The Entropy of ARMA (p,q) Process

摘要

It is well known that the ARMA model is a tool for understanding, representing, analyzing and, perhaps, predicting future values of a very wide range of phenomena. The model consists of two parts, the first one is an autoregressive (AR) and the second part is a moving average (MA). The model is usually then referred to as the ARMA(p ,q ) model where p is the order of the autoregressive part and q is the order of the moving average part. Abid in 2006[2], found a general formula to represent ARMA(p,q) process characteristic function in terms of its residuals characteristic function and then solved the problem of writing causal function parameters in terms of corresponding ARMA(p,q) process. In this paper we introduce a formula for the entropy of ARMA(p,q) process and then give some examples where the noise term distributed as normal, Cauchy and levy.