Locally Stationary Multiplicative Volatility Modeling
研究了一个半参数乘法波动率模型，将非参数部分（含确定性时间趋势和随机回归变量）与参数GARCH成分结合，提出两步估计法并证明估计量的一致性和渐近正态性，模拟显示忽略随机回归变量会导致GARCH参数估计严重偏误。
In this article, we study a semiparametric multiplicative volatility model, which splits up into a nonparametric part and a parametric GARCH component. The nonparametric part is modeled as a product of a deterministic time trend component and of further components that depend on stochastic regressors. We propose a two-step procedure to estimate the model. To estimate the nonparametric components, we transform the model and apply a backfitting procedure. The GARCH parameters are estimated in a second step via quasi maximum likelihood. We show consistency and asymptotic normality of our estimators. Our results are obtained using mixing properties and local stationarity. We illustrate our method using financial data. Finally, a small simulation study illustrates a substantial bias in the GARCH parameter estimates when omitting the stochastic regressors.