Models for nonnegative (incl. zero) positively skewed multivariate time series (trade volumes) I want to build a Monte Carlo simulation that is based in part on share amounts that are traded in the market for a set of stocks. I need to be able to take into account the co-dependence of trade volumes between stocks. For example, Microsoft might have a high volume day on the same day as IBM. Obviously trade volumes cannot be less than zero and are positively skewed.
If I were just looking at liquid stocks like IBM and Microsoft, it would not be so difficult. I would do something like a log transform then fit a multivariate skewed $t$ distribution.
The problem is that for small-cap/illiquid stocks, often there will be days that have zero volume traded. And you can't do a log transform on zero.
If it were just one stock (univariate) I would look at fitting some kind of mixture distribution where one of the components is a discrete probability of having zero volume.
I can kind of see how a mixture distribution can be extended to a multivariate setting, but I've never done something like this before. 


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*Is this the right approach? 

*Do you know of any examples/resources I can read on this? 

*Is there a better way?

 A: This should be relevant:


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*Hautsch et al. "Capturing the zero: a new class of zero-augmented distributions and multiplicative error processes" (2014).


Here is their abstract, where I highlighted some key points:

We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed at high frequencies, such as cumulated trading volumes. We introduce a flexible point-mass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of both liquid and illiquid NYSE stocks, we show that the model captures the dynamic and distributional properties of the data well and is able to correctly predict future distributions.

While the focus in the paper is on a univariate setting, the authors claim in the last paragraph of their Conclusions that 

<...> it should be straightforward to extend the model to a multivariate setting, in the spirit of, e.g., Manganelli (2005), Cipollini, Engle, and Gallo (2006), or Hautsch (2008) <...>

and subsequently give some ideas of possible applications.
