egcm (version 1.0.8)

rcoint: Random generation of cointegrated sequences

Description

Generates a random pair of cointegrated sequences

Usage

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

Value

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

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: $$X[i] = X[i-1] + \epsilon[i]$$ $$R[i] = \rho R[i-1] + \delta[i]$$ $$Y[i] = \alpha + \beta X[i] + R[i]$$

See Also

rar1 sim.egcm egcm

Examples

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