Conditional Autoregressive Hilbertian Processes

• Activity Number: 567
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jairo Cugliari*+
• Companies: INRIA
• Keywords: Conditional Autoregressive Hilbertian process ; Functional Data ; Nonparametric forecasting ; Electricity consumption ; Exogenous variable

Abstract

We focus on the problem of predicting a function-valued stochastic process. The approach we adopt is based on the notion of Autoregressive Hilbert (ARH) processes. Estimation and prediction of ARH processes impose interesting challenges due to the infinite dimension of the space where the process is defined.

If an additional exogenous information is available, we may want to use it in for estimation and prediction purposes. We aim here at introducing an exogenous covariate in the ARH process in such a way that conditionally on the covariate the process becomes an ARH. We call the new process Conditional Autoregressive Hilbertian process (CARH).

In addition to its definition, we propose estimation and prediction procedures. For them, we give consistency results that justify the theoretical relevance of our propositions. Finally, we perform numerical experiences on simulated data as well as on real data.