Regression with Nonstationary Volatility
提出了一种新的渐近理论，用于处理可能非平稳时间序列的回归问题，其中回归变量由鞅差创新线性过程生成，条件方差为自回归随机波动过程。研究给出了最小二乘估计一致且渐近正态的条件，并提出了无需参数假设的自适应估计量。
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.