Linear Time Series

We can treat a time series as a sequence of random observations. This random sequence, or stochastic process, may exhibit a degree of correlation from one observation to the next. This correlation structure can be used to predict future values of the process based on the past history of observations.

To Exploit the correlation structure, we decompose the time series into the following components:

Where

1. A deterministic component: past observation, and exogenous factors
2. : A random component (the error, or uncertainty