Title: Constrained functional time series: Applications to the Italian gas market
Authors: Antonio Canale - University of Padua (Italy) [presenting]
Simone Vantini - Politecnico di Milano (Italy)
Abstract: Motivated by market dynamic modelling in the Italian natural gas balancing platform, a model is proposed to analyze time series of monotone functions subject to an equality and inequality constraint at the two edges of the domain, respectively, such as daily demand and offer curves. In detail, we provide the constrained functions with a suitable pre-Hilbert structure and introduce a useful isometric bijective map associating each possible bounded and monotonic function to an unconstrained one. We introduce a functional-to-functional autoregressive model that is used to forecast future demand/offer functions. We estimate the model via minimization of a penalized mean squared error of prediction with a penalty term based on the Hilbert-Schmidt squared norm of autoregressive lagged operators. The approach is of general interest and is suited for generalizations in any situation in which one has to deal with functions subject to the above constraints which evolve through time.