This repository provides a brief introduction and Python implementations of various regression techniques applied to noisy and nonlinear time series data. The main objective is to evaluate the performance of different regression models under varying noise levels using synthetic datasets, particularly in the context of astronomical signal analysis.
- Linear Regression
- Polynomial Regression
- Fourier Regression
- Splines
- Kernel Regression
- GRNN (General Regression Neural Network)
Each method is applied to reconstruct nonlinear curves from artificially generated datasets.
The analysis involves the following steps:
- Use two nonlinear datasets:
DS-5-1-GAP-1-1-N-1_v2.dat(noise ≈ 0.106%)DS-5-1-GAP-5-1-N-3_v2.dat(noise ≈ 0.466%)
- Each dataset contains 201 rows (time samples) and over 100 columns (A1, A2, ..., A100)
- Use the first 100 curves (A1 to A100) per dataset
- For each curve:
- Train a regression model
- Measure Mean Squared Error (MSE) on:
- Training data
- Testing data (ground truth =
DS-5-1-GAP-0-1-N-0_v2.dat)
- Measure bias:
- Compute the difference between the mean regression curve and the ground truth
- Take the mean across all time steps
- Measure variance:
- Compute the standard deviation of all 100 models at each time step
- Take the mean across all time steps
Regression-Methods-Time-Series-Analysis/
│
├── ArtificialData/
│ ├── DS-5-1-GAP-0-1-N-0_v2.dat # Ground truth data (noise = 0)
│ ├── DS-5-1-GAP-1-1-N-1_v2.dat # Low noise level (0.106%)
│ └── DS-5-1-GAP-5-1-N-3_v2.dat # Higher noise level (0.466%)
│
├── src/ # Python scripts for regression methods
│
├── results/ # Output: MSE, bias, variance metrics
│
└── README.md
This project serves as a benchmarking platform to understand how different regression methods perform in reconstructing underlying patterns from noisy, irregular datasets — a common challenge in fields like astrophysics, signal processing, and time series analysis.
This project uses datasets provided by Dr. Juan Carlos Cuevas-Tello and is inspired by the methodology described in the following work
J. C. Cuevas-Tello, P. Tino, S. Raychaudhury, X. Yao, and M. Harva, "Uncovering delayed patterns in noisy and irregularly sampled time series: an astronomy application," arXiv preprint arXiv:0908.3706, 2009. [Online]. Available: https://doi.org/10.48550/arXiv.0908.3706
This study explores time delay estimation in gravitationally lensed quasar signals using kernel-based methods and evolutionary optimization.
Acknowledgments I would like to thank Dr. Juan Carlos Cuevas-Tello for providing the datasets used in this project and for his guidance on time delay estimation techniques in noisy and irregular time series.
- Astronomical signal reconstruction
- Time delay estimation in astrophysics
- General purpose time series denoising and modeling
- Benchmarking regression models under noise
You can run each method separately using Python 3.8+ and libraries like NumPy, SciPy, scikit-learn, etc.
Each model outputs error metrics and reconstructed curves for further analysis.
Patricia Sarahi Jimenez-Leura
Last updated: October 1, 2025
This project is open for academic and research purposes. Please cite the original paper if used in publications.