Modeling Time-Varying Dependencies Between Positive-Valued High-Frequency Time Series

Abstract

Multiplicative error models (MEM) became a standard tool for modeling conditional durations of intraday transactions, realized volatilities and trading volumes. The parametric estimation of the corresponding multivariate model, the so-called vector MEM (VMEM), requires a specification of the joint error term distribution, which is due to the lack of multivariate distribution functions on R d + defined via a copula. Maximum likelihood estimation is based on the assumption of constant copula parameters and therefore, leads to invalid inference, if the dependence exhibits time variations or structural breaks. Hence, we suggest to test for time-varying dependence by calibrating a time-varying copula model and to reestimate the VMEM based on identified intervals of homogenous dependence. This paper summarizes the important aspects of (V)MEM, its estimation and a sequential test for changes in the dependence structure. The techniques are applied in an empirical example.

Efficient Iterative Maximum Likelihood Estimation of High-Parameterized Time Series Models

“…Therefore, extant literature captures the contemporaneous dependence between ε i by copulas, see, e.g., Bodnar and Hautsch (2012) or Hautsch, Okhrin, and Ristig (2013). Here, we induce dependence between the errors through an R-vine copula, which can generate a broad range of dependence structures including non-linearities, asymmetries and tail dependence.…”