Abstract-Inferring causal dependences in a family of dynamic systems from a finite set of observations is a problem encountered in many applications that arise in a diverse variety of fields; ranging from economics and finance to climatology and neuroscience. Given a set of random processes, the objective is to determine whether one process is influenced by the others and to investigate the nature of this influence in case a dependence relation is identified. The notion of Granger-causality may be used in this context to measure and quantify causal structures. Ideally, in order to infer the complete interdependence structure of a complex system, one should simultaneously consider the dynamic behaviour of all the processes involved. However, for large networks, such a method becomes exceedingly complicated. In this paper, we consider an interdependent group of jointly wide sense stationary real-valued stochastic processes and investigate the problem of determining Granger-causality by identifying pairwise causal relations. It is seen that while such methods may not reveal all details of a system, they can nonetheless provide useful and reasonably accurate information.
This paper examines the impact of the gossip procedure on distributed particle filters that employ averaging to estimate the global likelihood function. We consider a model where a gossip-driven algorithm leads to the use of a slightly distorted version of the likelihood function, in lieu of its true value. Under standard regularity conditions, and a mild assumption on the true likelihood function, we derive a time-uniform bound on the weaksense Lp error of the filter. Furthermore, we present an associated exponential inequality for the large deviations of the filter. These bounds capture the combined effects of sampling and consensusbased approximation. The results allow us to evaluate the impact of such approximations on the overall performance of the distributed particle filter, and analyze its stability. Finally, through numerical experiments, we demonstrate the practical implications of these results and explore the relationship of the performance of the filter with these theoretical error bounds.
The approximation of a stationary time-series by finite order autoregressive (AR) and moving averages (MA) is a problem that occurs in many applications. In this paper we study asymptotic behavior of the spectral density of finite order approximations of wide sense stationary time series. It is shown that when the on the spectral density is non-vanishing in [−π, π] and the covariance is summable, the spectral density of the approximating autoregressive sequence converges at the origin. Under additional mild conditions on the coefficients of the Wold decomposition it is also shown that the spectral densities of both moving average and autoregressive approximations converge in L 2 as the order of approximation increases.
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