Confusion about ensembles and averages in autocorrelation matrices

1. What is ensemble autocorrelation?
2. How do you interpret an autocorrelation plot?
3. What does the autocorrelation function tell you?
4. What is autocorrelation matrix?

What is ensemble autocorrelation?

1 Mean and Autocorrelation Function. The mean of X(t) is a function of time called the ensemble average and is denoted by. (10.1) The autocorrelation function provides a measure of similarity between two observations of the random process X(t) at different points in time t and s.

How do you interpret an autocorrelation plot?

If autocorrelation values are close to 0, then values between consecutive observations are not correlated with one another. Inversely, autocorrelations values close to 1 or -1 indicate that there exists strong positive or negative correlations between consecutive observations, respectively.

What does the autocorrelation function tell you?

The autocorrelation function is a statistical representation used to analyze the degree of similarity between a time series and a lagged version of itself. This function allows the analyst to compare the current value of a data set to its past value.

What is autocorrelation matrix?

The autocorrelation matrix is a Hermitian matrix for complex random vectors and a symmetric matrix for real random vectors. The autocorrelation matrix is a positive semidefinite matrix, i.e. for a real random vector, and respectively. in case of a complex random vector.