ensemble

hf.ensemble(estimates, var_weights, cov_weights)

Ensemble multiple covariance matrix estimates with weights given by var_weights and cov_weights for the diagonal and off-diagonal elements, respectively. This function is used in the ensembled pairwise integrated covariance (EPIC) estimator of Woeltjen (2020). The msrc() estimator , the mrc() estimator, the krvm() estimator and the preaveraged hayashi_yoshida() estimator are ensembled to compute an improved finite sample estimate of the pairwise integrated covariance matrix. The EPIC estimator uses every available tick, and compares favorable in finite samples to its constituents on their own. The preaveraged HY estimates of the off-diagonals have better finite sample properties than the other estimators so it might be preferable to overweight them by setting the corresponding cov_weights element to a number >1/4.

Parameters

estimateslist of numpy.ndarrays with shape = (p, p)

The covariance matrix estimates. var_weights : numpy.ndarray The weights with which the diagonal elements of the MSRC, MRC, and the preaveraged HY covariance estimates are weighted, respectively. The weights must sum to one.

cov_weightsnumpy.ndarray

The weights with which the off-diagonal elements of the MSRC, MRC, and the preaveraged HY covariance estimates are weighted, respectively. The HY estimator uses the data more efficiently and thus may deserve a higher weight. The weights must sum to one.

Returns

covnumpy.ndarray

The ensemble estimate of the integrated covariance matrix.