补充下，我的意思是说，比较传统的方法是说将各个序列的平均收益率与波动率（协防差矩阵）求出来再优化，而我是讲这个协方差矩阵的对角线用预测得方差代替本来的历史波动率。。。  请问这样行不行

自己顶一个

你这就是历史模拟啊，因为你的GARCh模型就是通过历史数据分析得到的。你要对收益预测，那收益和方差应该有很多个不同的路径，蒙特卡洛模拟

的确，模型是通过历史数据得到的，我外推了一期做预测而但网上和书上的方法，直接是用历史数据的样本估计出方差，没有预测。。。。   这个是让我比较纠结的地方。 我想用预测的方差代替样本协防差矩阵的对角线，再优化得到最优组合。    我想想觉得可以这么做   
     

I think you are almost in the right way. What you need to do is not just replace the variance on the diagonal of cov matrix, but use multidimensional GARCH model to predict the whole covariance matrix. Such as BEKK model.

Portfolio optimization has nothing to do with historical data or forecasted data. If you have a return vector and a covariance matrix, the optimization can be done. So if you can predict the covariance matrix and return vector by multidimensional GARCH model, everything is done.

I recommend a paper by Woodridge. Perhaps it is not so close but it may be helpful. At least it gives some basic idea.

Hope Help~