Second, Equation (3) can be used recursively to obtain the conditional distribution
at longer horizons:
Using the conditional mean and the conditional variance obtained from the estimated GARCH family models, the quantiles of the conditional distribution
can be easily obtained for the calculation of VaR (Tsay, 2005).
If Yt, t = 1,2,...,T, follows a gamma conditional distribution
G([p.sub.t], [q.sub.t] ), where G(p,q) denotes a gamma distribution with mean pq and variance [pq.sup,2], the conditional mean and variance are related to the original parameters by the equations [[micro].sub.t]= p.sub.t [q.sub.t] and [h.sub.t = [[micro].sub.t] [q.sub.t].
Secondly, quantile regressions are performed in order to observe whether there are any heterogeneous effects along the conditional distribution
of the two measures of export activity.
This is very important to our estimation of the conditional distribution
function and its inverse.
Lemahieu, "Source extraction by maximizing the variance in the conditional distribution
tails," IEEE Transactions on Signal Processing, vol.
For a binary variable, a Bernoulli-Bernoulli energy function [34, 35] and the conditional distribution
of a single stochastic hidden variable are given by
where [r.sub.t] stands for risk-free interest rate; [[epsilon].sub.t] satisfies certain conditional distribution
process, that is, [[epsilon].sub.t] | [[phi].sub.t] ~ D(0, [h.sub.t]), where [h.sub.t] stands for conditional variance satisfying [h.sub.t] = P([h.sub.t-1], [[epsilon].sub.t-1]).
What this means is that the conditional distribution
of [X.sub.t] given observations of the process at several moments in the past, is the same as the one given only the latest observation.
By capturing the full conditional distribution
rather than a single estimate, the method can directly characterize the uncertainty in model predictions.
By applying the conditional distribution
theorem, the joint PDF discussed in (4) can be described as
However, (5) does not consider the role of each feature on reducing the mismatch of conditional distribution
. Therefore, it is natural to select the features that can reduce the mismatch of conditional distribution