A meta extreme learning machine method for forecasting financial time series

In the last decade, the problem of forecasting time series in very different fields has received increasing attention due to its many real-world applications. In particular, in the very challenging case of financial time series, the underlying phenomenon of stock time series exhibits complex behaviors, including non-stationary, non-linearity and non-trivial scaling properties. In the literature, a wide-used strategy to improve the forecasting capability is the combination of several models. However, the majority of the published researches in the field of financial time series use different machine learning models where only one type of predictor, either linear or nonlinear, is considered. In this paper we first measure relevant features present in the underlying process to propose a forecast method. We select the Sample Entropy and Hurst Exponent to characterize the behavior of stock time series. The characterization reveals the presence of moderate randomness, long-term memory and scaling properties. Thus, based on the measured properties, this paper proposes a novel one-step-ahead off-line meta-learning model, called -XNW, for the prediction of the next value x(t+1) of a financial time series xt, t = 1, 2, 3, ... , that integrates a naive or linear predictor (LP), for which the predicted value of xt+1 is just repeating the last value xt, an extreme learning machine (ELM) and a discrete wavelet transform (DWT), both based on the nprevious values of xt+1. LP, ELM and DWT are the constituent of the proposed model -XNW. We evaluate the proposed model using four well-known performance measures and validated the usefulness of the model using six high-frequency stock time series belong to the technology sector. The experimental results validate that including internal estimators that are able to the capture the relevant features measured (randomness, long-term memory and scaling properties) successfully improve the accuracy of the forecasting over methods that do not include them.