Hybrid Methods for Time Series Forecasting

Abstract

Time series forecasting is a crucial task in various fields of business and science. There are two coexisting approaches to time series forecasting, which are statistical methods and machine learning methods. Both come with different strengths and limitations. Statistical methods such as the Holt-Winters’ Method or ARIMA have been practiced for decades. They stand out due to their robustness and flexibility. Furthermore, these methods work well when few data is available and can exploit a priori knowledge. However, statistical methods assume linear relationships in the data, which is not necessarily the case in real-world data, inhibiting forecasting performance. On the other hand, machine learning methods such as Multilayer Perceptrons or Long Short-Term Memory Networks do not have the assumption of linearity and have the exceptional advantage of universally approximating almost any function. In addition to that, machine learning methods can exploit cross-series information to enhance an individual forecast. Besides these strengths, machine learning methods face several limitations in terms of data and computation requirements. Hybrid methods promise to advance time series forecasting by combining the best of statistical and machine learning methods. The fundamental idea is that the combination compensates for the limitations of one approach with the strengths of the other. This thesis shows that the combination of a Holt-Winters’ Method and a Long Short-Term Memory Network is promising when the periodicity of a time series can be precisely specified. The precise specification enables the Holt-Winters’ Method to simplify the forecasting task for the Long Short-Term Memory Network and, consequently, facilitates the hybrid method to obtain accurate forecasts. The research question to be answered is which characteristics of a time series determine the superiority of either statistical, machine learning, or hybrid approaches. The result of the conducted experiment shows that this research question can not be answered generally. Nevertheless, the results propose findings for specific forecasting methods. The Holt-Winters’ Method provides reliable forecasts when the periodicity can be precisely determined. ARIMA, however, handles overlying seasonalities better than the Holt-Winters’ Method due to its autoregressive approach. Furthermore, the results suggest the hypothesis that machine learning methods have difficulties extrapolating time series with trend. Finally, the Multilayer Perceptron can conduct accurate forecasts for various time series despite its simplicity, and the Long Short-Term Memory Network proves that it needs relevant datasets of adequate length to conduct accurate forecasts.