A hybrid supervised semi-supervised graph-based model to predict one-day ahead movement of global stock markets and commodity prices

Highlights

• A hybrid supervised semi-supervised model for financial prediction is proposed.

• The model uses both past data of markets being predicted and markets interactions.

• A network construction algorithm for modeling markets interactions is proposed.

• The network is constructed from the outset on the basis of prediction purpose.

• Markets interactions can be more important than past data of markets in prediction.

Abstract

Market prediction has been an important machine learning research topic in recent decades. A neglected issue in prediction is having a model that can simultaneously pay attention to the interaction of global markets along historical data of the target markets being predicted. As a solution, we present a hybrid supervised semi-supervised model called HyS3 for direction of movement prediction. The graph-based semi-supervised part of HyS3 models the markets global interactions through a network designed with a novel continuous Kruskal-based graph construction algorithm called ConKruG. The supervised part of the model injects results extracted from each market’s historical data to the network whenever the hybrid model allows with an innovative conditional mechanism. The significance of higher prediction accuracy of HyS3 is comparing to other models is proved statistically against other models including supervised models and network-based semi-supervised predictions.

Introduction

Prediction of financial time series has been an interesting machine learning topic according to many surveys (Atsalakis, Valavanis, 2009, Rather, Sastry, Agarwal, 2017, Sapankevych, Sankar, 2009, Soni, 2011). In this research, we will focus on predicting one-day ahead, falls and rises of financial time series that is referred to as direction of movement. The financial time series used in this study are some famous stock market indexes across the world, the gold spot price of 10 AM London and prices of different types of crude oil. There are complex interrelations among these financial markets. Some models are developed to show these relations in the field of econophysics (Gao, An, Zhong, 2013, Liu, Tse, 2012, Mantegna, Stanley, 1999, Papana, Kyrtsou, Kugiumtzis, Diks, 2017). They look at the global market environment as a complex system and model it using networks. Network modeling of relations among direction of movements of these markets showed to be useful for improving performance of prediction in the works of Park and Shin (2013) and Shin, Hou, Park, Park, and Choi (2013). We will provide a novel hybrid supervised semi-supervised model called HyS3 for market prediction using network modeling. A novel algorithm is also developed using a continuous Kruskal-based approach for making a graph called ConKruG to model complex markets interactions. In Table 1 the advantages of HyS3 to other models in the literature are presented briefly. Further descriptions and examples of existing researches related to the points mentioned in Table 1 are given in the following part of the introduction.

It can be assumed that direction of movement prediction is a binary classification problem. There are two major methods to classify unknown directions in machine learning literature: supervised and semi-supervised. In supervised learning, there are enough historical data and the aim of the model is to learn the past patterns to predict future directions. In semi-supervised learning, there are a few known market directions for markets that revealed their prices information. Graph-based semi-supervised learning¹ market prediction, models the interactions among markets with known or unknown direction with a graph. Zhu (2005) has explained graph-based semi-supervised models in his research. The known markets directions will be spread or propagated to markets with unknown directions. In this study, the earth is partitioned into four time zones in a way that for any given time, only markets in one time zone have revealed their close price information. Therefore, the direction of movement for them is known and the other zones have markets with unknown directions that can be predicted through a GSSL method. HyS3 uses ConKruG algorithm to make the graph. HyS3 uses a novel approach to inject the information from a supervised model (SVM² in our case), to the ConKruG network.

Many researches in machine learning like Patel, Shah, Thakkar, and Kotecha (2015), Kia, Fathian, and Gholamian (2012), Kara, Boyacioglu, and Baykan (2011) and Yao and Tan (2000) tried to predict a stock index or commodity price simply by its historical data. Some other researches like Fathian and Kia (2012), Huang, Nakamori, and Wang (2005) and Thawornwong and Enke (2004) tried to improve the performance of financial predictions by using some external factors as inputs of their supervised models along with historical data of the target market. Park and Shin (2013) and Shin et al. (2013) used some stock prices data in South Korean market and commodity prices in a network-based semi-supervised model without paying attention to the historical data of the time series being predicted and they achieved better results compared to their rival models using only historical data of the target market. The question that arises here is when to use the past data of target markets and when to use the data from other markets to predict the future direction of a market. HyS3 model has a novel approach for deciding how and when to combine information from historical data of target markets and information achieved from global markets interactions.

Finding the external factor(s) that can help the prediction is sometimes a trial and error task. Sometimes having a prior knowledge of the research domain makes this task easier. Researchers choose some helping markets to add as input next to the historical data of the market being predicted and then test if these helping markets make the prediction performance increase (Jaruszewicz & Mańdziuk, 2004). Other times, researchers choose among a list of time series by the means of a feature reduction algorithm (Tsai & Hsiao, 2010). We show that by using a network structure of relations among external factors ,the model can use a large number of external factors according to their distance and position to the markets that are going to be predicted. The network can regulate the effect of external factors in prediction if made with a purposeful method like ConKruG.

As the surveys like Rather et al. (2017), Soni (2011) Atsalakis and Valavanis (2009) and Sapankevych and Sankar (2009) show, in most studies one or a short list of stock indexes or commodity price time series are selected to be predicted by a model. The lack of a general prediction model is seen in the literature. ConKruG network can model interactions among any number of markets for prediction with HyS3.

Using network structure for market prediction is a newly opened research topic and therefore there are not enough studies up to now. Kia, Haratizadeh, and Heshmati (2016), Park and Shin (2013) and Shin et al. (2013) constructed networks that seemed to be helpful in modeling the complex relations among movements of financial time series. They first assumed that a special distance function or a special rule derived from their datasets may be helpful in constructing a prediction network and then tested their assumption. In our approach, ConKruG designs the network gradually by adding any helpful link for the prediction aim.

Another aspect of the research, is the time period of prediction. Narayan, Sharma, and Thuraisamy (2015) discuss the importance of data frequency in sampling. Noisy nature of financial time series makes it difficult to predict direction for short period frequencies. Therefore many models try to predict a threshold of change in the direction (Homm, Breitung, 2012, Roy, Sarkar, 2013) or use longer time periods like week or month (Boyacioglu & Avci, 2010) or simply try to predict the trend by smoothing the time series with moving averages or other methods (Park & Shin, 2013). In this paper, we construct a model for predicting daily direction of movement for everyday in markets across the globe despite the difficulties of improving the accuracy in the noisy financial environment and short time period.

The structure of the paper is as follows: in the next section some preliminaries about the GSSL and SVM are explained. At the end of the section two, we discuss our most important rival models prediction algorithms in brief. The third section explains our hybrid proposed model, HyS3 in detail and describes the proposed novel graph construction algorithm, ConKruG. The final section, explains the model settings and parameters, presents the results and discusses their interpretation. The last section concludes and has some suggestions for further researches.