Question

Explain what is meant by the following time series terms

i) Sample autocorrelation function

ii) The if and only if conditions for the stationarity of the ARMA(p,q) process

iii) The partial autocorrelation function

Answer 1

Autocorrelation in statistics is a mathematical tool that is usually used for analyzing functions or series of values, for example, time domain signals. In other words, autocorrelation determines the presence of correlation between the values of variables that are based on associated aspects. So, for the sample data we compute sample auto correlation to determine the relationship.

Root of the above function should not lie on the unit circle. This is the exact meaning of the if and only if condition for stationarity of an ARMA(p,q) process

A partial autocorrelation is a summary of the relationship between an observation in a time series with observations at prior time steps with the relationships of intervening observations removed.