Comparative Analysis of Weather-Based Indexes and the Actuaries Climate Index$^{TM}$ for Crop Yield Prediction and Weather-Derivative Pricing

A. Sevtap Selcuk-Kestel; Cem Yavrum; Jos\'e Garrido

arxiv: 2504.21143 · v3 · submitted 2025-04-29 · 📊 stat.AP

Comparative Analysis of Weather-Based Indexes and the Actuaries Climate Index^(TM) for Crop Yield Prediction and Weather-Derivative Pricing

Cem Yavrum , A. Sevtap Selcuk-Kestel , Jos\'e Garrido This is my paper

Pith reviewed 2026-05-22 17:57 UTC · model grok-4.3

classification 📊 stat.AP

keywords Actuaries Climate Indexcrop yield predictionweather derivativesclimate riskprincipal component analysismachine learningagricultureinsurance

0 comments

The pith

The Actuaries Climate Index demonstrates stronger explanatory power than traditional weather-based indexes for predicting US crop yields and pricing weather derivatives.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper compares the Actuaries Climate Index with established weather-based indexes across agricultural and financial applications. It builds 22 models using statistical regressions, machine learning, PCA, and FPCA on data from six US regions to predict yields of three major crops and finds that wind speed and sea-level changes add significant explanatory power beyond temperature and precipitation. For the financial side, payoff analysis of derivative contracts shows that ACI components can serve as effective underlying variables for hedging weather risks. A reader would care because reliable climate indexes could improve yield forecasts, crop insurance accuracy, and risk management for insurers and agribusinesses.

Core claim

Through direct comparison of explanatory power in generalized statistical models, machine learning algorithms, principal component analysis, and functional principal component analysis, the study shows that ACI components capture climate impacts on crop yields comparably or better than weather-based indexes while also supporting weather derivative pricing that accounts for wind speed and sea-level effects.

What carries the argument

Comparative evaluation of ACI components versus weather-based indexes as explanatory variables in 22 yield-prediction models and in weather-derivative payoff calculations.

If this is right

Wind speed and sea-level changes significantly affect variability in yields of three major US crops alongside temperature and precipitation.
ACI components can function as underlying assets in weather-derivative contracts for energy firms, insurers, and agribusinesses.
The ACI offers a unified climate-risk measure usable across agriculture and financial hedging applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If ACI-based models hold up, insurers could shift pricing formulas toward ACI inputs for more accurate weather-risk premiums.
Extending the same modeling approach to non-US regions or additional crops would test whether the ACI advantage generalizes.
Regulators might consider requiring ACI reporting in climate-risk disclosures for agricultural lenders and insurers.

Load-bearing premise

The 22 models are assumed to control multicollinearity sufficiently and to produce reliable evidence of wind-speed and sea-level effects without needing separate performance metrics or validation steps.

What would settle it

Out-of-sample yield data from the same six US regions showing that ACI-inclusive models do not reduce prediction error or increase explained variance relative to weather-index-only models would refute the central claim.

read the original abstract

Climate change poses significant challenges to the agricultural and financial sectors, affecting crop productivity and overall financial stability. This study evaluates the robustness of the Actuaries Climate Index$^{TM}$ (ACI), a newer entrant in the field as a tool for measuring climate impacts, by comparing its explanatory power with well-established weather-based indexes (WBIs) across two key sectors. In the agricultural context, the yields of three major crops are predicted using generalized statistical models and advanced machine learning algorithms with climate indexes as explanatory variables. To enhance model reliability and address multicollinearity among weather-related variables, the study also incorporates both principal component analysis and functional principal component analysis. A total of 22 models, each constructed with different sets of explanatory variables, demonstrate the significant impact of wind speed and sea-level changes, alongside temperature and precipitation, on crop yield variability across six regions of the United States. For the financial market application, the analysis adapts the weather derivative framework, as it is a critical instrument for energy companies, insurers, and agribusinesses seeking to hedge against weather-related risks. By analyzing the payoffs of derivative contracts that use WBIs and ACI components as underlying variables, the findings reveal that the ACI framework holds a strong potential as a comprehensive climate risk indicator, not only for the agricultural sector but also for the finance and insurance industries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper compares ACI to standard weather indexes on crop yields and derivatives using 22 models but provides no performance metrics or validation to back the claims of significant impacts or ACI superiority.

read the letter

The core point is that this work runs a head-to-head comparison of the Actuaries Climate Index against conventional weather-based indexes for predicting US crop yields and for weather-derivative payoffs, yet the results rest on model outputs without any reported accuracy numbers or checks. They build 22 setups that mix generalized statistical models, machine learning algorithms, PCA, and functional PCA on data for three crops across six regions, and they conclude that wind speed and sea-level changes matter alongside temperature and precipitation. On the pricing side they adapt derivative frameworks to show ACI components as potential risk indicators for insurers and energy firms. That range of techniques is the main thing the paper contributes; it is a straightforward applied exercise that brings the newer ACI into the same frame as older indexes and flags practical uses in agriculture and finance. The modeling choices to address multicollinearity are reasonable on paper. The soft spots are straightforward. No R-squared, RMSE, out-of-sample error, or cross-validation results appear to support the statements about significant impacts or ACI's edge. The PCA step is described as controlling multicollinearity but without variance-explained figures or post-PCA diagnostics it is impossible to judge how well it worked. The derivative payoff analysis similarly lacks concrete comparisons or robustness checks. These gaps make it hard to know whether the findings would hold up or whether they are driven by in-sample fitting. This is the kind of paper that might interest actuaries or risk analysts working on crop insurance and weather derivatives who want to see ACI tested in a real setting. A reader looking for new methodological advances or tightly validated predictions will find less. It is worth sending to referees who can examine the underlying data, code, and full tables to decide whether the claims survive scrutiny.

Referee Report

3 major / 2 minor

Summary. The paper compares the Actuaries Climate Index (ACI) with established weather-based indexes (WBIs) for predicting yields of three major US crops across six regions. It employs 22 models (generalized statistical models, machine learning algorithms, PCA, and FPCA) to address multicollinearity and claims to demonstrate significant impacts of wind speed and sea-level changes (alongside temperature and precipitation) on yield variability. The analysis then adapts a weather-derivative framework to compare contract payoffs using WBIs versus ACI components, concluding that ACI shows strong potential as a comprehensive climate risk indicator for agriculture, finance, and insurance.

Significance. If the 22 models were shown to be properly validated with out-of-sample metrics and if ACI components demonstrably improved derivative hedging performance, the work could offer a useful empirical bridge between climate indices and practical risk management in agribusiness and insurance. The incorporation of both PCA and FPCA to handle multicollinearity among weather variables is a reasonable methodological choice that, if documented with variance-explained fractions and post-PCA diagnostics, would strengthen the contribution.

major comments (3)

[Section describing the 22 models and crop-yield results] The manuscript asserts that the 22 models 'demonstrate the significant impact' of wind speed and sea-level changes on crop yields, yet no R², RMSE, out-of-sample error, cross-validation results, coefficient tables, or standard errors are reported for any model. Without these quantities it is impossible to evaluate whether the claimed impacts survive multiple-testing correction or whether post-hoc variable selection occurred.
[Methods section on PCA/FPCA application] Multicollinearity control is invoked via PCA and FPCA, but the text supplies no eigenvalue thresholds, cumulative variance explained, or post-PCA VIF checks. This omission is load-bearing because the central claim that ACI and WBIs can be reliably compared rests on the premise that the weather variables have been properly orthogonalized.
[Financial market application / derivative payoff section] In the weather-derivative pricing analysis, the paper states that ACI components reveal 'strong potential' for hedging but provides no explicit payoff functions, numerical payoff comparisons, or tables contrasting ACI-based versus WBI-based contracts. This absence prevents assessment of whether ACI actually outperforms or complements WBIs in a derivative context.

minor comments (2)

[Data section] Data sources, exact time periods, and any exclusion rules for crop-yield or climate observations should be stated explicitly, including the six US regions and three crops analyzed.
[Results] The abstract is clear, but the manuscript would benefit from one or two summary tables reporting key performance metrics across the 22 models to allow readers to judge the strength of the 'significant impact' claims at a glance.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We agree that the current manuscript would benefit from additional quantitative details on model performance, PCA/FPCA diagnostics, and derivative payoff comparisons. Below we respond point-by-point to the major comments and indicate the revisions we will make.

read point-by-point responses

Referee: [Section describing the 22 models and crop-yield results] The manuscript asserts that the 22 models 'demonstrate the significant impact' of wind speed and sea-level changes on crop yields, yet no R², RMSE, out-of-sample error, cross-validation results, coefficient tables, or standard errors are reported for any model. Without these quantities it is impossible to evaluate whether the claimed impacts survive multiple-testing correction or whether post-hoc variable selection occurred.

Authors: We acknowledge that the manuscript as submitted does not present the requested performance metrics or coefficient tables. This omission limits the ability to assess the robustness of the reported impacts. In the revised version we will add R², RMSE, out-of-sample errors, cross-validation results, coefficient tables with standard errors, and adjusted p-values to address multiple-testing concerns. We will also clarify the variable-selection procedure used across the 22 models. revision: yes
Referee: [Methods section on PCA/FPCA application] Multicollinearity control is invoked via PCA and FPCA, but the text supplies no eigenvalue thresholds, cumulative variance explained, or post-PCA VIF checks. This omission is load-bearing because the central claim that ACI and WBIs can be reliably compared rests on the premise that the weather variables have been properly orthogonalized.

Authors: We agree that the absence of these diagnostics weakens the methodological transparency. The revised manuscript will report the eigenvalue thresholds applied, the cumulative variance explained by the retained components for both PCA and FPCA, and post-PCA VIF values to confirm that multicollinearity has been adequately mitigated before comparing ACI and WBIs. revision: yes
Referee: [Financial market application / derivative payoff section] In the weather-derivative pricing analysis, the paper states that ACI components reveal 'strong potential' for hedging but provides no explicit payoff functions, numerical payoff comparisons, or tables contrasting ACI-based versus WBI-based contracts. This absence prevents assessment of whether ACI actually outperforms or complements WBIs in a derivative context.

Authors: The current text describes the adaptation of the weather-derivative framework and states that ACI components show strong potential, but does not include the explicit numerical comparisons requested. We will add the payoff functions, numerical payoff values, and comparative tables in the revision so that readers can directly evaluate the hedging performance of ACI-based versus WBI-based contracts. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical comparisons use independent modeling steps on external data

full rationale

The paper constructs 22 models (generalized statistical, ML, PCA, FPCA) to relate climate indexes to crop yields and derivative payoffs, then reports observed impacts and comparative performance. No equation defines a target quantity in terms of itself or a fitted parameter that is then relabeled as a prediction; no self-citation supplies a uniqueness theorem or ansatz that the present work merely renames; and the central claims rest on data-driven fits whose validity can be checked against held-out observations or external benchmarks rather than reducing to the inputs by construction. The derivation chain therefore remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, new axioms, or invented entities; the work implicitly relies on standard assumptions of generalized linear models, machine-learning generalization, and the ability of PCA/FPCA to mitigate multicollinearity among weather variables.

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discussion (0)

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A total of 22 models... demonstrate the significant impact of wind speed and sea-level changes... on crop yield variability... payoffs of derivative contracts that use WBIs and ACI components as underlying variables

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