A Reconstruction Approach for Noisy Data by using Techniques Based on Hankel Matrix and Least-Squares Approximation

บทคัดย่อ

Estimating missing data in volatile time series with oscillatory and noisy patterns is a challenging issue in many applications. This work introduces a technique for missing data imputation that combines data denoising and least-squares approximation. Our method first applies the Hankel Singular Value Decomposition (HSVD) to the dataset to filter out noise and capture the underlying data trend. The cleaned, trend-focused data then serves as the basis for a least-squares approximation to accurately estimate the missing values. This approach is specifically applicable for noisy datasets where related information is available, such as financial data from a stock market. The efficiency of this combined approach is validated through a numerical case study on the stock prices of companies within Thailand's healthcare sector. The results confirm that preprocessing the data with HSVD before applying the least-squares estimation leads to a more accurate and reliable reconstruction of missing entries, highlighting the method's potential for financial time series analysis.