Variance and Covariance

#1
My question could be very easy or not. Sorry about two quenstions my level of english an my ignorancy.

I want to now why when we estimate the relation between two stocastic processes we multiply both....why?

Another simple thing is why we elevate to the sqare to calculate the variance....it is clear that because if not positive numbers and negative will compensate.

And why to obtain the standard deviation whe do the square root.

The other thing is if you know some reference hard and easy and intuitive that explain perfectly how we caracterize a stocastic proces....trough the mean, variance, skewness, kurtosis, and so on....implications.

If you write me your email to writte you I will agree.

Thanks in advance.
 

mp83

TS Contributor
#2
Let {Xt,t} and {Yt,t} two s.p

A.
E[Xt*Yt]-E[Xt]E[Yt]=:Cov[Xt,Yt] and we usually assume E[Xt]=E[Yt]=0 so just multiplying do the work

B
As E[Xt]=E[Yt]=0 and Var[Xt]=E[Xt^2]-{E[Xt]^2}=E[Xt^2]

C.
sd[X]:=sqrt(Var[X]) # ":=" means "is defined as"

Any book on Stochastic Processes will do (eg. Stochastic Processes and Models by David Stirzaker)