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Journal Article

Regression with Nonstationary Volatility

Bruce E. Hansen
Econometrica
Vol. 63, No. 5 (Sep., 1995), pp. 1113-1132
Published by: The Econometric Society
DOI: 10.2307/2171723
Stable URL: http://www.jstor.org/stable/2171723
Page Count: 20
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Regression with Nonstationary Volatility
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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 which are local to unity. We find 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 parametric assumptions for the stochastic volatility process.

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