gen_ar1: Generate an Autoregressive Order 1 ( AR(1) ) sequence
In schoi355/gmwm: Generalized Method of Wavelet Moments

gen_ar1

R Documentation

Generate an Autoregressive Order 1 ( AR(1) ) sequence

Description

Generate an Autoregressive Order 1 sequence given φ and σ^2.

Usage

gen_ar1(N, phi = 0.3, sigma2 = 1)

Arguments

`N`	An `unsigned integer` for signal length.
`phi`	A `double` that contains autocorrection.
`sigma2`	A `double` that contains process variance.

Details

The function implements a way to generate the AR(1)'s x[t] values without calling the general ARMA function. Thus, the function is able to generate values much faster than gen_arma.

Value

A vec containing the AR(1) process.

Process Definition

The Autoregressive order 1 (AR1) process with non-zero parameter phi in (-1,1) and sigma^2 in R^{+}. This process is defined as:

X[t] = phi[1]X[t-1] + W[t]

, where

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

AR(1) processes are sometimes used as an approximation for Bias Instability noises.

Generation Algorithm

The function first generates a vector of White Noise with length N+1 using gen_wn and then obtains the autoregressive values under the above process definition.

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