Improved Forecasting for Multivariate Time Series using GNAR models with General Inverse Distance Weights
Year: 2026
Type: preprint
Abstract: Many multivariate time series arise on networks where relationships between variables depend on physical or more general distances. Standard vector autoregressive models struggle in such settings due to their quadratic parameter growth, while generalised network autoregressive (GNAR) models offer a parsimonious alternative by explicitly incorporating network structures. Existing GNAR formulations assume fixed weights, typically uniform or reciprocal distances, which may not reflect the true influence of distance in real systems. We introduce a novel model with general inverse distance weights (GNARID) that extends GNAR by introducing a tunable exponent parameter that controls the strength of distance penalisation. We establish theoretical results on the consistency and asymptotic normality of new GNARID estimators, including an extension to the setting where the number of nodes grows. We analyse the effect of misspecifying the exponent on forecasting error, which helps assess how much GNAR models could be improved by our tunable weights. Simulation studies confirm the theoretical properties and show measurable benefits from correct weight specification. Using the Brumadinho ground displacement dataset, we show that proper tuning of the weight exponent improves predictive performance, highlighting the practical value of flexible distance-based weighting in network time series models.
Source: arXiv (Cornell University)
Institutions: Imperial College London, Curtin University
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222123323