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
