  The covariance matrix is formulated in the framework of a linear multivariate
ARCH process with long memory, where the natural cross product structure of the
covariance is generalized by adding two linear terms with their respective
parameter. The residuals of the linear ARCH process are computed using
historical data and the (inverse square root of the) covariance matrix. Simple
measure of qualities assessing the independence and unit magnitude of the
residual distributions are proposed. The salient properties of the computed
residuals are studied for three data sets of size 54, 55 and 330. Both new
terms introduced in the covariance help in producing uncorrelated residuals,
but the residual magnitudes are very different from unity. The large sizes of
the inferred residuals are due to the limited information that can be extracted
from the empirical data when the number of time series is large, and denotes a
fundamental limitation to the inference that can be achieved.
