An MCMC Approach to Multivariate Density Forecasting: An Application to Liquidity

We analyze the construction of multivariate forecasting densities based on conditional models for each variable, given the other variables; a joint predictive density is obtained by iteratively simulating from the conditional models. This idea has been pursued in the context of missing data imputation, but is new to the field of econometric forecasting. Its main advantage is that only univariate models for the variables in question are needed as inputs. Within a Monte Carlo study we illustrate the flexibility and robustness of this approach especially for the case of model misspecification. We then consider forecasting the bivariate mixed discrete-continuous distribution of returns and order flows on a high frequency level. This distribution can be related to an ex-post concept of market liquidity. A simulation-based forecasting distribution constructed from the conditional models for returns and order flows is found to outperform a vector autoregressive benchmark for several large-cap US stocks.