自回归滑动平均建模中观测噪声方差估计的新方法

A new measurement noise estimation method for autoregressive and moving average modeling

中文关键词  自回归滑动平均  自回归  有色噪声  白噪声  时间序列

英文关键词  autoregressive and moving average  autoregressive  colored noise  white noise  time series

中文摘要

      目前的自回归滑动平均(ARMA)建模方法由于只利用了观测数据的高阶自协方差构建Yule–Walker方程, 而没有利用观测数据的低阶自协方差信息, 导致观测噪声方差的估计精度不高, 并且在自回归(AR)阶次p小于或等于滑动平均(MA)阶次q时无法估计出观测噪声方差. 为此, 本文提出了一种单独估计观测噪声方差的新方法, 即先将ARMA模型近似为一高阶AR模型, 再构建从观测数据1阶自协方差开始的Yule–Walker方程. 由于充分利用了观测数据的统计信息, 有利于提高观测噪声方差的估计精度, 为后续的AR和MA参数估计精度的提高奠定了基础, 也解决了p小于或等于q时观测噪声方差无法估计的问题, 仿真和实验结果验证了该方法的有效性.

英文摘要

      In the existing autoregressive and moving average (ARMA) modeling methods, only the higher-order measurement autocovariances are used to form the Yule-Walker equations, so that the estimation accuracy of measurement noise variance deteriorates due to the unemployment of low-order measurement autocovariances. Moreover, if the AR order p is not greater than the MA order q, the measurement noise variance cannot be estimated in the existing methods. To deal with this problem, we propose a method for estimating the measurement noise variance independently. In this method, the ARMA model is first approximated by a higher-order AR model; then, the Yule–Walker equations of measurement autocovariances are formed with orders starting from one. Because of the full use of statistical information, the estimation accuracy of the measurement noise variance is improved. This not only lays the foundation for improving the accuracy in estimating AR and MA parameters, but also solves the problem occurred when the AR order p is not greater than the MA order q. Simulation and experiment results validated the effectiveness of the method.