http://home.ubalt.edu/ntsbarsh/statdata/Forecast.htm
Autoregressive Models
The autoregressive model is one of a group of linear prediction formulas
that attempt to predict an output of a system based on the previous outputs
and inputs, such as:
Y(t) = 1 + 2Y(t-1) + 3X(t-1) + t,
where X(t-1) and Y(t-1) are the actual value (inputs) and the forecast
(outputs), respectively. These types of regressions are often referred to as
Distributed Lag Autoregressive Models, Geometric Distributed Lags, and
Adaptive Models in Expectation , among others.
A model which depends only on the previous outputs of the system is
called an autoregressive model (AR), while a model which depends only
on the inputs to the system is called a moving average model (MA), and of
course a model based on both inputs and outputs is an autoregressivemoving-average model (ARMA). Note that by definition, the AR model
has only poles while the MA model has only zeros. Deriving the
autoregressive model (AR) involves estimating the coefficients of the
model using the method of least squared error.
Autoregressive processes as their name implies, regress on themselves. If
an observation made at time (t), then, p-order, [AR(p)], autoregressive
model satisfies the equation:
X(t) = 0 + 1X(t-1) + 2X(t-2) + 2X(t-3) + . . . . + pX(t-p) + t,
where t is a White-Noise series.
The current value of the series is a linear combination of the p most recent
past values of itself plus an error term, which incorporates everything new
in the series at time t that is not explained by the past values. This is like a
multiple regressions model but is regressed not on independent variables,
but on past values; hence the term "Autoregressive" is used.