I am new to time series. I understand that the sample autocorrelation function (SACF), if Xt is white noise, then for large (n), the SACF is approximately normally distributed with zero mean and standard deviation 1/sqrt(n). For Yt = signal + white noise, if we make a model and subtract it from Yt. If the residuals are close to white noise by using 1/sqrt(n) hypothesis test, we can conclude that the model is good.
The confusing thing to me is this:
It works only if Xt and Yt are independent linear processes then the large sample distribution of sample cross correlation function has mean 0 and standard deviation 1/sqrt(n).
If we use these equations: There is strong seasonality.
The removal of signal from Yt:
Why does the cross correlation function of the residual of yt and Xt tell you that Xt and Yt are cross independence? Shouldn't Xt and Yt tell you directly?