title: On the limits of probabilistic forecasting in nonlinear times series analysis.
abstract: The ignorance score measures the quality of probabilistic forecasting. In this paper, we study its basic properties in the perfect model scenario, i.e., under the assumption that the system producing the data is perfectly known. Two further qualifications are added to this general setting. First, the system is a discrete-time, measure-preserving dynamical system. Moreover, randomness results from the quantization of the state space (i.e., from the finite precision of the observations), rather than being introduced via observational noise. In this "non-linear" perfect model scenario we derive, in particular, the admissible domain of the ignorance score and relate it with the ignorance score in imperfect models.
authors.affiliation: Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain.
authors.forename: José M
authors.initials: JM
authors.lastname: Amigó
authors.affiliation: The Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
authors.forename: Yoshito
authors.initials: Y
authors.lastname: Hirata
authors.affiliation: The Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Aihara