# Simulation from a multivariate AR(p) model

### Description

Simulation from an m-variate AR(p) model

### Usage

1 |

### Arguments

`w` |
vector of intercept terms |

`A` |
matrix of AR coefficients |

`C` |
noise covariance matrix |

`N` |
length of output time series |

`...` |
additional arguments |

### Details

Simulation from an m-variate AR(p) model given by

*X[t]=w + A1 X[t-1] +...+ Ap X[t-p] +e[t]*

where

X[t]=[X1(t)...Xm(t)]' is a vector of length m

w is a m-length vector of intercept terms

A=[A1 ... Ap] is a m x mp matrix of autoregressive coefficients

e(t) is a m-length uncorrelated noise vector with mean 0 and m x m covariance matrix C

### Value

returns a list containg the N simulated observations for each of the m time series

### Author(s)

S. M. Barbosa

### References

Neumaier, A. and Schneider, T. (2001), Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Transactions on Mathematical Software, 27, 1, 27-57.

Schneider, T. and Neumaier, A. (2001), A Matlab package fo the estimation of parameters and eigenmodes of multivariate autoregressive models, 27, 1, 58-65.

Lutkepohl, H. (1993), Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin.

### Examples

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