In this paper we present a copula-based model for a binary and a continuous variable in a time series setup. Within this modeling framework both marginals can be equipped with their own dynamics whereas the contemporaneous dependence between both processes can be flexibly captured via a copula function. We propose a method for testing the goodness-of-fit of such a time series model using probability integral transforms (PIT). This verification procedure allows not only a verification of the goodness-of-fit of the estimated marginal distribution for a continuous variable but also the conditional distribution of a continuous variable given the outcome of its binary counterpart (i.e. the adequacy of the copula choice). We test the model on an empirical example: investigating the relationship between trading volume and the indicators of arbitrarily ’large’ price movements on the interbank EUR/PLN spot market.
The paper considers the modeling and estimation of the stochastic frontier model where the error components are assumed to be correlated and the inefficiency error is assumed to be autocorrelated. The multivariate Farlie-Gumble-Morgenstern (FGM) and normal copula are used to capture both the contemporaneous and the temporal dependence between, and among, the noise and the inefficiency components. The intractable multiple integrals that appear in the likelihood function of the model are evaluated using the Halton sequence based Monte Carlo (MC) simulation technique. The consistency and the asymptotic efficiency of the resulting simulated maximum likelihood (SML) estimators of the present model parameters are established. Finally, the application of model using the SML method to the real life US airline data shows significant noise-inefficiency dependence and temporal dependence of inefficiency.