Peter Reinhard Hansen, Chen Tong
arXiv 3 May 2026 · Econometrics
arXiv:2605.01665 · PDF · DOI · OpenAlex · Extracted main text
The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its density, score, Hessian, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt approximations. The conditional expectation of the latent Gaussian component is governed by a redescending location score, so extreme observations are automatically discounted rather than propagated. This structure motivates the Gauss-Cauchy Convolution (GCC) filter for state-space models with Gaussian latent dynamics and heavy-tailed measurement errors. In an application to log realized volatility for the Technology Select Sector SPDR Fund, the GCC filter separates persistent latent variation from transient measurement noise and improves on Gaussian, Student-$t$, Huber, and related robust alternatives.
appendix boundary found by appendix_command · 61% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kendall, D. G (1938) The effect of radiation damping and Doppler broadening on the atomic absorption coefficient | 0.644 | 2 | 2 | 100% |
| 2 | Masreliez, C. J (1975) Approximate Non-Gaussian Filtering with Linear State and Observation Relations | 0.585 | 3 | 1 | 100% |
| 3 | Ali, Sajad Mohammed and van Zijl, Peter C. M. and Prasuhn, Jannik an… (2025) Machine learning-based multi-pool Voigt fitting of CEST, rNOE, and MTC in Z-spectra | 0.405 | 1 | 1 | 100% |
| 4 | Berg, Christian and Vignat, Christophe (2010) On the density of the sum of two independent Student t-random vectors | 0.405 | 1 | 1 | 100% |
| 5 | Cannas, Massimo and Piras, Nicola (2025) Estimation of Voigt Distribution Parameters: A Bayesian Approach | 0.405 | 1 | 1 | 100% |
| 6 | Catania, Leopoldo and D'Innocenzo, Enzo and Luati, Alessandra (2026) Unobserved Component Models, Approximate Filters and Dynamic Adaptive Mixture Models | 0.405 | 1 | 1 | 100% |
| 7 | Drew Creal and Siem Jan Koopman and André Lucas (2013) Generalized Autoregressive Score Models With Applications | 0.405 | 1 | 1 | 100% |
| 8 | D'Innocenzo, Enzo and Luati, Alessandra and Mazzocchi, Mario (2023) A Robust Score-Driven Filter for Multivariate Time Series | 0.405 | 1 | 1 | 100% |
| 9 | Di Rocco, H. O. and Aguirre Téllez, M (2004) Evaluation of the Asymmetric Voigt Profile and Complex Error Functions in Terms of the Kummer Functions | 0.405 | 1 | 1 | 100% |
| 10 | Durbin, James and Koopman, Siem Jan (2012) Time Series Analysis by State Space Methods | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Tweedie’s Formula and Score-Driven Updating | 0.405 | 1 | 1 |