Band Spectral Regression with Trending Data

Posted: 16 May 2002

See all articles by Philip Dean Corbae

Philip Dean Corbae

University of Wisconsin - Madison - Department of Finance, Investment and Banking

Sam Ouliaris

National University of Singapore (NUS) - Department of Economics

Peter C. B. Phillips

Yale University - Cowles Foundation; University of Auckland; University of Southampton; Singapore Management University - School of Economics

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.

Suggested Citation

Corbae, Philip Dean and Ouliaris, Sam and Phillips, Peter C. B., Band Spectral Regression with Trending Data. Available at SSRN: https://ssrn.com/abstract=312467

Philip Dean Corbae

University of Wisconsin - Madison - Department of Finance, Investment and Banking ( email )

975 University Avenue
Madison, WI 53706
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Sam Ouliaris

National University of Singapore (NUS) - Department of Economics ( email )

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Singapore 117570, Singapore 119077
Singapore

Peter C. B. Phillips (Contact Author)

Yale University - Cowles Foundation ( email )

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University of Auckland ( email )

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University of Southampton

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Singapore Management University - School of Economics

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Singapore

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