Distributional regression for seasonal data: an application to river flows

Paper: arXiv 2510.18639

Authors: Samuel Perreault, Silvana M. Pesenti, Daniyal Shahzad

Abstract

Risk assessment in casualty insurance, such as flood risk, traditionally relies on extreme-value methods that emphasizes rare events. These approaches are well-suited for characterizing tail risk, but do not capture the broader dynamics of environmental variables such as moderate or frequent loss events. To complement these methods, we propose a modelling framework for estimating the full (daily) distribution of environmental variables as a function of time, that is a distributional version of typical climatological summary statistics, thereby incorporating both seasonal variation and gradual long-term changes. Aside from the time trend, to capture seasonal variation our approach simultaneously estimates the distribution for each instant of the seasonal cycle, without explicitly modelling the temporal dependence present in the data. To do so, we adopt a framework inspired by GAMLSS (Generalized Additive Models for Location, Scale, and Shape), where the parameters of the distribution vary over the seasonal cycle as a function of explanatory variables depending only on the time of year, and not on the past values of the process under study. Ignoring the temporal dependence in the seasonal variation greatly simplifies the modelling but poses inference challenges that we clarify and overcome. We apply our framework to daily river flow data from three hydrometric stations along the Fraser River in British Columbia, Canada, and analyse the flood of the Fraser River in early winter of 2021.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous statistical framework extending GAMLSS for seasonal environmental risk modeling, carefully addressing inference challenges in misspecified models with temporal dependence. The methodology is thoroughly validated using extensive daily river flow data from the Fraser River, offering a flexible distributional regression alternative to classical extreme-value techniques for casualty insurance risk assessment.

Research Flowchart

  flowchart TD
    A[Research Goal: Model full daily distribution of environmental variables for risk assessment] --> B[Data Inputs: Daily river flow from 3 Fraser River stations, BC]
    B --> C[Methodology: GAMLSS-inspired Distributional Regression Framework]
    C --> D[Model Features: Parameterize seasonal cycles & long-term trends without past-value dependence]
    D --> E[Inference Adjustment: Overcome challenges from ignoring temporal dependence]
    E --> F[Case Study & Outcomes: Successfully characterized non-stationary distributions & analyzed 2021 Fraser River flood]

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0 of 82 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.