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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!

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$\overline{XY}$ 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.

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  • $\begingroup$ Great answer, thank you. But I think you forgot to divide by n in the formula! $\endgroup$
    – DamiToma
    Nov 5, 2018 at 16:04

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