simts (version 0.2.2)

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

Description

Generate an Autoregressive Order 1 sequence given $\varphi$ and ${\sigma }^2$.

Usage

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

Value

A vec containing the AR(1) process.

Arguments

N

An unsigned integer for signal length.

phi

A double that contains autocorrection.

sigma2

A double that contains process variance.

Process Definition

The Autoregressive order 1 (AR1) process with non-zero parameter $\varphi \in (-1,+1)$ and ${\sigma }^2\in {\mathrm{I}\mathrm{R}}^2$. This process is defined as: $$X_t={\varphi }_1{X}_{t-1}+{\epsilon }_t$$, where $${\epsilon }_t\stackrel{iid}{\sim }N\left(0,{\sigma }^2\right)$$ 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.

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.