Practical Time-Series Analysis

Autocorrelation and Partial autocorrelation

After applying the mathematical transformations discussed in the previous section, we will often be left with what is known as a stationary (or weakly stationary) time series, which is characterized by a constant mean E(x_t) and correlation that depends only on the time lag between two time steps, but independent of the value of the time step. This type of covariance is the key in time series analysis and is called autocovariance or autocorrelation when normalized to the range of -1 to 1. Autocorrelation is therefore expressed as the second order moment E(x_t,x_t+h) = g(h) that evidently is a function of only the time lag h and independent of the actual time index t. This special definition of autocorrelation ...