An introduction to Machine learning methods and forecasting of time series in financial markets

Transcription

1 An introduction to Machine learning methods and forecasting of time series in financial markets Mark Wong December 10, 2016 Abstract The goal of this paper is to give the reader an introduction to basic Machine learning methods and its use in financial markets, more specifically predicting future time series of stocks and indices. This paper then presents the findings of papers that have implemented these methods in terms of result, performance and reliability. The findings are then critically discussed and and the conclusion is that there exists some proof for prediction of time series for stocks and indices for certain industries. In a real life application, factors such as transaction costs would heavily affect the success of using these methods. Thus, the author concludes that the methods do not beat a buy and hold strategy meaning that there exists support for the EMH [7]. 1

2 CONTENTS DD1395 Contents 1 Terminology 3 2 Introduction Machine learning Financial market Purpose 4 4 Method Financial markets Machine learning algorithms Decision Trees Support Vector Machines (SVM) Support Vector Regression (SVR) Experiments and results 7 6 Discussion 9 2

3 1 Terminology DD Terminology MA-50: The mean of the price of a stock/index for the past 50 trading days. MA-200: The mean of the price of a stock/index for the past 200 trading days. RSI: A technical indicator intended to show current and historical strength of a stock/index. EMH: Investment theory that states that stocks/indices price always fully reflect all available information. This implies that it is impossible to beat the market. [7] OBX: The OBX Index is a stock market index which lists the 25 most liquid companies on the main index of the Oslo Stock Exchange in Norway DOW: The DOW Index is a stock market index which lists the 30 most liquid companies on the main index of the New York Stock Exchange in the United States. TAIEX: The TAIEX Index is a stock market index which lists all the companies on the main index of the Taiwan Stock Exchange in Taiwan. S&P500: The S&P500 Index is a stock market index which lists the 500 largest companies on the main index of the New York Stock Exchange in the United States. 3

4 2 Introduction DD Introduction Being able to predict the future is something that has always fascinated mankind. Since the inception of the digital era scientists have researched the possibility of building Artificial Intelligence (AI). The definition of the term has undergone changes since its birth. Informally AI has from a layman s perspective been seen as a robot machine that is able to mimic the behaviour of humans in terms of knowledge and to some degree self-awareness. The AI that many scientists today focus on is building a machine that based on a source takes actions that maximizes a goal function. Depending on the goal, the actions taken differ. 2.1 Machine learning Machine learning (ML) on the other hand is a field in computer science and is also a subset of Artificial Intelligence. To get a grasp of what machine learning is, one can think of it as the practice of getting a computer to make rational guesses without having seen the question before by feeding it similar questions before with the corresponding answer. This type of task is called supervised learning and is one of the three categories that ML typically is classified into [5]. The other two categories are unsupervised learning and reinforcement learning that this paper will not touch. The use of machine learning in our society is widespread and has its use in all kind of fields. A few examples where machine learning techniques are used and relied on are insurance companies, medical facilities, services and economics. In the insurance field it can be used to detect fraudulent behaviour by detecting anomalies. In medical facilities it can assist medical personell to detect diseases before symptoms appear. In services it can help detect unwanted spam s. Lastly in economics it can be used for forecasting prices and simulating/assessing performance and risk. 2.2 Financial market A financial market is a trading place in which people exchange equities, financial instruments such as futures, commodities and bonds (ETF). A trade has two counterparties and is priced at a level that both sides settle on. As the financial markets operate in real time, the trade price is effectively based on the current supply and demand. Efficient market hypothesis (EMH) states that the price of an asset fully reflect all available information. This implies that the future stock price is completely unpredictable and independent given previous trading history of the stock [7]. 3 Purpose With the increasing computational power and storage possibilities and decrease in computational cost we have never had a better opportunity to use the big data that is out there for forecasting with machine learning methods. The purpose of this paper is to delve into how ML methods are used in the financial markets and how successful it is compared to traditional strategies. In other words this paper will investigate if there is any support for the EMH. 4

5 4 Method DD Method The author has an academic background in Machine Learning and some basic knowledge in financial markets. The author has furthered his knowledge in both areas and how it can be used by reading course literature from the Machine Learning courses at KTH and further combining them by pre-existing journal articles and scientific papers. All results are based on scientific experiments conducted by authors referenced in this paper. Conclusions made in this paper are based both on the authors own analysis but also the underlying papers conclusions. 4.1 Financial markets The financial markets this paper will investigate is primarily the stock market. A stock in a company represents an ownership in the equity of the company. The stock market is a public market for trading stocks for companies that are listed in the market. As the value of a company fluctuates with time depending on factors as how well they generate revenue, at what rate the economic growth is increasing etc. it will naturally effect the value of its stock. This paper will partly investigate how well we can model the history to be able to predict future the time-series of the price of a stock using Machine learning. It will also take in to consideration the risk factor where a low-risk/high-return is preferred over a high-risk/high-return result. 4.2 Machine learning algorithms As previously mentioned this paper will only discuss supervised learning methods. In essence supervised learning is the process of trying to estimate some unknown feature associated with a data point [1]. This data point is typically represented in a high dimensional space and is a combination of all the features we deem are relevant for a data point. In the learning phase we have a data set with data points and their corresponding label that the model later use to base its classification or regression output Decision Trees Decision trees is a method that can be both be applied to classification and regression problems. It is commonly used in more basic scenarios due to it being intuitive to construct and read, and for its simplistic tree-structure. The idea behind Decision trees is that we construct a tree data structure with decisions/splits based on a criteria at every node until we reach a leaf. When constructing a Decision tree one would like to identify the attributes that increases the information gain. Before we move on to information gain I must mention that entropy in this field is a measure of uncertainty. The entropy can be given as: Ent = p i log 2 p i (1) i where i is the number of different outputs and p i is the probability of that output occurring. To maximize information we would naturally like to reduce the uncertainty and this is can done by choosing an attribute A such that the entropy of the 5

6 4 Method DD1395 data set prior to the split is greater than after the split. In other words we would like to utilise an attribute which will give us the greatest gain: Gain = Ent(S) v V alues(a) S v S Ent(S v) (2) where S is a dataset and A is the attribute we want to calculate the gain in entropy for. An fictive example of how it can be used for a binary classification problem where we would like to know if a stock s trading price will increase or decrease is given in the figure 1: Figure 1: Decision tree showing splits and classifications. In this example we split on the decisions whether: the MA-50 of the stock price has crossed the MA-200 the average trading volume is greater than USD the RSI Index is greater than Support Vector Machines (SVM) Support Vector Machines is a Machine Learning method developed in the 1990s used for binary classification problems [5]. Given labeled training data the SVM algorithm first transforms the data points into high-dimensional space [2]. This step is crucial as the data needs to be linearly separable for there to exist a hyperplane that separates our data. SVM then aims to create a hyperplane or a set of hyperplanes in high dimensional space so that it separates clusters of data points belonging to the corresponding class. The parameters that make up the hyperplane is given by maximizing the margin from the hyperplane to the two data clusters [1]. Some variations of SVM allow less strict margins in the sense that it allows some overlap between the data clusters. [5] Since we usually operate in high-dimensional space we need a computationally efficient and moderately accurate way to compute the similarity between a new data point and the existing data points in the SVM. Using kernel functions is the most common way to bypass the high-dimensional computations [8]. 6

7 5 Experiments and results DD1395 The idea behind kernels is to compute the scalar product between two points in low-dimensional space. Depending on the complexity of the data set different kernel functions are suitable. Two of the most commonly used kernel functions are the linear kernel and radial kernel. K( x, y) = x T y + 1 (3) K( x, y) = e ( x y) 2 2σ 2 (4) In figure 2 and 3 we have examples of two support vector machines using different kernel functions with their corresponding hyperplane(s) and margins: Figure 2: Linear kernel Figure 3: Radial kernel Support Vector Regression (SVR) Support Vector Regression is an alternative variant to SVM but is instead used for regression. The same ideas apply but instead of returning a classification the actual hyperplane(s) is/are returned [10]. 5 Experiments and results In [1] the authors created a series of trading systems using various Machine Learning techniques. Two of the techniques used were SVM and SVR which were tested on a dataset from the Dow Jones Industrial Average (DOW) and the Oslo Stock Exchange (OBX). The DOW index is one of the most stable and efficient indices in the world [4]. For the DOW dataset it included the index value as well as all the companies listed in the with their corresponding price per stock between year 2000 to For the OBX dataset it included the same type of data but only for from year 2006 to These two datasets where split in separate sets of data. The training set was set as the first 50 days. The model would after that try to predict the next day s price for the index and stock price. On day 51 it would then use data from day 2 to day 51 to predict day 52 and so on. To be able to compare the result they used a buy-and-hold strategy as benchmark meaning that they simulated a portfolio consisting of N shares in the corresponding index with 1/N weight each. 7

8 5 Experiments and results DD1395 The authors found that when including the transaction cost of a trade none of the techniques used achieved greater returns compared to the benchmark portfolio or a fund mirroring the corresponding index achieved. When the transaction cost for a trade was disregarded the authors noticed that the techniques applied performed differently in the OBX and DOW data set. In the OBX result both the SVM and SVR delievered cumulative returns that surpassed the benchmark. The SVR also dominated the other techniques in terms of risk-adjusted returns. In the DOW result no technique were able to surpass the benchmark. In [11] the authors have performed similar experiments on the Taiwan stock index (TAIEX), which is a very IT/electronics dominated index. The authors have included ANN or artifical neural networks which is a machine learning method created in 1943 inspired by the human nervous system [5]. This paper will assume prior knowledge of the basics in ANN. The authors have compared four different methods/hybrid-methods: ANN, decision trees, ANN combined with decision trees and two decision trees combined. The data set they used contained all public data including price, financial reports etc. of the companies included in TAIEX and ranged from year 2002 to mid They used 80% of the data as training data and the remainder as test data. After training each method they evaluated the method in terms of prediction accuracy, Type-I & Type-II errors. The Type-I error means that the model predicted increase but the stock decreased. Type-II error means that the model predicted decrease but the stock increased. Neither one of these error are desirable but a high percentage of Type-I error is more serious in terms of the end result. Method Type-I Type-II ANN 49.5% 43.7% DT 87.1% 21.4% DT+ANN 71.9% 1.95% DT+DT 88.4% 6.64% Table 1: Type-I and Type-II errors for each method. In terms of prediction accuracy the following was the result for each method tested: Method Prediction accuracy ANN % DT % DT+ANN % DT+DT % Table 2: Prediction accuracy for each method. In [6] they conducted an experiment with involving SVM and evaluated the prediction accuracy. This experiment was run on the Standard & Poor 500 index (S&P500) with stock data from year 2000 to March The major difference in this paper from the previous papers was that the they used five different time aspects as training data. The algorithm used 2,3,5,10, and 30 8

9 6 Discussion DD1395 previous trading days as training data. In terms to the prediction accuracy the SVM had the following accuracy for the different time aspects: Days looking backward Prediction accuracy % % % % % Table 3: Prediction accuracy for time aspects ranging from 2,3,5,10 or 30 days. From table 3 we can see that the prediction accuracy tends to increase when we increase the number of previous days we use. 6 Discussion All the papers investigated used a combination of different methods and had different data sets. The quality of the experiments differed greatly as well. For example [1] was the only authors who took transaction cost in consideration. Since the other papers did not mention the transaction cost I assume that this was neglected. Given that the transaction cost had an impact in [1] experiment and affected the return of the methods one should note that the effect is most likely similar in [6] and [11]. In [1] the authors noticed a difference in performance for the OBX and DOW data set which could be due to difference in transaction costs as they operate in different countries. It could also be due to the difference in time periods as the training data used in the DOW was a period where the whole index decreased 30% while the training data in the OBX was a period where the index increased 35%. As the benchmark portolio performed better than both the SVM and SVR including the transaction cost we can say that the [1] experiment strengthens the EMH. In [11] the DT+ANN method showed promising prediction accuracy. The authors reported a prediction accuracy of % which is very impressive. An explanation for this could be that the TAIEX index used in the experiment is a smaller index compared to the DOW and OBX. The TAIEX is also largely composed by a single industry. Since the success of the DT and DT+ANN methods relies heavily on making the best splits in the tree it is easier to make favorable splits if the companies in the index are similar. As the authors mention in the discussion a future extensions that would strengthen their findings and conclusions would be to include more methods and use a data set that is less homogeneous in terms of size and industries. In [6] they evaluated the performance of SVM in terms of prediction accuracy. The trend we can see is that the prediction accuracy tends to increase when the number of previous days are increased, with the exception of 10 days where the accuracy drops. Given the hypothesis that there is a trend and connection in the stock market I believe it makes sense that the prediction accuracy should 9

10 6 Discussion DD1395 increase when we observe more data (up to a certain limit, as too many days in the data could make the model disregard trends). The most surprising result is that the prediction accuracy of 2 days and 30 days only differs % which is objectively an improvement, albeit a small one. To be able to evaluate the result we need to compare it with some benchmark. Given that a uniform random classifier should in theory result in 50% prediction accuracy (predicting increase or decrease is a binary decision problem) and that the prediction accuracy of SVM lies in the range of % %, I believe it is fair to conclude that the SVM used in the paper was not very effective. 10

11 REFERENCES DD1395 References [1] A.-C Andersen and Mikelsen S. A Novel Algorithmic Trading Framework Applying Evolution and Machine Learning for Portfolio Optimization [2] M Atsuto. Decision Trees, Support Vector Machines [3] C Bishop. Pattern recognition and machine learning. Springer Science, [4] R Edelman. The truth about money. Rodale, [5] G James et al. An introduction to statistical learning. Vol. 6. Springer, [6] G Kihlström and P Przybysz. Technical Analysis inspired Machine Learning for Stock Market Data. Royal Institute of Technology, [7] B-G Malkiel. Efficient market hypothesis. In: The World of Economics. Springer, 1991, pp [8] B Schölkopf and A-J Smola. Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT press, [9] V Sha. Machine Learning Techniques for Stock Prediction Vatsal H. Shah. In: (2007). [10] A-J Smola and B Schölkopf. A tutorial on support vector regression. In: Statistics and computing 14.3 (2004), pp [11] C.-F Tsai and S.-P Wang. Stock Price Forecasting by Hybrid Machine Learning Techniques. In: Proceedings of the International MultiConference of Engineers and Computer Scientists (2009). 11