Statistical measurements

When using time-series models to work with serially correlated data sets, we need to understand mean and variance – within the context of time – in addition to autocorrelation and cross-correlation. Understanding these variables helps build an intuition about how time-series models work and when they are more useful than models that do not account for time.

Mean

In time-series analysis, the sample mean of a series is the sum of all values across each point in time in the series divided by the count of values. Where t represents each discrete time step and n is the total number of time steps, we can calculate the sample mean of a time series as follows:

 _ X  =  1 _ n  ∑ t=1 n x t

There are two types of processes generating time series; one is an ergodic process and the other is non-ergodic. An ergodic process has consistent output independent of time, whereas a non-ergodic...