REGRESSION WITH NONSTATIONARY VOLATILITY

A new asymptotic theory of regression is introduced for possibly nonst ationary 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 autoregres sive stochastic volatility processes, with autoregressive roots which are local to unity. We find conditions under which the least squares e stimates are consistent and asymptotically normal. A simple adaptive e stimator is proposed which achieves the same asymptotic distribution a s the generalized least squares estimator, without requiring parametri c assumptions for the stochastic volatility process.