# qar.sim: Simulate a first-order quadratic AR model In TSA: Time Series Analysis

## Description

Simulates a first-order quadratic AR model with normally distributed noise.

## Usage

 1 qar.sim(const = 0, phi0 = 0, phi1 = 0.5, sigma = 1, n = 20, init = 0) 

## Arguments

 const intercept phi0 coefficient of the lag 1 phi1 coefficient of the squared lag 1 sigma noise standard deviation n sample size init number of burn-in values

## Details

The quadratic AR(1) model specifies that

Y_t = \mathrm{const}+φ_0 Y_{t-1}+φ_1 Y^2_{t-1}+e_t

where e_t are iid normally distributed with zero mean and standard deviation σ. If σ=0, the model is deterministic.

## Value

A simulated series from the quadratic AR(1) model, as a vector

## Author(s)

Kung-Sik Chan

tar.sim
 1 2 3 4 5 set.seed(1234567) plot(y=qar.sim(n=15,phi1=.5,sigma=1),x=1:15,type='l',ylab=expression(Y[t]),xlab='t') y=qar.sim(n=100,const=0.0,phi0=3.97, phi1=-3.97,sigma=0,init=.377) plot(y,x=1:100,type='l',ylab=expression(Y[t]),xlab='t') acf(y,main='')