Dynamic Functional Data Analysis with Nonparametric State Space Models.

In this article we introduce a new methodology for modeling curves with a dynamic structure, using a non-parametric approach formulated as a state space model. The non-parametric approach is based on the use of penalized splines, represented as a dynamic mixed model. This formulation can capture the dynamic evolution of curves using a limited number of latent factors, allowing a accurate fit with a limited number of parameters. We also present a new method to determine the optimal smoothing parameter through an adaptive procedure using a formulation analogous to a model of stochastic volatility. This methodology allows unifying different methodologies applied to data with a functional structure in finance. We present the advantages and limitations of this methodology through a simulation study and also comparing its predictive performance with other parametric and non-parametric methods used in financial applications using data from term structure of interest rates.