def simulate_bekk(param, nobs=1000, distr='normal', degf=10, lam=0): """Simulate data. Parameters ---------- param : BEKKParams instance Attributes of this class hold parameter matrices nobs : int Number of observations to generate. Time series length distr : str Name of the distribution from which to generate innovations. Must be - 'normal' - 'student' - 'skewt' degf : int Degrees of freedom for Student or SkewStudent distributions lam : float Skewness parameter for Student or SkewStudent distributions. Must be between (-1, 1) Returns ------- innov : (nobs, nstocks) array Multivariate innovation matrix """ nstocks = param.amat.shape[0] if distr == 'normal': # Normal innovations mean, cov = np.zeros(nstocks), np.eye(nstocks) error = np.random.multivariate_normal(mean, cov, nobs) elif distr == 'student': # Student innovations error = np.random.standard_t(degf, size=(nobs, nstocks)) elif distr == 'skewt': # Skewed Student innovations error = SkewStudent(eta=degf, lam=lam).rvs(size=(nobs, nstocks)) else: raise ValueError('Unknown distribution!') # Standardize innovations error = (error - error.mean(0)) / error.std(0) hvar = np.empty((nobs, nstocks, nstocks)) innov = np.zeros((nobs, nstocks)) hvar[0] = param.get_uvar() intercept = param.cmat.dot(param.cmat.T) for i in range(1, nobs): innov2 = innov[i-1, np.newaxis].T * innov[i-1] hvar[i] = intercept + param.amat.dot(innov2).dot(param.amat.T) \ + param.bmat.dot(hvar[i-1]).dot(param.bmat.T) hvar12 = sl.cholesky(hvar[i], 1) innov[i] = hvar12.dot(np.atleast_2d(error[i]).T).flatten() return innov, hvar