# rar1: Random AR(1) vector In matthewclegg/egcm: Engle-Granger Cointegration Models

 rar1 R Documentation

## Random AR(1) vector

### Description

Generates a random realization of an AR(1) sequence

### Usage

```rar1(n, a0 = 0, a1 = 1, trend = 0, sd = 1, x0 = 0)
```

### Arguments

 `n` Length of vector to produce `a0` Constant term in AR(1) sequence `a1` Coefficient of mean-reversion `trend` Linear trend `sd` Standard deviation of sequence of innovations `x0` Starting value of sequence

### Value

If `trend=0`, returns a vector of length `n` representing a simulation of an AR(1) process

X[k] = a_0 + a_1 * X[k-1] + ε[t]

where ε[t] is a sequence of independent and identically distributed samples from a normal distribution with mean zero and standard deviation `sd`.

If `trend != 0`, returns a vector of length `n` representing a simulation of a trend-stationary AR(1) process

R[k] = a_0 + a_1 * R[k-1] + ε[t]

X[k] = k * trend + R[k]

### Author(s)

Matthew Clegg matthewcleggphd@gmail.com

`rcoint`

### Examples

```rar1(100, 0, 0)          # Equivalent to rnorm(100)
rar1(100, 0, 1)          # Equivalent to cumsum(rnorm(100))
acor(rar1(100, 1, .5))   # Should be about 0.5
tseries::adf.test(rar1(100, 0, .5))  # Should have a low p-value
```

matthewclegg/egcm documentation built on March 5, 2023, 6:33 a.m.