Stochastic Models for Time Series by Paul Doukhan

Author:Paul Doukhan
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Hence we again write this as a model with independent and identically distributed innovations

Here hence .

For and we derive

and

Many other integer models contain the same idea. A simple example is the following bilinear model:

The following exercise is immediate:

Exercise 43

Prove that the contraction assumption (on a, b and on ’s distribution) in the previous theorem, if , can be written as:

Integer valued extensions of AR(p) models are also easy to define as well as vector valued models.

Definition 7.3.3

(INMA-models) Define a sequence of iid thinning operators as above. Let . Define integer moving averages with order m as

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