Can someone help me understand the difference between a 1-dim autocorrelation function and a 2-dim autocorrelation matrix of a random process aka time series?
My Leon-Garcia textbook defines CX(τ) and RX(τ) as 1-dim functions, yet Haykin's Adaptive Filter Theory defines what looks like the same thing, but as the correlation matrix R instead. I see that the matrix appears to arise when the time series is represented by complex numbers (sinusoids), but is that the only real difference, or is there a fundamental distinction that I'm missing?
And does the correlation matrix R reduce to the 1-dim autocorrelation function when the time series can be represented by only real numbers instead of complex numbers, i.e. in that case the correlation matrix is unnecessary?