The H-IAR Model for Irregular Multispectral Time Series. Quaternion Formulation, Mapping of Resilience Indicators, and Exploratory Identification of Forest Edges

RESUMO

We propose the Hypercomplex Irregular Autoregressive (\HIAR) model, a quaternion extension of the \IAR/\CIAR/\BIAR{} family for four-component observations at irregular times. Temporal dependence is represented by a real power of a quaternion parameter and estimated in state-space form through the Gaussian innovation likelihood of the Kalman filter, conditional on the adopted covariance specifications. Across 12,000 Monte Carlo fits, mean absolute bias decreased with sample size and ranged from 0.0009 to 0.0023 at $N=300$. We applied the model to 30,824 Sentinel-2 pixel series covering the Mata de Santa Genebra ARIE from 2020 to 2023. The optimizer reported successful numerical termination in 98.73\% of the fits; the median $\|{\Phihat}\|$ was 0.6248, 3,872 pixels met the operational high-persistence threshold ($\|{\Phihat}\}\geq0.95$), and the median residual RMSE for band B8 was 5.1551 percentage points. The results demonstrate the computational feasibility of \HIAR{} and its ability to generate descriptors of multispectral persistence, vector dynamics, predictive error, and spatial discontinuities potentially associated with forest edges.