gen_arma11: Generate an ARMA(1,1) sequence

In schoi355/gmwm: Generalized Method of Wavelet Moments

Generate an ARMA(1,1) sequence

Description

Generate an ARMA(1,1) sequence given φ, θ, and σ^2.

Usage

gen_arma11(N, phi = 0.1, theta = 0.3, sigma2 = 1)

Arguments

N	An integer for signal length.
phi	A double that contains autoregressive.
theta	A double that contains moving average.
sigma2	A double that contains process variance.

Details

The function implements a way to generate the x[t] values without calling the general ARMA function.

Value

A vec containing the MA(1) process.

Process Definition

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

W[t] = phi*W[t-1] + theta*W[t-1] + W[t]

, where

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

Generation Algorithm

The function first generates a vector of white noise using gen_wn and then obtains the ARMA values under the above equation.

The X[0] (first value of X[t]) is discarded.

Examples

gen_ma1(10, .2, 1.2)

schoi355/gmwm documentation built on April 11, 2022, 1:21 a.m.