Novel hybrid model based on echo state neural network applied to the prediction of stock price return volatility

Gabriel Trierweiler Ribeiro, André Santos, Viviana Cocco Mariani, Leandro dos Santos Coelho

Research output: Contribution to journalArticlepeer-review


The prediction of stock price return volatilities is important for financial companies and investors to help to measure and managing market risk and to support financial decision-making. The literature points out alternative prediction models - such as the widely used heterogeneous autoregressive (HAR) specification - which attempt to forecast realized volatilities accurately. However, recent variants of artificial neural networks, such as the echo state network (ESN), which is a recurrent neural network based on the reservoir computing paradigm, have the potential for improving time series prediction. This paper proposes a novel hybrid model that combines HAR specification, the ESN, and the particle swarm optimization (PSO) metaheuristic, named HAR-PSO-ESN, which combines the feature design of the HAR model with the prediction power of ESN, and the consistent PSO metaheuristic approach for hyperparameters tuning. The proposed model is benchmarked against existing specifications, such as autoregressive integrated moving average (ARIMA), HAR, multilayer perceptron (MLP), and ESN, in forecasting daily realized volatilities of three Nasdaq (National Association of Securities Dealers Automated Quotations) stocks, considering 1-day, 5-days, and 21-days ahead forecasting horizons. The predictions are evaluated in terms of r-squared and mean squared error performance metrics, and the statistical comparison is made through a Friedman test followed by a post-hoc Nemenyi test. Results show that the proposed HAR-PSO-ESN hybrid model produces more accurate predictions on most of the cases, with an average R2 (coefficient of determination) of 0.635, 0.510, and 0.298, an average mean squared error of 5.78x10-8, 5.78x10-8, and 1.16x10-7, for 1, 5, and 21 days ahead on the test set, respectively. The improvement is statistically significant with an average rank of 1.44 considering the three different datasets and forecasting horizons.
Original languageEnglish
Article number115490
JournalExpert Systems with Applications
Early online date29 Jun 2021
Publication statusPublished - 1 Dec 2021


  • volatility prediction
  • echo state network
  • heterogenous autoregressive model
  • particle swarm optimization


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