Autocorrelation and variance

1. How do you find the variance of autocorrelation?
2. What is the difference between autocorrelation and autocovariance?
3. What is the difference between covariance and autocovariance?
4. What does autocorrelation tell you?

How do you find the variance of autocorrelation?

Definition 1: The autocorrelation function (ACF) at lag k, denoted ρ_k, of a stationary stochastic process, is defined as ρ_k = γ_k/γ₀ where γ_k = cov(y_i, y_i+k) for any i. Note that γ₀ is the variance of the stochastic process. The variance of the time series is s₀. A plot of r_k against k is known as a correlogram.

What is the difference between autocorrelation and autocovariance?

Autocorrelation is the cross-correlation of a signal with itself, and autocovariance is the cross-covariance of a signal with itself.

What is the difference between covariance and autocovariance?

Covariance is defined for a pair of random variables defined on the same probability space. Autocovariance is defined for a pair of values in a discrete-time stochastic process.

What does autocorrelation tell you?

Autocorrelation represents the degree of similarity between a given time series and a lagged version of itself over successive time intervals. Autocorrelation measures the relationship between a variable's current value and its past values.