# Time series modeling by a regression approach based on a latent process

arXiv: https://arxiv.org/abs/1312.6969 · HTML: https://mlsanity.com/paper/1312.6969/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2013.

## Built on by (most cited first, 6 of 6)

- [Demystifying Softmax Gating Function in Gaussian Mixture of Experts](https://mlsanity.com/paper/2305.03288/) (2023)
- [Statistical Perspective of Top-K Sparse Softmax Gating Mixture of Experts](https://mlsanity.com/paper/2309.13850/) (2023)
- [Functional mixture-of-experts for classification](https://mlsanity.com/paper/2202.13934/) (2022)
- [Dendrograms of Mixing Measures for Softmax-Gated Gaussian Mixture of Experts: Consistency Without Model Sweeps](https://mlsanity.com/paper/2510.12744/) (2025)
- [An Introduction to the Practical and Theoretical Aspects of Mixture-of-Experts Modeling](https://mlsanity.com/paper/1707.03538/) (2017)
- [Rethinking Multinomial Logistic Mixture of Experts with Sigmoid Gating Function](https://mlsanity.com/paper/2602.01466/) (2026)

## Abstract (arXiv)

Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such data. A new approach for time series modeling is proposed in this paper. It consists of a regression model incorporating a discrete hidden logistic process allowing for activating smoothly or abruptly different polynomial regression models. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The M step of the EM algorithm uses a multi-class Iterative Reweighted Least-Squares (IRLS) algorithm to estimate the hidden process parameters. To evaluate the proposed approach, an experimental study on simulated data and real world data was performed using two alternative approaches: a heteroskedastic piecewise regression model using a global optimization algorithm based on dynamic programming, and a Hidden Markov Regression Model whose parameters are estimated by the Baum-Welch algorithm. Finally, in the context of the remote monitoring of components of the French railway infrastructure, and more particularly the switch mechanism, the proposed approach has been applied to modeling and classifying time series representing the condition measurements acquired during switch operations.