Forecasting data with long multi-seasonal periods in the arima model using discrete fourier transform regressors

Yap, Yi Xian (2024) Forecasting data with long multi-seasonal periods in the arima model using discrete fourier transform regressors. Final Year Project, UTAR.

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Abstract

Time series data with multiple seasonalities often appear in data observed at high frequency. For instance, daily observed data may exhibit multiple seasonal patterns due to the combination of weekly, monthly, or annual periodicities. Traditional forecasting methods, such as the Autoregressive Integrated Moving Average (ARIMA) model, face significant challenges when dealing with long, multiple seasonal cycles. Specifically, the ARIMA model fitting function may suffer from memory insufficiency when handling long seasonal periods and is generally designed to handle univariate time series with a single seasonal pattern. To address these challenges, this study proposed a novel forecasting approach by integrating Multiple Seasonal Trend decomposition using Loess (MSTL), Discrete Fourier Transform (DFT), and ARIMA. Firstly, the MSTL algorithm was employed to decompose the time series into their constituent components. For the seasonal components, the properties of the Discrete Fourier Transform were utilized to serve as regressors in the ARIMA framework. The non-seasonal components, including the trend and remainder, were fitted using the ARIMA model. The proposed MSTL-DFT-ARIMA approach was then compared with the TBATS model, a known benchmark for handling multiple seasonalities. From the results, MSTL-DFT-ARIMA approach outperforms TBATS in both forecast accuracy and computational efficiency. Hence, the integration of MSTL, DFT, and ARIMA provides a promising alternative for managing time series data with long multi-seasonal periods.

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