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Band Spectral Regression with Trending Data

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Author Info
Dean Corbae (University of Iowa)
Sam Ouliaris (National University of Singapore)
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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Abstract

Band spectral regression with deterministic and stochastic trends is considered. It is shown that conventional trend removal by regression in the time domain prior to band spectral regression leads to biased and inconsistent estimates of the parameters in a model with frequency dependent coefficients. Time domain and frequency domain procedures for dealing with this problem are examined. Trend removal in the frequency domain produces unbiased estimates and is recommended. An asymptotic theory is developed and the two cases of stationary data and cointegrated nonstationary data are compared. Efficient band spectral regression estimators and associated inferential methods are provided for models with deterministic and stochastic trends. Some supporting Monte Carlo evidence is presented. An empirical application to the present value model of stock prices is discussed. After removing trends in the frequency domain, we show that, while stock prices and dividends have significant coherence at low frequencies, transitory fluctuations in dividends (i.e., less than 3 years) do not have significant coherence with stock price movements.

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File URL: http://cowles.econ.yale.edu/P/cd/d11b/d1163.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1163.

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Length: 46 pages
Date of creation: Sep 1997
Date of revision:
Publication status: Published in Econometrica (May 2002), 70(3): 57-93
Handle: RePEc:cwl:cwldpp:1163

Note: CFDP 1039.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Band spectral regression; deterministic and stochastic trends; nonstationary time series; integrated process; present value model of stock prices;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  2. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation, Yale University. [Downloadable!]
  3. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Blackwell Publishing, vol. 57(1), pages 99-125, January. [Downloadable!] (restricted)
  4. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Peter C.B. Phillips, 2004. "Challenges of Trending Time Series Econometrics," Cowles Foundation Discussion Papers 1472, Cowles Foundation, Yale University. [Downloadable!]
  2. Paul Cashin, 2004. "Caribbean Business Cycles," IMF Working Papers 04/136, International Monetary Fund. [Downloadable!]
  3. Li Gan & Qinghua Zhang, 2005. "The Thick Market Effect on Local Unemployment Rate Fluctuations," NBER Working Papers 11248, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Andra C. Ghent & Michael T. Owyang, 2009. "Is housing the business cycle? evidence from U.S. cities," Working Papers 2009-007, Federal Reserve Bank of St. Louis. [Downloadable!]
  5. Charlotte S. Hansen & Bjorn E. Tuypens, 2004. "Long-Run Regressions: Theory and Application to US Asset Markets," Finance 0410018, EconWPA. [Downloadable!]
  6. Assenmacher-Wesche, Katrin & Gerlach, Stefan, 2006. "Money Growth, Output Gaps and Inflation at Low and High Frequency: Spectral Estimates for Switzerland," CEPR Discussion Papers 5723, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  7. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation, Yale University. [Downloadable!]
  8. Alfredo Baldini, 2005. "Fiscal Policy and Business Cycles in an Oil-Producing Economy: The Case of Venezuela," IMF Working Papers 05/237, International Monetary Fund. [Downloadable!]
  9. Paul Cashin & Sam Ouliaris, 2001. "Key Features of Australian Business Cycles," IMF Working Papers 01/171, International Monetary Fund. [Downloadable!]
    Other versions:
  10. Richard A. Ashley. & Randall J. Verbrugge, 2006. "Frequency Dependence in Regression Model Coefficients: An Alternative Approach for Modeling Nonlinear Dynamic Relationships in Time Series," Working Papers e06-7, Virginia Polytechnic Institute and State University, Department of Economics. [Downloadable!]
    Other versions:
  11. Erik Hjalmarsson, 2006. "New methods for inference in long-run predictive regressions," International Finance Discussion Papers 853, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  12. Ivanna Vladkova Hollar & Jeromin Zettelmeyer, 2008. "Fiscal Positions in Latin America:Have They Really Improved?," IMF Working Papers 08/137, International Monetary Fund. [Downloadable!]
  13. Zhijie Xiao & Peter C.B. Phillips, 1998. "Higher Order Approximations for Wald Statistics in Cointegrating Regressions," Cowles Foundation Discussion Papers 1192, Cowles Foundation, Yale University. [Downloadable!]
  14. Chambers, M.J. & McCrorie, J.R., 2004. "Frequency domain gaussian estimation of temporally aggregated cointegrated systems," Discussion Paper 40, Tilburg University, Center for Economic Research. [Downloadable!]
  15. Tommaso Proietti, 2007. "Band Spectral Estimation for Signal Extraction," CEIS Research Paper 104, Tor Vergata University, CEIS. [Downloadable!]
    Other versions:
  16. Peter C.B. Phillips, 2003. "Laws and Limits of Econometrics," Cowles Foundation Discussion Papers 1397, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  17. Mototsugu Shintani, 2000. "A Simple Cointegrating Rank Test Without Vector Autoregression," Working Papers 0044, Department of Economics, Vanderbilt University. [Downloadable!]
    Other versions:
  18. W. Kim, . "Nonparametric Kernel Estimation of Evolutionary Autoregressive Processes," Sonderforschungsbereich 373 2001-103, Humboldt Universitaet Berlin.
  19. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation, Yale University, revised Sep 2003. [Downloadable!]
  20. Peter C.B. Phillips, 1999. "Unit Root Log Periodogram Regression," Cowles Foundation Discussion Papers 1244, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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