gen_ar1: Generate an Autoregressive Order 1 ( AR(1) ) sequence

In SMAC-Group/simts: Time Series Analysis Tools

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

Description

Generate an Autoregressive Order 1 sequence given \phi and \sigma^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 {\rm I\!R}^{2}. This process is defined as:

{X_t} = {\phi _1}{X_{t - 1}} + {\varepsilon_t}

, where

{\varepsilon_t}\mathop \sim \limits^{iid} N\left( {0,\sigma^2} \right)

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.

SMAC-Group/simts documentation built on Sept. 4, 2023, 5:25 a.m.