Speaker
Description
Functional autoregressive (FAR) processes have become an important methodological tool in functional data analysis (FDA), particularly for modeling and forecasting observations represented by continuous curves or time-dependent functions. In contrast to conventional autoregressive models, which are designed for scalar or finite-dimensional vector observations, FAR models consider each observation as a function belonging to an infinite-dimensional Hilbert space. This functional framework provides greater flexibility in representing temporal dependence and the smooth structural features commonly encountered in complex functional datasets.
This research investigates the theoretical basis and practical use of FAR processes in forecasting functional time series. The proposed framework combines the principles of functional data analysis with autoregressive modeling to describe the dependence between successive functional observations. Since the infinite-dimensional nature of functional data presents significant computational and statistical challenges, functional principal component analysis (FPCA) is employed to extract the main modes of variation and achieve an effective dimensionality reduction. The resulting principal component scores are subsequently used to estimate the autoregressive operator and construct forecasting procedures.
The performance of the FAR methodology is evaluated through both simulation studies and applications to real-world datasets from several domains, including climate science, electricity consumption, financial modeling, and biomedical signal analysis. The results indicate that FAR models can provide accurate and reliable forecasts by effectively representing both smooth temporal evolution and complex dependence structures within functional observations. Overall, functional autoregressive processes constitute a flexible, robust, and computationally efficient framework for forecasting functional time series in a wide range of modern statistical applications.