I want to check if a time series is (a) random (b) independent. For these I am using the autocorrelation (AC). Autocorrelation refers to the correlation of a time series with its own past and future values.
If random variables are independent then there should be no correlation between them. The reverse is not true.
I have two different vectors as observations obtained from sensor measurement that are a sequence of samples and I treat this as a time series -denoted by variables
Question 1: I cannot interpret the graph, what the spike indicates. Please help
Question 2: For time series generated from linear system in order to check for randomness, what is the test to perform and what is the value to expect??
Question 3: For time series obtained from linear system in order to check for independence between samples, what test to perform and what is the value to expect?
Question 4: The given time series is obtained from nonlinear dynamical system that is chaotic. If correlation test is not valid, then what tests should I perform to check for (a) randomness (b) independence?