Bayesian Multivariate Time Series for Climate Event Forecasting

Thesis Abstract

Climate variability and extreme weather events pose escalating risks to socio-economic systems, demanding robust predictive tools that can accommodate interdependent climate variables across spatial and temporal scales. This study addresses the challenge of forecasting climate events by advancing a Bayesian multivariate time series framework capable of capturing complex cross-variable dependencies and non-stationarities inherent in climate data. The aim is to develop, implement, and evaluate a probabilistic forecasting model that integrates multiple climate indicators (e.g., temperature, precipitation, sea-level pressure, and atmospheric indices) to improve the predictive accuracy and reliability of event forecasts such as heatwaves, droughts, and heavy rainfall episodes. The specific objectives are (i) to formulate a hierarchical Bayesian vector autoregressive model with dynamic correlation structures and regime-switching capabilities; (ii) to incorporate spatially aggregated data via a hierarchical spatio-temporal extension to reflect regional heterogeneity; (iii) to compare forecast performance against univariate benchmarks, classical VAR models, and machine learning surrogates using proper scoring rules; (iv) to conduct a rigorous sensitivity analysis on prior choices, model misspecification, and data quality issues; and (v) to translate probabilistic forecasts into operational decision-support metrics for climate risk management. The methodology adopts a design-based, empirical research approach grounded in Bayesian statistics and time-series theory. A multivariate climate dataset comprising monthly observations for 40 years (1980–2019) across 25 grid cells within a defined basin is employed, yielding approximately 300 data points per series and a total of 7,500 observations after pre-processing. Population-level inference is conducted on the aggregated grid-cell panel, while sub-sample analyses assess regional transferability. Data collection relies on publicly available, high-quality reanalysis products (e.g., ERA5) and satellite-derived precipitation estimates, harmonized to a common spatial resolution. Instruments include standardized climate indices, gridded rainfall accumulations, and surface air temperatures, with quality control procedures addressing missingness, measurement error, and temporal alignment. The analysis proceeds with (i) specification of a Bayesian VAR model with time-varying residual covariances implemented via a Wishart-Gaussian hierarchical prior, (ii) incorporation of a regime-switching mechanism to capture abrupt shifts linked to large-scale patterns such as ENSO and NAO, and (iii) the extension to a hierarchical spatio-temporal structure to balance regional specificity with cross-region borrowing of strength. Model estimation uses Markov chain Monte Carlo techniques, including Gibbs sampling and Metropolis-Hastings steps, executed on a high-performance computing cluster to ensure convergence diagnostics and adequate effective sample sizes. Model validation employs prequential scoring (predictive likelihood, continuous ranked probability scores) and after-hoc calibration assessments, with cross-validation across hold-out time windows and spatial blocks. Expected findings include improved probabilistic forecasts of climate events relative to univariate and standard VAR benchmarks, evidenced by reductions in log predictive density loss and superior CRPS scores across multiple horizons (1–12 months) and regions. The dynamic correlation structure is anticipated to reveal varying interdependencies among climate variables during different regimes, highlighting periods of heightened joint variability. The spatio-temporal extension is expected to demonstrate enhanced forecast skill in regions with stronger teleconnections, while maintaining robust performance in peripheral areas through partial pooling. The study will also quantify the value of incorporating regime-switching components and external forcings in shaping forecast uncertainty. The study contributes to knowledge by (i) delivering a coherent Bayesian multivariate framework that integrates regime dynamics and spatial heterogeneity for climate event forecasting; (ii) providing empirical evidence on the benefits of dynamic correlation modeling for improving forecast accuracy and reliability in climate risk applications; and (iii) offering methodological guidance for practitioners on model specification, prior elicitation, and decision-relevant forecast interpretation under uncertainty. The main conclusions anticipate that multivariate, regime-aware Bayesian models yield meaningful gains in forecast quality and decision-support value over traditional methods, particularly for tail-event prediction. Recommendations include adopting probabilistic, multivariate forecasting in operational climate services, extending the framework to incorporate nonlinearities and non-Gaussian observation processes, and expanding the spatial scope to multi-basin studies to enhance generalizability.