Definition
The notation AR(p) indicates an autoregressive model of order p. The AR(p) model is defined as
where are the parameters of the model, is a constant (often omitted for simplicity) and is white noise.
An autoregressive model can thus be viewed as the output of an all-pole infinite impulse response filter whose input is white noise.
Some constraints are necessary on the values of the parameters of this model in order that the model remains wide-sense stationary. For example, processes in the AR(1) model with |φ1| ≥ 1 are not stationary. More generally, for an AR(p) model to be wide-sense stationary, the roots of the polynomial must lie within the unit circle, i.e., each root must satisfy .
Read more about this topic: Autoregressive Model
Famous quotes containing the word definition:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)