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Band Spectral Regression with Trending Data

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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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Paper provided by Cowles Foundation for Research in Economics, 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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Keywords: Band spectral regression; deterministic and stochastic trends; nonstationary time series; integrated process; present value model of stock prices;

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  1. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation for Research in Economics, Yale University.
  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.
  5. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  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.
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