Statistical inference for spherical functional autoregressions

The main purpose of this thesis is to address some foundational questions regarding time-dependent spherical random fields and, then, to investigate some new estimation procedures for the class of spherical functional autoregressions

Asymptotics and Regularization in Spherical Functional Autoregressive Models

A class of space-time random fields, which are functional autoregressive processes taking values in the space of square integrable functions on the sphere, is presented. We discuss the estimation of the corresponding autoregressive kernels. In particular, we investigate asymptotic properties of a form of least squares regression and LASSO-type estimators

How robust is the skill score of probabilistic earthquake forecasts?

Earthquake scientists continue to improve models of the spatio–temporal evolution of seismicity, including complex aftershock sequences. The Collaboratory for the Study of Earthquake Predictability (CSEP) prospectively evaluates the predictive skill of probabilistic forecasts by such models. Here, we assess the robustness of one popular skill score, the information gain per earthquake, with respect to temporal fluctuations of the seismicity rate. We conduct a numerical experiment with a widely-used temporal stochastic seismicity model, a special case of Hawkes process. Our simulations reveal that the information gain fluctuates substantially with time, because a central limit theorem does not hold in a realistic parameter regime. Our results may eventually contribute to more robust inferences

Spherical autoregressive change-point detection with applications

I processi spatio-temporali sorgono naturalmente in numerosi campi applicativi, come la Cosmologia, l'Astrofisica, la Geofisica, le Scienze del Clima e dell'Atmosfera. In molti di questi ambiti, l'individuazione di break strutturali nella serie dei dati è fondamentale. A tal fine, nel presente lavoro, ci proponiamo di generalizzare i processi SPHAR(p) introducendo cambiamenti temporali nei parametri funzionali e nella loro struttura di variabilità. Il nostro approccio, oltre ad integrare esplicitamente sia la dimensione spaziale che quella temporale del fenomeno in studio, permette al contempo di estrarre informazioni multiscala che meglio qualificano e caratterizzano i punti di cambio individuati. Le prestazioni della modellistica proposta saranno testate su un dataset reale relativo ad anomalie della temperatura superficiale globale.Spatio-temporal processes arise very naturally in a number of different applied fields, like Cosmology, Astrophysics, Geophysics, Climate and Atmospheric Science. In most of these areas, the detection of structural breaks or regime shifts in the data stream is key. To this end, in the present work, we aim at generalizing the recently introduced SPHAR(p) process by allowing for temporal changes in its functional parameters and variability structure. Our approach, which intrinsically integrates the spatial and temporal dimensions, could give multiscale insights into both the global and local behavior of changes, and its performance will be tested on a real dataset of global surface temperature anomalies