Functional time series (FTS) extend traditional methodologies to accommodate data observed as functions/curves. A significant challenge in FTS consists of accurately capturing the time-dependence structure, especially with the presence of time-varying covariates. When analyzing time series with time-varying statistical properties, locally stationary time series (LSTS) provide a robust framework that allows smooth changes in mean and variance over time. This work investigates Nadaraya-Watson (NW) estimation procedure for the conditional distribution of locally stationary functional time series (LSFTS), where the covariates reside in a semi-metric space endowed with a semi-metric. Under small ball probability and mixing condition, we establish convergence rates of NW estimator for LSFTS with respect to Wasserstein distance. The finite-sample performances of the model and the estimation method are illustrated through extensive numerical experiments both on functional simulated and real data.

Locally stationary processes (LSPs) provide a robust framework for modeling time-varying phenomena, allowing for smooth variations in statistical properties such as mean and variance over time. In this paper, we address the estimation of the conditional probability distribution of LSPs using Nadaraya-Watson (NW) type estimators. The NW estimator approximates the conditional distribution of a target variable given covariates through kernel smoothing techniques. We establish the convergence rate of the NW conditional probability estimator for LSPs in the univariate setting under the Wasserstein distance and extend this analysis to the multivariate case using the sliced Wasserstein distance. Theoretical results are supported by numerical experiments on both synthetic and real-world datasets, demonstrating the practical usefulness of the proposed estimators.

A total of nine Artificial Intelligence (AI) research and development (R&D) projects by the DOST-Advanced Science and Technology Institute (DOST-ASTI), University of the Philippines Mindanao (UPMin), De La Salle University (DLSU), University of the Philippines Los Baños (UPLB), and Caraga State University (CarSU) were launched by the Philippines' Department of Science and Technology (DOST Philippines) in April 2021. The AI R&D projects ranging from applications in agriculture to the education sector were launched on April 8 by the Department of Science and Technology – Philippine Council for Industry, Energy and Emerging Technology Research and Development (DOST-PCIEERD) to spur growth in the AI industry in the Philippines. "AI is one of our priority areas as it truly can boost the country and usher us to the fourth industrial revolution. As a powerful agent for good, AI can disrupt traditional processes and provide solutions and opportunities that Filipinos can maximize," said DOST-PCIEERD Executive Director Dr. Enrico C. Paringit during the virtual launch. The Autonomous Societally Inspired Mission Oriented Vehicles (ASIMOV) Program, composed of two-component projects, will be implemented by DOST-ASTI and UPMin.