Title: Generalized binary time series models
Authors: Lena Reichmann - University of Mannheim (Germany) [presenting]
Carsten Jentsch - TU Dortmund University (Germany)
Abstract: The serial dependence of categorical data is commonly described using Markovian models. As a result of their flexibility, they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters in the univariate case, a more parsimonious and nicely interpretable class of Discrete AutoRegressive Moving-Average (DARMA) models has been introduced in the literature. For binary data, we propose two model extensions. First, we allow for negative model coefficients to allow also for negative autocorrelations, which is not possible using DARMA models. Second, we consider the vector-valued case that is suitable e.g. for dynamic network modeling. In this case, the effect of Markov models having a huge number of parameters becomes even more pronounced. Both extensions are simple and maintain the nice interpretability and the autoregressive moving-average structure leading to a new generalized DARMA model class. We provide sufficient stationarity conditions and derive the stationary solution of the model equations. For the purely autoregressive case, we prove Yule-Walker-type equations that facilitate the task of parameter estimation in these models to some large extent. Further, we discuss mixing properties of these models. For illustration, we study the estimation performance in these models by simulations and apply our model to quarterly OECD recession data from G7 countries.