Bruce E. Hansen

"Regression with non-stationary volatility", Econometrica, Vol. 63, No. 5. (Sep., 1995), pp. 1113-1132.


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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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.