Ensemble of Time Series Forecasting Models through Copula Functions
Forecast; Machine Learning; Copulas function; Time series.
The financial market is a highly dynamic environment, characterized by significant volatility in the data associated with its processes. Consequently, modeling and predicting time series derived from these markets pose substantial challenges. However, comprehending the behavior of financial time series plays a pivotal role in making more informed decisions in the business domain. Consequently, numerous studies aim to develop sophisticated methodologies for forecasting series, with a particular emphasis on financial time series prediction. Notably, studies that employ multiple models to perform forecasts have garnered attention. The combination of time series forecasting models has consistently yielded more accurate results than individual models, as demonstrated by several works in the literature. As a result, numerous techniques promoting the combination of forecasting models have been introduced since the previous century. Research efforts have focused on devising accurate combination models that effectively weight all the involved models. In this study, our objective is to showcase the potential of utilizing copula functions to combine deep learning techniques for predicting financial time series. Specifically, we employ established individual forecasting models, such as ARIMA, Artificial Neural Networks (ANN), and recurrent deep learning networks (Long Short Term Memory - LSTM), to predict five financial time series. Performance metrics, including Rooted Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Prediction of Change in Direction (POCID), are used to compare the results. The ensemble techniques employed in this article include simple mean, simple median, copula functions, and MLPs. The findings of this study demonstrate that combining copula functions with deep learning approaches yields superior results compared to other approaches documented in the literature. Overall, we conclude that, in the context of financial time series, combining deep learning techniques using copula functions generally leads to more accurate predictions in terms of accuracy.