.png){kind=icon}
.png){kind=icon}
Return
Functional recurrent neural network for vector-on-functional data modeling
.png){kind=icon}
PRE
AI
DOI：10.1080/02331888.2026.2645115.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In recent years, functional neural networks (FNNs) have been widely employed to model independently and identically distributed (i.i.d.) functional data. However, functional time series typically exhibit strong temporal dependence across observations. Existing approaches generally incorporate several lags of the series as inputs to construct an FNN model, but this strategy fails to fully exploit historical information. To effectively capture the potential nonlinear, dynamic, and temporal dependencies between vector (or scalar) responses and functional time series, we propose three novel frameworks that integrate recurrent neural networks with functional data characteristics: the functional recurrent neural network (FRNN), the functional long short-term memory (FLSTM), and the functional gated recurrent unit (FGRU). Unlike conventional methods that discretize functional data into high-dimensional vectors, our approach directly processes functional objects, thereby preserving their inherent structure and more effectively modeling temporal dependencies. This design mitigates the adverse effects of high dimensionality and inter-variable correlation. Extensive simulation studies and real-world applications confirm that the proposed methods provide substantial improvements in modeling dependence within functional time series and enhance prediction accuracy.
Keywords:
FGRU
FLSTM
FRNN
vector-on-functional data model