Behavioural Pattern of Causality Parameter of Autoregressive Moving Average Model

Abstract

In this paper, a causal form of Autoregressive Moving Average process, ARMA (p, q) of various orders and behaviour of the causality parameter of ARMA model is investigated. It is deduced that the behaviour of causality parameter ψ_i depends on positive and negative values of autoregressive parameter φ and moving average parameter θ. The causality parameter is skewed to the right for positive values of φ and sinusoidal for negative values of φ while invertibility parameter is sinusoidal for positive values of θ.

Keyword: invertibility, causality, stationarity, autoregressive

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 583 – 590