Date Published: July 14, 2017
Publisher: Public Library of Science
Author(s): Wei Bao, Jun Yue, Yulei Rao, Boris Podobnik.
The application of deep learning approaches to finance has received a great deal of attention from both investors and researchers. This study presents a novel deep learning framework where wavelet transforms (WT), stacked autoencoders (SAEs) and long-short term memory (LSTM) are combined for stock price forecasting. The SAEs for hierarchically extracted deep features is introduced into stock price forecasting for the first time. The deep learning framework comprises three stages. First, the stock price time series is decomposed by WT to eliminate noise. Second, SAEs is applied to generate deep high-level features for predicting the stock price. Third, high-level denoising features are fed into LSTM to forecast the next day’s closing price. Six market indices and their corresponding index futures are chosen to examine the performance of the proposed model. Results show that the proposed model outperforms other similar models in both predictive accuracy and profitability performance.
Stock market prediction is usually considered as one of the most challenging issues among time series predictions  due to its noise and volatile features. How to accurately predict stock movement is still an open question with respect to the economic and social organization of modern society. During the past decades, machine learning models, such as Artificial Neural Networks (ANNs)  and the Support Vector Regression (SVR) , have been widely used to predict financial time series and gain high predictive accuracy [4–8]. In the literature, however, a recent trend in the machine learning and pattern recognition communities considers that a deep nonlinear topology should be applied to time series prediction. An improvement over traditional machine learning models, the new one can successfully model complex real-world data by extracting robust features that capture the relevant information  and achieve even better performance than before . Considering the complexity of financial time series, combining deep learning with financial market prediction is regarded as one of the most charming topics . However, this field still remains relatively unexplored.
To generate the deep and invariant features for one-step-ahead stock price prediction, this work presents a deep learning framework for financial time series using a deep learning-based forecasting scheme that integrates the architecture of stacked autoencoders and long-short term memory. Fig 1 shows the flow chart of this framework. The framework involves three stages:(1) data preprocessing using the wavelet transform, which is applied to decompose the stock price time series to eliminate noise; (2) application of the stacked autoencoders, which has a deep architecture trained in an unsupervised manner; and (3) the use of long-short term memory with delays to generate the one-step-ahead output. The detailed approach of each block is further detailed as follows.
In this part, we present details regarding our sample selection and the input variables we choose for model prediction. Also, the data resources are provided in this section.
We present the details regarding how we obtain the predicted value and evaluate the performance of each model.
For each stock index, we show the yearly predicted data from the four models and the corresponding actual data in the graph. Fig 8 illustrates Year 1 results and the remaining figures for Year 2 to Year 6 can be found in S1–S5 Figs. According to Fig 8 and S1–S5 Figs, we can find that LSTM and RNN have larger variations and distances to the actual data than WSAEs-LSTM and WLSTM. Furthermore, comparing WSAEs-LSTM with WLSTM, the former outperforms the latter: WSAEs-LSTM has less volatility and is closer to the actual trading data than WLSTM. Specifically, the advantage of WSAEs-LSTM in predicting is more obvious in less developed markets than in developed market.
This paper builds a novel forecasting framework to predict the one-step-ahead closing price of six popular stock indices traded in different financial markets. The procedure for building this forecasting framework is as follows: First, the denoised time series is generated via discrete wavelet transform using the Haar wavelet; second, the deep daily features are extracted via SAEs in an unsupervised manner; third, long-short term memory is used to generate the one-step-ahead output in a supervised manner. Our input variables include the daily OHLC variables, technical indicators and macroeconomic variables. The main contribution of this work to the community is that it is the first attempt to introduce SAEs method to extract deep invariant daily features of financial time series. In addition, the deep learning framework is proposed with a complete set of modules for denoising, deep feature extracting instead of feature selection and financial time series fitting. Within this framework, the forecasting model can be developed by replacing each module with a state-of-the-art method in the areas of denoising, deep feature extracting or time series fitting.