume Chevillon, 2004. "`Weak` trends for inference and forecasting in finite samples," Economics Series Working Papers 210, University of Oxford, Department of Economics.
    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. 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.
    7. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
    8. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    9. Maynard, Alex & Shimotsu, Katsumi, 2009. "Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence," Econometric Theory, Cambridge University Press, vol. 25(01), pages 63-116, February.
    10. T. C. Mills & K. D. Patterson, 2015. "Modelling The Trend: The Historical Origins Of Some Modern Methods And Ideas," Journal of Economic Surveys, Wiley Blackwell, vol. 29(3), pages 527-548, July.
    11. Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
    12. repec:rdg:wpaper:em-dp2013-03 is not listed on IDEAS
    13. Yonghui Zhang & Liangjun Su & Peter C. B. Phillips, 2012. "Testing for common trends in semi‐parametric panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 56-100, February.
    14. Ulrich Fritsche & Vladimir Kuzin, 2008. "Analysing Convergence in Europe Using a Non-linear Single Factor Model," Macroeconomics and Finance Series 200802, University of Hamburg, Department of Socioeconomics.
    15. Terence Mills & Kerry Patterson, 2013. "Modelling the Trend: The Historical Origins of Some Modern Methods and Ideas," Economics & Management Discussion Papers em-dp2013-03, Henley Business School, Reading University.
    16. Peter C. B. Phillips & Donggyu Sul, 2009. "Economic transition and growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1153-1185.
    17. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60 Edward Elgar Publishing.
    18. Akinfenwa, Samson O. & Qasmi, Bashir A., 2014. "Ethanol, the Agricultural Economy, and Rural Incomes in the United States: A Bivariate Econometric Approach," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 43(2), August.
    19. Qin, Duo, 2006. "Is China's growing service sector leading to cost disease?," Structural Change and Economic Dynamics, Elsevier, vol. 17(3), pages 267-287, September.
    20. White Halbert & Granger Clive W.J., 2011. "Consideration of Trends in Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-40, February.
    21. Jianning Kong & Peter C.B. Phillips & Donggyu Sul, 2017. "Weak s- Convergence: Theory and Applications," Cowles Foundation Discussion Papers 2072, Cowles Foundation for Research in Economics, Yale University.
    22. Akinfenwa, Samson O. & Qasmi, Bashir A., 0. "Ethanol, the Agricultural Economy, and Rural Incomes in the United States: A Bivariate Econometric Approach," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association.
    23. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1466-1497, December.

    More about this item

    Keywords

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

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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