Visit of Ta-Hsin Li to Unicamp, 2025

• Grant number: 25/13929-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: September 15, 2025
• End date: October 02, 2025
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Aluísio de Souza Pinheiro
• Visiting researcher: Ta-Hsin Li
• Visiting researcher institution: Ibm Thomas J. Watson Research Center - Cambridge/Ibmtwrc, United States
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/02538-0 - Time series, wavelets, high dimensional data and applications, AP.TEM

Abstract

This proposal focus on the following themes from the aforementioned thematic project: (a) generalizations of ARMA models; (b) wavelets - theory and applications; (c) machine learning and time series; (d) functional data spectral and applications; and (f) high-dimensional data analysis and applications, with emphasis on time series methods.We discuss here wavelet clustering and classification of high-dimensional data, under the machine learning paradigm. The discrete wavelt transform (DWT) is applied to the data before the employment of machine learning techniques. For SVM (support vector machines) and deep convolutional neural networks (RCP), the usual kernels and filters are replaced by wavelet kernels and wavelet filters, respectively.Another topic is wavelet variable selection. We follow Fonseca and Pinheiro (2020) and Fonseca et al. (2024). These works are based on wavelet representation to reduce the temporal dynamics' dimension and the number of co-variables, respectively. To reduce the complexity of the temporal dynamics, both procedures will be simultaneously applied.We consider here heteroskedastic time series models, specifically from the family GARCH(p,q), both on the time domain and well as on the frequency domain. For the former we estimate the (p+q)-dimensional parameter through M-quantiles. On the latter, we have employ the discrete Fourier transform (DFT), the cpestrum, and the wavelet spectrum. Two main cpestrum class of estimators based on the smoothed empirical periodogram are studied in this project. The first is defined through the $M$-quantile periodogram. The second is based on the thresholded empirical DWT. The estimators' statistical properties will be developed in this project. Moreover, scalability and on-line feasibility issues will be discussed here. For these high- and ultra-high dimensional properties, several approximate DFT and DWT methods will be employed, such as the fast DFT (FFT) and fast DWT (DFWT), among others. Simulation studies will be used to: compare the proposed methods to the state-of-the-art; and to illustrate the feasibility of such methods for high- and ultra-high dimension data. The proposed methodologies will be employed in three relevant real data problems: Air Quality Real-Time Monitoring; Cronic Respiratory Diseases; and Early Asymptomatic Degenerative Diseases Detection. (AU)