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Regression with Nonstationary Volatility

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Author Info
Hansen, Bruce E

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Abstract

A new asymptotic theory of regression is introduced for possibly nonstationary time series. The regressors are assumed to be generated by a linear process with martingale difference innovations. The conditional variances of these martingale differences are specified as autoregressive stochastic volatility processes with autoregressive roots that are local to unity. The author finds conditions under which the least squares estimates are consistent and asymptotically normal. A simple adaptive estimator is proposed which achieves the same asymptotic distribution as the generalized least squares estimator without requiring parameter assumptions for the stochastic volatility process. Copyright 1995 by The Econometric Society.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 63 (1995)
Issue (Month): 5 (September)
Pages: 1113-32
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Handle: RePEc:ecm:emetrp:v:63:y:1995:i:5:p:1113-32

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  1. Paulo M. M. Rodrigues & Antonio Rubia, 2004. "On the Small Sample Properties of Dickey Fuller and Maximum Likelihood Unit Root Tests on Discrete-Sampled Short-Term Interest Rates," Econometrics 0405004, EconWPA. [Downloadable!]
    Other versions:
  2. Joon Y. Park, 2000. "Nonstationary Nonlinear Heteroskedasticity: An Alternative to ARCH," CIRJE F-Series CIRJE-F-86, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  3. Boswijk, H.P., 2000. "Testing for a Unit Root with Near-Integrated Volatility," CeNDEF Working Papers 00-09, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    Other versions:
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Econometric Analysis of Realised Covariation: High Frequency Covariance, Regression and Correlation in Financial Economics," Economics Papers 2002-W13, Economics Group, Nuffield College, University of Oxford, revised 18 Mar 2002. [Downloadable!]
    Other versions:
  5. Brendan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Papers 2008-W06, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  6. Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2008. "Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility," CREATES Research Papers 2008-50, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  7. Ke-Li Xu & Peter C.B. Phillips, 2006. "Adaptive Estimation of Autoregressive Models with Time-Varying Variances," Cowles Foundation Discussion Papers 1585R, Cowles Foundation, Yale University, revised Nov 2006. [Downloadable!]
    Other versions:
  8. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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