Forecasting of Multiple Seasonal Categorical Time Series Using Fourier Series with Application to AQI Data of Kolkata

2026-03-04

AI Summary

This study addresses the challenge of effectively modeling ordinal categorical time series exhibiting multiple seasonal patterns—such as daily, weekly, and annual cycles—as commonly observed in air quality index (AQI) data. The authors propose a novel modeling framework that integrates Fourier series with indicator functions, extending multi-seasonal Fourier representations to ordinal categorical responses for the first time. This approach explicitly captures complex seasonal dynamics while preserving the inherent ordering of categories. The method offers both interpretability and flexibility, with theoretical analysis establishing consistency of parameter estimates. Comprehensive simulations and empirical analysis of AQI data from Kolkata demonstrate that the proposed model significantly outperforms Markov models and prevailing machine learning approaches, achieving substantial improvements in both predictive accuracy and the ability to capture intricate seasonal patterns.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Multimodal Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Multiple seasonalities have been widely studied in continuous time series using models such as TBATS, for instance in electricity demand forecasting. However, their treatment in categorical time series, such as air quality index (AQI) data, remains limited. Categorical AQI often exhibits distinct seasonal patterns at multiple frequencies, which are not captured by standard models. In this paper, we propose a framework that models multiple seasonalities using Fourier series and indicator functions, inspired by the TBATS methodology. The approach accommodates the ordinal nature of AQI categories while explicitly capturing daily, weekly and yearly seasonal cycles. Simulation studies demonstrate the empirical consistency of parameter estimates under the proposed model. We further illustrate its applicability using real categorical AQI data from Kolkata and compare forecasting performance with Markov models and machine learning methods. Results indicate that our approach effectively captures complex seasonal dynamics and provides improved predictive accuracy. The proposed methodology offers a flexible and interpretable framework for analyzing categorical time series exhibiting multiple seasonal patterns, with potential applications in air quality monitoring, energy consumption and other environmental domains.

Problem

• categorical time series
• multiple seasonalities
• air quality index
• forecasting
• seasonal patterns

Innovation

• Fourier series
• categorical time series
• multiple seasonality
• AQI forecasting
• ordinal data