Description

Generate an ARMA(p,q) process with supplied vector of Autoregressive Coefficients (φ), Moving Average Coefficients (θ), and σ^2.

Usage

Arguments

Details

For AR(1), MA(1), and ARMA(1,1) please use their functions if speed is important as this function is designed to generate generic ARMA processes.

Value

A vec that contains the generated observations.

Process Definition

The Autoregressive order p and Moving Average order q (ARMA(p,q)) process with non-zero parameters phi[i] in (-1,1) for the AR components, theta[j] in (-1,+1) for the MA components, and sigma^2 in R^{+}. This process is defined as:

X[t] = sum(phi[p]*X[t-1]) + sum(theta[q]*W[t-1]) + W[t]

where

W[t] ~ N(0,sigma^2) iid

Generation Algorithm

The innovations are generated from a normal distribution. The σ^2 parameter is indeed a variance parameter. This differs from R's use of the standard deviation, σ.