异方差回归与自回归模型

建立时间序列异方差回归和预测模型,将现行的误差项方差相同、均值为零的回归分析推广到误差项方差变化且均值不为零的情况,解决了实际中常见的异方差以及由于自变量不能充分解释因变量而引起的误差项均值不为零的问题。针对误差项相关且均值、方差都变化的情况,文中还进一步建立异方差回归-自回归模型,将误差项为传统平稳序列(均值和方差为常数)的回归-自回归模型推广到误差项为相关系数平稳序列(均值和方差变化)的情况,给出回归-CCAR(P)模型和回归-CCARMA(p,q)模型的参数估计方法,提出异方差回归-自回归预测模型。该模型能充分发挥回归和自回归各自的优点,对时问序列进行高精度的分析和预测,可广泛用于自动控制、结构响应分析、故障诊断以及经济和商业预测等。

HETEROSCEDASTIC MODEL OF REGRESSION AND AUTOREGRESSION

A heteroscedastic regression model of time series is established, which extends the traditional regression that is only suitable to homoscedasticity and zero mean error to the case of variance and mean changing with time. It can solve the heteroscedasticity and nonzero mean problems, which is the result that the independent variables can't explain the dependent variable adequately. For the error being correlated and its mean and variance changing with time, a heteroscedastic regression-autoregression model is presented. The parameter estimation of regression-CCAR(p) and regression-CCARMA(p, q)models is also established. It extends the traditional regression-autoregression model with the correlation function stationary error series to that with the correlation coefficient stationary error series. The method can combine regression with autoregression and promote the precision of analysis and forecast in automatic control, structure response analysis, fault diagnosis and economic forecast, etc.