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Title: Modeling and prediction of dynamic networks using binary autoregressive time series processes Authors:  Lena Reichmann - University of Mannheim (Germany)
Shaikh Tanvir Hossain - University of Mannheim (Germany)
Carsten Jentsch - TU Dortmund University (Germany) [presenting]
Abstract: Suppose a time series of networks is identified by their adjacency matrices $A_1,\ldots,A_T$, where $A_t=(a_{ij;t})_{i,j=1,\ldots,N}$ with $a_{ij;t}\in\{0,1\}$ and $a_{ij,t}=1$ indicating that there is a directed edge pointing from vertex $i$ to vertex $j$ at time $t$. To model the joint dynamics of the edges, we propose to use multivariate binary time series processes. For this purpose, we adopt the class of Discrete AutoRegressive Moving-Average (DARMA) models for univariate categorical data. Recent extensions of these models allow the application to vector-valued data and to model negative autocorrelations by a simple modification. The resulting model class is flexible enough to capture very general autocorrelations driving the dynamic network structure. For the purely autoregressive case, Yule-Walker-type equations hold that allow in principle an explicit estimation of all model parameters. However, as the dimension of the adjacency matrices grows quadratically with the number of vertices, we shall make use of Lasso-penalization techniques to estimate sparse models. For this purpose, we adopt a previous approach which provides with consistent estimators for high-dimensional vector autoregressive models under sparsity. Our modeling approach is suitable for prediction of single and joint edge probabilities in dynamic networks. We illustrate our method by simulations and for real data.