11 Outubro 2016, 17:24 • Ana Maria Santos Ferreira Gorjão Henriques
Spatial and Spatio-Temporal Nonlinear Time Series
Wolfgang Schmid (European University, Frankfurt (Oder), Germany)
October 25 (Tue.), 11:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)
In this talk we present a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model. We show additionally how the introduced spatial ARCH model can be used in spatiotemporal settings. In contrast to the temporal ARCH model, in which the distribution is known given the full information set of the prior periods, the distribution is not straightforward in the spatial and spatiotemporal setting. However, it is possible to estimate the parameters of the model using the maximum-likelihood approach. Via Monte Carlo simulations, we demonstrate the performance of the estimator for a specific spatial weighting matrix. Moreover, we combine the known spatial autoregressive model with the spatial ARCH model assuming heteroscedastic errors. Eventually, the proposed autoregressive process is illustrated using an empirical example. Specifically, we model lung cancer mortality in 3108 U.S. counties and compare the introduced model with two benchmark approaches.
(joint work with Robert Gartho and Philipp Otto)