4时间序列参数估计.doc

时间序列模型参数估计 理论基础 矩估计 AR模型 矩估计法参数估计的思路： 即从样本中依次求中rk然后求其对应的参数Φk值 方差： MA模型 对于MA模型采用矩估计是比较不精确的，所以这里不予讨论 ARMA（1，1） 矩估计法参数估计的思路： 方差： 最小二乘估计 AR模型 最小二乘参数估计的思路： 对于AR（P）而言也可以得到类似矩估计得到的方程，即最小二乘与矩估计得到的估计量相同。 MA模型 最小二乘参数估计的思路： ARMA模型 最小二乘参数估计的思路： 极大似然估计与无条件最小二乘估计 R中如何实现时间序列参数估计 对于AR模型 ar(x, aic = TRUE, order.max = NULL, method=c(yule-walker, burg, ols, mle, yw), na.action, series, ...) ar(ar1.s,order.max=1,AIC=F,method=yw)#即矩估计 Call: ar(x = ar1.s, order.max = 1, method = yw, AIC = F) Coefficients: 1 0.8314 Order selected 1 sigma^2 estimated as 1.382 ar(ar1.s,order.max=1,AIC=F,method=ols)#最小二乘估计 Call: ar(x = ar1.s, order.max = 1, method = ols, AIC = F) Coefficients: 1 0.857 Intercept: 0.02499 (0.1308) Order selected 1 sigma^2 estimated as 1.008 ar(ar1.s,order.max=1,AIC=F,method=mle)#极大似然估计 Call: ar(x = ar1.s, order.max = 1, method = mle, AIC = F) Coefficients: 1 0.8924 Order selected 1 sigma^2 estimated as 1.041 采用自编函数总结三个不同的估计值 Myar(ar2.s,order.max=3) 最小二乘估计 矩估计 极大似然估计 1 1.5137146 1.4694476 1.5061369 2 -0.8049905 -0.7646034 -0.7964453 arima(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA), xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL, init = NULL, method = c(CSS-ML, ML, CSS), n.cond, optim.control = list(), kappa = 1e+06, io = NULL, xtransf, transfer = NULL) order的三个参数分别代表AR，差分 MA的阶数 arima(arma11.s,order=c(1,0,1),method=CSS) Call: arima(x = arma11.s, order = c(1, 0, 1), method = CSS) Coefficients: ar1 ma1 intercept 0.5586 0.3669 0.3928 s.e. 0.1219 0.1564 0.3380 sigma^2 estimated as 1.199: part log likelihood = -150.98 arima(arma11.s,order=c(1,0,1),method=ML) Call: arima(x = arma11.s, order = c(1, 0, 1), method = ML) Coefficients: ar1 ma1 intercept 0.5647 0.3557 0.3216 s.e. 0.1205 0.1585 0.3358 sigma^2 estimated as 1.197: log likelihood = -15