Performance Evaluation of Wavelet-Based Models for Climate Extremes: A Simulation Study

Climate extremes, such as heatwaves and floods, exhibit seasonal patterns that are gradually shifting in both amplitude and timing due to climate change. Existing statistical models for extremes typically assume either stationarity or fixed periodic seasonality, failing to capture these evolving patterns. This limitation can lead to biased risk assessments and underestimation of future extreme events. We propose a novel wavelet-based framework for modelling non-stationary extremes that allows both the magnitude and timing of seasonal patterns to shift gradually over time. Our approach embeds time-localised wavelet transforms into the scale parameter of the Generalised Pareto Distribution (GPD), enabling flexible representation of evolving seasonal structures without imposing rigid periodicity assumptions. Through extensive Monte Carlo simulations across three scenarios (amplitude shifts, timing shifts, and combined shifts), we demonstrate that the wavelet-based model substantially outperforms conventional approaches. Compared with stationary models, our method reduces the root mean square error (RMSE) by up to 75% in amplitude shift scenarios, while Fourier-based and B-spline alternatives achieve only 53% and 47% reductions, respectively. The wavelet framework maintains robust parameter recovery across all scenarios and achieves consistently lower AIC and BIC values. Sensitivity analyses confirm model stability across sample sizes (15-100 years), thresholds (85th-99th percentiles), and wavelet specifications, with optimal performance at 2-3 wavelet components. These findings establish wavelet-based modelling as a powerful and practical tool for characterising evolving climate extremes, with direct implications for improved risk assessment and adaptation planning.