Title: On the parameters estimation of the new Seasonal FISSAR model and simulations
Authors: Papa Ousmane Cisse - Le Mans University (Senegal) [presenting]
Dominique Guegan - Universite Paris 1 - Pantheon-Sorbonne (France)
Abdou Ka Diongue - Gaston Berger (Senegal)
Abstract: The model called Fractionally Integrated Separable Spatial Autoregressive processes with Seasonality, and denoted Seasonal FISSAR, for two-dimensional spatial data is considered. This new model will be able to take into account long memory in spatial data and periodic or cyclical behaviours presented in a lot of applications, including temperatures, agricultural data, epidemiology when the data are collected during different seasons at different locations, and also financial data, to take into account the specific systemic risk observed on the global market. We discuss on the methods of estimating the parameters of the Seasonal FISSAR model and show the asymptotic properties. First, we implement the regression method based on the log-periodogram and the classical Whittle method for estimating memory parameters. For estimating all model parameters simultaneously, innovation parameters and memory parameters MLE and Whittle method based on the MCMC are considered. We show the consistency empirically, and we investigate the asymptotic normality of the estimators by simulations. The first motivation behind MLE is to estimate all parameters simultaneously unlike our proposal regression method and Wittle method. However, the computational complexity of MLE may be outweighed by its convenience as a very widely applicable method of estimation.