In a stochastic process we have a mapping from a variable (time) to a random variable.
Time could be discrete, or continuous.
Temperature over time is a stochastic process, as is the number of cars sold each day.
The state space for temperature is continous, the number of people on the moon is discrete.
We can describe processes by their evolution.
\(p(x_t|x_{t-1}...)\)
\(AC(a,b)=cov(X_a, X_b)\)
The autocorrelation between two time periods is their covariance, normlised by their variances
\(AC(a,b)=\dfrac{E[(X_a-\mu_a)(X_b-\mu_b)]}{\sigma_a \sigma_b}\)
This is also called serial correlation.