回归与时变自回归模型

提出回归-时变自回归（regression and time-varying autoregression，RTVAR）模型和广义回归-时变自回归（generized regression and time-varying autoregression，GRTVAR）模型，将误差项为平稳序列（均值和方差为常数）的回归-自回归模型推广到误差项为广义时变自回归序列（均值、方差及自回归系数都变化）的情况。文中给出RTVAR模型和GRTVAR模型参数的估计方法，并建立广义回归-时变自回归预测公式。该模型能充分发挥回归和时变自回归各自的特点，通过自回归对回归分析中的误差项进行补偿，同时采用回归分析解释变量的作用，大大提高时间序列的分析与预测精度，可广泛用于自动控制、故障诊断以及经济预测等领域。

METHOD OF REGRESSION AND TIME-VARYING AUTOREGRESSION

A regression and time-varying autoregression (RTVAR) model and a generalized regression and time-varying autoregression (GRTVAR) model are presented. They extend the regression and autoregression model with the covariance stationary error series to that with the generalized time-varying error series. The parameter estimation of RTVAR and GRTVAR models and the GRTVAR prediction formulas are also established. By combining regression and time-varying autoregression, the models can enhance the precision of analysis and forecast in automatic control, fault diagnosis, economic forecast and other fields.