Exploiting Functional Time Series Prediction for PM2.5 Based on Multivariate Variational Mode Decomposition and Anomaly Detection

Abstract

This paper presents a novel approach to high-frequency time series forecasting in the context of functional time series, addressing challenges such as data complexity and outliers. The proposed hybrid model integrates outlier detection, multivariate variational mode decomposition (MVMD), and model pooling to enhance forecasting accuracy. Initially, outliers are identified using the isolation forest technique and subsequently replaced with smoothed values via a sliding window moving average. MVMD is then employed to decompose the time series into high-, mid-, and low-frequency components, based on sample entropy. Discrete daily observations are transformed into functional data using Fourier basis functions, and functional principal component analysis (FPCA) is applied for dimensionality reduction, generating principal component scores and functions. Forecasting is carried out through model pooling, which combines statistical, machine learning, and deep learning techniques to predict the principal component scores. The final prediction is obtained by aggregating the forecasts of the predicted scores and their corresponding principal component functions. Empirical results, based on PM2.5 forecasting, demonstrate that the proposed approach significantly outperforms alternative models, offering valuable contributions to air quality monitoring and informed decision-making.