0
$\begingroup$

I'm trying to estimate the covariance of two time series using the formula Covariance

where X and Y are two time series.
I don't understand how to calculate the value of the first term: does that mean I have to calculate the mean of the means, or do I have to multiply the X serie by the Y serie, and then calculate the mean?
If so, how do you multiply two series?

Forgive me if I'm asking a silly question, I'm new to this subject and it is pretty confusing.
Thanks!

$\endgroup$
1
$\begingroup$

$\overline{XY}$ stands for the empirical mean of $XY$ where $XY$ is a random variable that equals the product of random variables $X$ and $Y$. That is, $$ \overline{XY}=\frac{1}{n}\sum_{i=1}^n x_i y_i $$ for a sample of size $n$ where $x_i$ is the $i$th observation of $X$ and $y_i$ is the $i$th observation of $Y$. Hence, you multiply the two vectors element by element, sum them up and divide by the number of elements in one vector.

$\endgroup$
  • $\begingroup$ Great answer, thank you. But I think you forgot to divide by n in the formula! $\endgroup$ – DamiToma Nov 5 '18 at 16:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.