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Main Authors: Maturo, Fabrizio, Rambaud, Salvador Cruz, Calzi, Vincenzo Li, Mazzitelli, Andrea, Porreca, Annamaria
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2605.31265
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author Maturo, Fabrizio
Rambaud, Salvador Cruz
Calzi, Vincenzo Li
Mazzitelli, Andrea
Porreca, Annamaria
author_facet Maturo, Fabrizio
Rambaud, Salvador Cruz
Calzi, Vincenzo Li
Mazzitelli, Andrea
Porreca, Annamaria
contents Intertemporal choice data are usually summarized through scalar discount-rate parameters or fitted by predetermined parametric discount functions, although relevant information may lie in the shape of the whole discounting trajectory. This paper proposes a Functional Data Analysis framework for reconstructing and analyzing implicit subjective-time trajectories from discrete intertemporal equivalence judgments. Monetary equivalence responses from a multilingual questionnaire are transformed into individual discount curves, regularized by monotone smoothing, and used to recover normalized implicit subjective-time trajectories. The trajectories are examined through derivative summaries, Functional Principal Component Analysis, and clustering on standardized component scores. The empirical application, based on 107 participants, shows that heterogeneity in intertemporal choice is not fully captured by scalar discount-rate variation. The first two functional principal components explain 97.44% of the variability, indicating a low-dimensional structure. Functional clustering identifies three stable profiles of temporal deformation, supported by bootstrap stability analysis and sensitivity checks on components, algorithms, distances, smoothing specifications, and outlier treatment. Parametric benchmarks based on exponential, Weber-Fechner, and Stevens specifications provide accurate fits for many individuals, but do not fully recover the functional clustering structure. The comparison with explicit subjective-time perception measures reveals only partial alignment between implicit trajectories reconstructed from choices and directly reported temporal perception. Functional Data Analysis provides an applied statistical framework for representing intertemporal choice heterogeneity as variation in functional shape, complementing scalar discount-rate and parametric subjective-time models.
format Preprint
id arxiv_https___arxiv_org_abs_2605_31265
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Subjective Time Deformation in Intertemporal Choice: A Functional Data Analysis Approach
Maturo, Fabrizio
Rambaud, Salvador Cruz
Calzi, Vincenzo Li
Mazzitelli, Andrea
Porreca, Annamaria
Applications
62R10, 62H30, 91B06
G.3; I.5.3; J.4
Intertemporal choice data are usually summarized through scalar discount-rate parameters or fitted by predetermined parametric discount functions, although relevant information may lie in the shape of the whole discounting trajectory. This paper proposes a Functional Data Analysis framework for reconstructing and analyzing implicit subjective-time trajectories from discrete intertemporal equivalence judgments. Monetary equivalence responses from a multilingual questionnaire are transformed into individual discount curves, regularized by monotone smoothing, and used to recover normalized implicit subjective-time trajectories. The trajectories are examined through derivative summaries, Functional Principal Component Analysis, and clustering on standardized component scores. The empirical application, based on 107 participants, shows that heterogeneity in intertemporal choice is not fully captured by scalar discount-rate variation. The first two functional principal components explain 97.44% of the variability, indicating a low-dimensional structure. Functional clustering identifies three stable profiles of temporal deformation, supported by bootstrap stability analysis and sensitivity checks on components, algorithms, distances, smoothing specifications, and outlier treatment. Parametric benchmarks based on exponential, Weber-Fechner, and Stevens specifications provide accurate fits for many individuals, but do not fully recover the functional clustering structure. The comparison with explicit subjective-time perception measures reveals only partial alignment between implicit trajectories reconstructed from choices and directly reported temporal perception. Functional Data Analysis provides an applied statistical framework for representing intertemporal choice heterogeneity as variation in functional shape, complementing scalar discount-rate and parametric subjective-time models.
title Subjective Time Deformation in Intertemporal Choice: A Functional Data Analysis Approach
topic Applications
62R10, 62H30, 91B06
G.3; I.5.3; J.4
url https://arxiv.org/abs/2605.31265