An Autoregressive Spectral Density Estimator At Frequency Zero For Nonstationarity Tests

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An Autoregressive Spectral Density Estimator At Frequency Zero For Nonstationarity Tests

Author Info

Perron, Pierre
Ng, Serena

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Abstract

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero of some process. Commonly used are kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. In this paper, we first show that this least-squares bias induces a significant increase in the bias and mean-squared error (MSE) of kernel-based estimators. We then consider a variant of the autoregressive spectral density estimator that does not share these shortcomings because it bypasses the use of the estimate from the AR(1) regression. Simulations and local asymptotic analyses show its bias and MSE to be much smaller than those of a kernel-based estimator when there is strong negative serial correlation. We also include a discussion about the appropriate choice of the truncation lag.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 14 (1998)
Issue (Month): 05 (October)
Pages: 560-603
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Handle: RePEc:cup:etheor:v:14:y:1998:i:05:p:560-603_14

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Paper
- Perron, P. & Ng, S., 1996. "An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests," Cahiers de recherche 9611, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Perron, P. & Ng, S., 1996. "An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests," Cahiers de recherche 9611, Universite de Montreal, Departement de sciences economiques. [Downloadable!]

Cited by:
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Niels Haldrup & Peter Lildholdt, . "Local Power Functions of Tests for Double Unit Roots," Economics Working Papers 2000-2, School of Economics and Management, University of Aarhus. [Downloadable!]
Other versions:
- Niels Haldrup & Peter Lildholdt, 2000. "Local Power Functions of Tests for Double Unit Roots," University of California at San Diego, Economics Working Paper Series 2000-12, Department of Economics, UC San Diego. [Downloadable!]
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Other versions:
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van Binh T. & Dumont M., 2008. "A Fishing Expedition in the Mekong Delta: Market Volatility and Price Substitutes for Vietnamese Fresh Water Fish," Working Papers 2008002, University of Antwerp, Faculty of Applied Economics. [Downloadable!]

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