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Band Spectral Regression with Trending Data

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  • Dean Corbae

    ()
    (Dept. of Economics, University of Texas at Austin, U.S.A.)

  • Sam Ouliaris

    ()
    (School of Business, National University of Singapore and Research Dept., IMF, Washington DC, U.S.A.)

  • Peter C. B. Phillips

    ()
    (Cowles Foundation for Research in Economics, Yale University, U.S.A. and University of Auckland and University of York)

Abstract

Band spectral regression with both deterministic and stochastic trends is considered. It is shown that trend removal by regression in the time domain prior to band spectral regression can lead to biased and inconsistent estimates in models with frequency dependent coefficients. Both semiparametric and nonparametric regression formulations are considered, the latter including general systems of two-sided distributed lags such as those arising in lead and lag regressions. The bias problem arises through omitted variables and is avoided by careful specification of the regression equation. Trend removal in the frequency domain is shown to be a convenient option in practice. An asymptotic theory is developed and the two cases of stationary data and cointegrated nonstationary data are compared. In the latter case, a levels and differences regression formulation is shown to be useful in estimating the frequency response function at nonzero as well as zero frequencies. Copyright The Econometric Society 2002.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 70 (2002)
Issue (Month): 3 (May)
Pages: 1067-1109

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Handle: RePEc:ecm:emetrp:v:70:y:2002:i:3:p:1067-1109

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  1. 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.
  2. 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.
  3. 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.
  4. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
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