# rcoint: Random generation of cointegrated sequences In matthewclegg/egcm: Engle-Granger Cointegration Models

## Description

Generates a random pair of cointegrated sequences

## Usage

 ```1 2 3 4 5 6 7 8``` ```rcoint(n, alpha = runif(1, -10, 10), beta = runif(1, -10, 10), rho = runif(1, 0, 1), sd_eps = 1, sd_delta = 1, X0=0, Y0=0) ```

## Arguments

 `n` number of observations in each sequence `alpha` constant term of linear relation `beta` slope term of linear relation `rho` coefficient of mean reversion `sd_eps` standard deviation of innovations in first sequence `sd_delta` standard deviation of innovations in residual sequence `X0` initial value of first sequence `Y0` initial value of second sequence

## Details

Generates a random pair of cointegrated sequences. The sequences are constructed by first generating two random sequences that are independent and normally distributed. The elements of the first sequence, epsilon[i], have standard deviation `sd_eps`, while those of the second sequence, delta[i], have standard deviation `sd_delta`. Having generated these two sequences, the cointegrated sequences `X[i]` and `Y[i]` are generated according to the following relations:

X[i] = X[i-1] + epsilon[i]

R[i] = rho * R[i-1] + delta[i]

Y[i] = alpha + beta * X[i] + R[i]

## Value

Returns a two-column data.frame containing the randomly generated cointegrated sequences.

## Author(s)

Matthew Clegg [email protected]

`rar1` `sim.egcm` `egcm`
 ```1 2``` ```xy <- rcoint(1000, alpha = 1, beta = 2, rho = 0.8) egcm(xy) ```