Lag Operator - Lag Polynomials

Lag Polynomials

Also polynomials of the lag operator can be used, and this is a common notation for ARMA (autoregressive moving average) models. For example,

specifies an AR(p) model.

A polynomial of lag operators is called a lag polynomial so that, for example, the ARMA model can be concisely specified as

where and respectively represent the lag polynomials

and

Polynomials of lag operators follow similar rules of multiplication and division as do numbers. For example,

means the same thing as

An annihilator operator, denoted, removes the entries of the polynomial with negative power (future values).