recserVAR#

Purpose#

Computes a vector autoregressive recursive (VAR) series.

Format#

y = recserVAR(x, y0, pi_)#

Parameters:

x (NxK matrix) – data matrix where \(N\) is the number of observations and \(K\) is the number of vectors in the series
y0 (PxK matrix) – \(P\) is the order of the VAR model, the starting values for each vector in the series.
pi_ (KxK matrix) – contains the VAR parameters.

Returns:

y (NxK matrix) – contains the series.

Examples#

VAR(1) without constant#

// Starting value for the time series
y0 = { 0 0 };

// VAR(1) parameter matrix
pi_ = { 0.6 -0.2,
        -0.4 0.3 };

// Innovations
eps = rndn(100, 2);

// Simulate VAR(1) model
y = recserVAR(eps, y0, pi_);

VAR(1) with constant#

// Starting value for the time series
y0 = { 0 0 0 };

// VAR(1) parameter matrix
pi_ = {  0.6 -0.2  0.1,
        -0.4  0.3 0.25,
        0.33 0.15  0.4 };

// Constant term
const = { -0.7 1.3 0.5 };

// Innovations
eps = rndn(100, 3);

// Simulate AR(2) model with constant
y = recserVAR(eps + const, y0, pi_);

Remarks#

recserVAR() currently only supports VAR(1) models.