Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.31265 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910272096043008 |
|---|---|
| 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 |