Matlab:计算时间序列的相关性 [英] Matlab: Calculating Correlation of time series

问题描述

时间序列模型表示为

y(t) = 0.5 + 0.3y(t-1) + n(t)

其中

n(t) = 0.1*randn(500,1) for t=1,2,...,500

幻灯片包含相关性和协方差矩阵.相关公式为:E[y(t)*y(t)^T]，可以使用xcorr进行调用.我想知道如何不使用内置命令就可以为滞后版本E[y(t-1)*y(t-1)^T]计算单个相关矩阵，以便最终实现以下表达式

Slides contain the Correlation and covariance matrix. The formula for correlation is: E[y(t)*y(t)^T] which can be invoked by using xcorr. I would like to know how one can calculate the individual Correlation matrix for its lagged version E[y(t-1)*y(t-1)^T] without using the inbuilt commands so that I can finally implement the following expression

 trace([E[y(t-1)*y(t-1)']]^-1) 

更新

例如，让

y = randn(10,1);

for t = 1:10
disp(y(t));
end

Expectation_y =  sum(y(1:end))/10

同样，如何对滞后变量执行期望，然后实现公式=

Likewise, how do I perform expectation for lagged variables and then implement the formula =

 trace([E[y(t-1)*y(t-1)']]^-1)

推荐答案

我不确定我是否了解您问题的所有详细信息，但是如果您只想对信号的延迟版本进行操作，则可以做这样的事情...

I'm not sure that I understand all of the details of your question, but if you just want to operate on a delayed version of a signal, you can do something like this...

%xcorr with a 1-sample shifted version of itself
[c,lags]=xcorr(t(1:end-1),t(2:end));  

%xcorr with a 2-sample shifted version of itself
[c,lags]=xcorr(t(1:end-2),t(3:end));

%etc

如果xcorr不是您想要的操作，则可以使用这种索引方法来创建信号的时移版本，从而执行所需的任何操作.

If xcorr is not the operation that you want, you can do whatever operations you'd like with this indexing method of creating a time-shifted version of your signal.

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