Reservoir computing and non-linear dynamics for time series analysis: An application in the financial market

In various time series analysis scenarios, especially when some type of forecasting is intended, a pre-analysis of volatility, seasonality, and other data characteristics is recommended before the use of a forecasting model. This is a common scenario, for example, in the financial market. In this sense, this research aims to develop a mathematical-computational solution at two levels. In the first one, non-linear dynamics techniques are applied. These are incorporated here through the Hurst exponent, so that the series are grouped and combined with this measure. The purpose here is to extract different characteristic patterns present in this non-linear dynamics metric. Next, a reservoir computing (RC) model is applied to each combination independently, aiming to obtain a more robust general system capable of significantly improving its performance compared to the original RC model and other state-of-the-art predictive techniques. We expect that the proposed model will be able to extract information on long-term dependence, trends, as well as persistence and antipersistence patterns present in the data, which are incorporated through the Hurst exponents. Such additional information is employed here to improve the forecasting capacity of the model.