ARIMA - Auto Regressive Integrated Moving Average
Overview
An ARIMA model is an ARMA model that is integrated. (see below)
ARMA
ARMA models are a general class of
stationary
models. They represent the integration of two types of stationary models
{% X_t - \phi_1 X_{t-1} - ... - \phi_p X_{t-p} = Z_t + \theta_1 Z_{t-1} + ... + \theta_q Z_{t-q} %}
where
{% Z_t \sim WN(0, \sigma^2) %}
Integrated Series
When a time series becomes
stationary
after a differencing, the series is said to be integrated. That is, you can recover
the original series from the differenced series by adding. (You will need an additional parameter to specify the start point)
The terminology mirrors that of calculus, you can recover a function after differentiating it by integration.
Typically when one speaks of an integrated time series, they refer to the order of the integration, such as
a series is integrated with order 1, or something to that effect. This just refers to the number of times
the series had to be differenced to achieve stationarity.
ARIMA
