simts (version 0.1.1)

gen_ma1: Generate an Moving Average Order 1 (MA(1)) Process

Description

Generate an MA(1) Process given $\theta$ and ${\sigma }^2$.

Usage

gen_ma1(N, theta = 0.3, sigma2 = 1)

Arguments

N

An integer for signal length.

theta

A double that contains moving average.

sigma2

A double that contains process variance.

Value

A vec containing the MA(1) process.

Process Definition

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

Generation Algorithm

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

The $X_0$ (first value of $X_t$) is discarded.

Details

The function implements a way to generate the $x_t$ values without calling the general ARMA function.