Prove that a specific auto-correlation function is even

1. Is the autocorrelation function even?
2. How do you prove autocorrelation?
3. Is auto correlation symmetric?
4. What does the autocorrelation function tell you?

Is the autocorrelation function even?

1 Properties of the Auto-correlation Function (1) The autocorrelation functions φff (τ) and ρff (τ) are even functions, that is φff (−τ) = φff (τ), and ρff (−τ) = ρff (τ).

How do you prove autocorrelation?

Testing for Autocorrelation

The most common method of test autocorrelation is the Durbin-Watson test. Without getting too technical, the Durbin-Watson is a statistic that detects autocorrelation from a regression analysis. The Durbin-Watson always produces a test number range from 0 to 4.

Is auto correlation symmetric?

The autocorrelation is the cross correlation of a signal with itself. Unlike the cross correlation between two different signals, the autocorrelation is always symmetric about zero (i.e. equal at lags +τ and −τ).

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.