Introduction and problem background

Transcription

1 CS 221, Fall 2016: Project Final Report Predicting Turning Points in Exchange Rate Price Trends Darren Baker Collaborators: none (solo project) Introduction and problem background The markets for trading currencies (a.k.a. foreign exchange, or forex ) are by far the largest financial markets in the world, with notional transaction value exceeding $5 trillion (USD) on an average day. 1 (For comparison, transaction volume on the New York Stock Exchange for the entire year of 2013 was estimated at less than 14 trillion USD. 2 ) Currency prices are always quoted in pairs, because exchange rates are based on the idea of trades from one currency to another. For example, the price for the pair EUR/USD in early December 2016 was roughly 1.07, meaning that one euro (EUR) can be purchased for 1.07 US dollars (USD). There are many factors that can cause the price of a currency to rise or fall relative to other currencies, including so-called fundamental factors such as global macroeconomic trends (i.e. economic booms or recessions) or central bank actions (i.e. changes in interest rates). However, currency prices are also influenced by technical factors that have to do with market structure and the behavior of individual market participants, from small retail traders to massive multinational banks. These technical factors are a source of both short-term volatility and of trending behavior in which the price of a currency can increase or decrease significantly over periods of hours, days, or longer timeframes. Because technical factors are prevalent in the forex markets, even those market participants who care primarily about fundamentals pay careful attention to timing and technical trends when trading currencies. (And of course, there are many speculative traders who attempt to use technicals as a guide for making profitable short-term trades.) A natural question that arises is this: is it possible to use technical factors to make systematic predictions of turning points in a price trend so as to get the best price for a trade? A turning point is the place where the trend reaches its peak/trough and then begins to rebound in the opposite direction prior to the start of a new trend. The ability to identify such turning points with even moderate reliability could make it possible for market participants to make currency trades at a time that minimizes their risk and/or maximizes their economic benefit. For example, a businessperson needing to buy euros in exchange for dollars might want to wait until the euro is slightly less expensive relative to the dollar or in more concrete terms, he/she would want to buy near the bottom of a downtrend in the EUR/USD pair, or at least avoid buying at the top of an uptrend in EUR/USD. Price fluctuations of EUR/USD in mid-2016: each vertical bar (a.k.a. candlestick ) represents a 4-hour interval, with green/red bars representing upward/downward price movement during that time period 1 See Bank of International Settlements: 2 See Statista: 1

2 Task definition I chose to frame the task of predicting turning points as a supervised learning problem involving binary classification. Specifically, I tried to answer the following question: Given a simple definition of a trend in currency prices, and information (including technical indicators) about the price movements that have taken place in a particular trend, can I predict for each fixed time interval in the trend whether that interval is before or after the turning point (peak/trough) of the trend? The following image gives an example of a downtrend in a single currency pair, where each vertical bar (known as a candlestick ) represents an interval of 2 hours. The downtrend begins at the first yellow star and ends at the second yellow star. (More details on my trend definition criteria will be given below.) The blue diamond represents the low point of the trend, so in this case a perfect version of my classifier would predict before (or equivalently, zero or FALSE) for each of the candlesticks between the start of the trend and the low point, and after (or equivalent, one or TRUE) for each of the candlesticks between the low point and the end of the trend. Using this formulation of the problem, the turning point of the trend is identified as the first candlestick in the trend where the classifier returns a value of TRUE. A downtrend begins at the first yellow arrow, reaches its turning point (low point) at the blue diamond, and then reverses direction before ending at the second yellow arrow. Literature review There are decades of research on methods for predicting the prices of financial assets based on past price information and other data. Most such studies focus on stocks (public equities), which are perhaps the bestknown type of financial asset, and the asset class with the largest available amount of historical price data. However, as awareness of currency markets and availability of forex price data to non-institutional players has grown since roughly the year 2000, there have been numerous studies attempting to make predictions (or analyze others claims of predictions) about currency prices, trends, and trading strategies using various types of statistical analysis and machine learning. Some prominent examples include: 2

3 [Olson 2004] reviewed a series of studies from the 1970s through the 1990s that identified profitable technical trading strategies in currencies to determine whether profits had declined over time. He concluded that there was a significant decline in profitability for the (relatively simplistic) moving average crossover class of strategies that he considered, suggesting that those strategies had relied on market inefficiencies that had gradually disappeared over time. [Neely, Weller 2003] applied two different prediction models (linear regression and a genetic algorithm) to explore whether some technical trading strategies that appeared profitable over long holding periods were also profitable when used for intraday trading (i.e. with much shorter holding periods). They concluded that practical constraints of trading costs and high-liquidity hours made such strategies unprofitable over short time periods. [Schulmeister 2006] examined currency price movements with the specific goal of identifying whether technical trading strategies might be self-fulfilling (i.e. that traders reliance on technical signals might actually play the role of creating trends, rather than just riding them). In reviewing more than 1000 statistical models using a range of parameters, he found that price dynamics were significantly affected by technical trading behavior, but also noted that strong trend patterns in currency data appear to continue to provide significant opportunities for profitable trading (perhaps in contrast to the claims of [Olson 2004] and [Neely, Weller 2003] with respect to certain strategies). [Cao, Pang, Bai 2005] made a direct application of the machine learning model called SVR (support vector regression) to currency price prediction. This team did not look at trends or technical factors at all, but simply tried to predict the price for each day based on the previous 4 days prices. They found that the SVR model did have some predictive power, but that it also seemed prone to overfitting. [Rehman, Khan, Mahmud 2014] made a similar direct attempt to predict currency prices based on price data from the recent past (with a 10-day lookback period in this case), but using different models: Cartesian genetic programming (CGP) and recurrent neural networks (RNNs). They reported predictive accuracy as high as ~98.8% (i.e. average prediction error of ~1.2% from the true price value), though it appears their work focused only on less liquid (and less volatile) currency pairs, such as the Australian dollar vs. the Korean won. [Talebi, Hoang, Gavrilova 2014] used ensemble classification methods to try to identify trend directions (upward, downward, or sideways) in currency data. They incorporated several technical indicators, including the zigzag indicator that attempts to overlay trend lines on top of price movements in real time. Using a multivariate Gaussian distribution to consider multiple possible trends, the team reported moderate accuracy in trend classification vs. hand-labeled data. [Nassirtoussi et al. 2015] adopted a novel approach of attempting to build a more fundamental - oriented prediction tool by performing text mining on news headlines to estimate the impact of various news events or economic data announcements on exchange rates. They compared the performance of several different models, including Naïve Bayes, K nearest neighbors, and SVM, and were able to achieve predictive accuracy levels as high as ~83%. Some observations on how these research efforts compare to my objective in this project: [Olson 2004], [Neely, Weller 2003], and [Schulmeister 2006] all have some similarity with my project in the sense that they are attempting to examine the profitability of technical trading strategies. However, the key difference in my approach is that I am layering a prediction element on top of the basic trend-following strategies examined by each of these papers. In fact, we will see in a later section that my results for the naïve trading strategy (i.e. trading trends with no prediction) appear broadly consistent with theirs i.e., the naïve strategy does not seem consistently profitable, at least over moderate holding periods but my overall goal is to use turning point prediction to achieve an edge vs. the naïve strategy. [Cao, Pang, Bai 2005] and [Rehman, Khan, Mahmud 2014] are using machine learning for currency price prediction, but their focus is on regression rather than classification, and their work appears more local (rather than trend-based) in the sense that they have a fixed, short lookback period and only care about predicting one datapoint into the future. In contrast, my goal is to examine price trends of arbitrary length and make predictions based on *all* the data that has been observed in the trend so far, whether that is from one candlestick or 200 candlesticks. 3

4 [Nassirtoussi et al. 2015] is an example of an approach that is mostly orthogonal to my project, even though we are both focused on currency price prediction in some form. My approach to prediction is purely based on technical data, while this paper relies on incorporating fundamental analysis using NLP techniques. [Talebi, Hoang, Gavrilova 2014] is perhaps the approach that is most similar to mine, since this team is explicitly focused on price trends, and also relies on technical analysis to make their predictions. The key distinction between our strategies is that this team has the goal of identifying trends, while I take trends as a given and try to find their turning points. Nevertheless, it is possible that either of our approaches could be adapted to accomplish the other s goal. In summary: although it s clear that there has been meaningful research effort invested in analyzing trading strategies and making predictions for currency prices, and there is some high-level similarity between these research approaches and my own, I have not found any prior work that attempts to accomplish the same specific goal of finding turning points in trends. Therefore, I hope my results in this project may constitute a useful addition to the literature around price movement prediction for foreign exchange. Predictive modeling approach Data model All of the data that I used in my project is derived from raw tick-level price data that I download from the FXCM API. (FXCM is a forex broker that caters to retail clients, rather than institutions like large banks or hedge funds.) Based on this raw data, there are 4 major types of higher-level data objects that I have defined to capture price movements in a way that will allow me to structure my supervised learning task appropriately. Candlesticks. These are the most basic element of my model. They take their name from their tall, skinny appearance on price charts (see an example below), and they represent the range of prices observed for a given currency pair over a specified time period. (Forex market traders may use time periods ranging anywhere from one minute to one month, though I am focusing on time periods between roughly 1 and 4 hours.) Each candlestick has 4 key data elements: o The open and close prices are the first and last prices at which the currency traded during the specified time period. o The high and low prices, as their names suggest, are simply the highest and lowest prices at which the currency traded during the specified time period. Technical indicators. In contrast with candlesticks, which simply capture facts about price changes in a specific time period, technical indicators are forms of metadata that are calculated on the basis of underlying price patterns. They are used to provide some context for how a currency pair s price compares with its movements over the relatively recent past. Different currency traders have personal preferences for various technical indicators, but I have chosen to focus on two types of well-known indicators: o Bollinger bands consist of a simple moving average of closing prices over a sliding, fixed-length time window, along with two lines (one each above and below the moving average) that create a channel around the moving average that fluctuates with the standard deviation of price movements. Many traders believe that when a currency s price moves outside of this channel, this is a clear signal of the formation of a major price trend. o Stochastic oscillators are a tool for price normalization, with several lines that fluctuate in a defined range of 0 to 100. They attempt to give a clear and consistent view of where the current price falls within the range defined by the highest and lowest prices observed for the currency pair over a sliding, fixed-length time window. (For example, if a 10-period stochastic oscillator currently has a value near 100, this means that the price is near the highest point that it reached over the past 10 periods.) This indicator also employs some weighting and averaging to smooth out erratic price fluctuations. Price trends. These objects are sequences of consecutive candlesticks that attempt to capture the significant price moves that occur in currency markets. There are many possible criteria for 4

5 identifying start and end points for price trends, but I have chosen to assume that a new price trend begins every time a pair s price crosses over the point that is 1 standard deviation above (for uptrends) or below (for downtrends) the moving average line given by the Bollinger bands. Price movement legs. These objects are also sequences of consecutive candlesticks, but they attempt to capture smaller price fluctuations that are not large enough to represent standalone trends (but still may signal changes in price momentum within the trend). A single price trend typically covers the same stretch of time as several price movement legs (PMLs). I have chosen to define a new PML each time the price rebounds at least 0.75 standard deviations from a recent local peak or trough. The following image illustrates several of these indicators and data objects using the example of an upward price trend for EUR/USD in the first week of February 2016: An upward price trend in EUR/USD, with each candlestick representing an interval of 4 hours. The thin red and yellow lines show the Bollinger bands (moving average in the center, plus channel boundaries above and below that fluctuate with the standard deviation of price movement). As above, the yellow arrows represent the start and end of the price trend, and the diamond shows the turning point in the trend (i.e. the peak, or highest closing price). The downward-sloping purple line at center-left shows an example of a price movement leg that captures a moderate price decline taking place in the middle of the broader upward trend. Creating training data and choosing classification mechanics From these data objects, I created training data for my prediction problem based on the following process: First, even though it s technically possible for currency traders to make trades on a continuous basis when the market is open which is anytime between 5pm ET on Sunday and 5pm ET on Friday each week I assumed for the sake of simplifying the prediction problem that we will only attempt to classify turning points at the boundary between each consecutive pair of candlesticks. This assumption implies that each training (and test) example in my dataset represents a collection of features that provide a snapshot of a currency pair including data from candlesticks, technical indicators, and trend sequences at the end of a particular time period. I won t outline the full list of features here (since there are roughly 60 in the final version of my datasets), but a sampling of my feature templates includes: 5

6 o o o o All the price levels for the current candlestick (open/high/low/close), plus the number of price quotes recorded during the candlestick. Data about the current price trend and current price movement leg, including direction (up or down) and length (number of candlesticks in the sequence thus far). Values and slopes (i.e. change from the previous candle) for the technical indicators at the current candle, including 50-period Bollinger bands and both 10-period and 50-period stochastic oscillators. Additional metadata that I calculate (using custom logic that I developed) from the data objects I described above, including a measure of the relative strength (i.e. magnitude and speed of price change) of the trend and whether the current candle and current PML have achieved a new high or low price compared with previous candles/pmls seen so far in the trend. Of course, the last critical piece of the training set is the actual binary field that represents the classification value of each training example. As described in the task definition section above, I insert a TRUE value for this field in the training set if the candlestick in question is at or beyond the observed turning point of the trend, and a FALSE value otherwise. Evaluation methodology It s extremely important to note that because of the time series nature of currency price data, standard evaluation metrics for classification problems are not necessarily useful or meaningful in the context of my task definition. For example, misclassification rate of examples is generally a poor standard by which to evaluate the performance of my prediction system. To understand why, consider the process followed by a currency trader attempting to use the output of my predictive model in conjunction with a trend-following trading strategy. This trader would enter a new trade at the start of a new trend, taking a long position for an upward trend and a short position for a downward trend. The trader would then be running turning point prediction at the end of each candlestick interval as the trend developed. The key observation here is that the only candlestick that really matters in the trader s view is the first one where the classifier outputs a value of TRUE, indicating that it thinks the peak of the trend has been reached. This is where the trader would exit the trade, taking a profit or loss, and simply wait for the next new trend to start. In order for the predictive model to deliver significant value, it is therefore critical that this *first* TRUE prediction doesn t come too early in which case the trader will exit prematurely and likely miss out on positive profit if the trend continues for a long time or too late in which case the trader will have missed the peak and the price will have rebounded significantly in the opposite direction before the trader exits the position. To address this issue, I chose profitability as the key evaluation metric for my predictive system. In foreign exchange markets, profit is measured in units called pips, which are units of one ten-thousandth of a major currency unit. (So for example, one pip of EUR/USD is USD.) If a (long) trade is entered when the price of EUR/USD is and exited when the price has risen to , then the trade has a positive profit of 10 pips. Since currencies are often traded with a certain degree of leverage, it is reasonable to assume for purposes of analysis that one pip equates to one dollar of profit or loss. Having selected profitability as the best metric for my system, I defined upper and lower bounds on my performance using an oracle and baseline as follows: The oracle represents the best level of performance we can possibly achieve, and is calculated by finding the maximum profit between the start of a trend and the close of any candlestick in the trend. This is precisely the profit that could be gained if the turning point classifier worked perfectly, since it would always identify the peak candlestick (allowing a trader to replicate this strategy and capture the max profit). The baseline is the level over which we want to see improvement in order for the turning point classifier to have any value. Therefore, the natural baseline in this problem is the profit (or loss) achieved using the naïve strategy of simply entering a trade in the trend direction at the start of each 6

7 trend, and then waiting until the end of the trend to exit. There is no prediction involved here, so this is the strategy we can always fall back to in the absence of a predictive model. Finally, evaluation of my classifier on test data proceeds as described above: I separate trends (not individual candlesticks) into the training and test sets, and then for each trend in the test set, I run my classifier on each candlestick to find the first one that gets a prediction of TRUE. I record the profit between the start of the trend and the close of this candlestick, then compare this profit with the profit I would have achieved using the baseline strategy (i.e. by waiting to exit until the end of the trend). Learning algorithms I chose to compare three different learning algorithms that perform binary classification: Decision trees are a type of non-linear classifier that looks for optimal ways to (recursively) split the training examples into two groups that are as pure as possible in terms of how they separate the FALSE/class-0 examples from the TRUE/class-1 examples. In mathematical terms, there are several ways to measure purity, including simple metrics like misclassification rate and more nuanced statistics like the Gini impurity or information gain (which is based on the concept of entropy, as defined in the information-theoretic sense). Decision trees have several nice properties, such as the fact that they are highly interpretable and they can handle discrete-valued features with no transformation required, though they are also prone to overfitting and generally lack the same predictive power of other classifiers. Random forests are a type of classifier that attempts to exploit the strengths of decision trees while addressing some of their key weaknesses. Specifically, random forests create many (typically a few hundred to a few thousand) decision trees, with each tree only using a subset of the features in the training data, and then allow the individual trees to vote on the data being classified. The classification assigned is then the one that receives the most votes from the trees in the random forest. This approach is an example of ensemble learning, and it typically helps reduce overfitting while improving overall classification accuracy. Logistic regression, which we discussed in class this quarter, is a linear classification method that attempts to find a set of weights over the training data that can then be remapped by the sigmoid function onto a smooth curve with a range between 0 and 1. The output of the sigmoid function can then be thresholded at 0.5 (or another value, if desired) to choose a classification value. Logistic regression produces powerful predictive models, though its output is generally much less intuitive to interpret than a decision tree (or even other linear models, like SVM). Although I have implemented all of these classifiers from scratch in the past, I chose in this project to build my predictive models using the statistical programming language R and its accompanying libraries. This allowed me to focus more on feature engineering, error analysis, and variable selection for my specific problem, rather than spending time on duplicating algorithms that have been implemented and optimized in a standard form. Parameter tuning and model selection As discussed in the results section below, I observed that even for a single predictive model, the profitability gains produced by that model over the baseline could vary significantly as I varied the decision threshold for the model. (This is perhaps unsurprising in the context of the previous discussion about how the profitability depends only on the *first* candle in the trend that is classified as TRUE, and therefore we would want to be relatively confident that that candle is near the true turning point of the trend.) In light of this observation, I decided to write additional code to run a parameter tuning process in the hope that I could find the best model to deliver improved profitability vs. the baseline. I used three methodological elements discussed in this and other classes: Grid search across several values for each of two key parameters: the decision threshold (0.5, 0.6, etc.) and the number of consecutive candlesticks with predictions over that threshold that we require to exit the trade. (This latter parameter is another way to introduce some conservatism in when we 7

8 decide we ve seen the turning point of the trend: for example, we might decide that we are comfortable with a decision threshold of 0.5, but want to see at least 2 or 3 consecutive candles with predictions above 0.5 before we declare that the trend has peaked.) K-fold cross-validation to get reliable evaluation estimates from the training set without having to set aside a portion of the training data as a development set. I used 5 folds to balance training data volume with computation time constraints. Forward variable selection to find the subset of features that produces the most accurate model. This process builds up models by adding one feature at a time through a greedy process that tries to improve classification performance as much as possible at each addition. I specifically wanted to use this process since my training data includes ~60 features that I custom-engineered on the basis of my own intuition, but I did not have a clear way to tell which features actually contributed the most value to the prediction process. Results, challenges, and error analysis Predictive model performance On a general level, the results of my experiments are somewhat mixed, but in many cases my predictive models appear to generate at least a moderate degree of positive profit vs. the baseline strategy. Consider the following three plots, which show the difference (i.e. gain) between the profitability of the model s predictions vs. the naïve strategy of entering and exiting at the start and end points of a trend: Three plots showing the comparison between profits under the naïve strategy and profits using one of the predictive models over a wide range of decision thresholds. Each model was built using all features and a random subset of 80% of the 635 trends observed in EUR/USD-60min candlesticks over a 5-year period between mid-2011 and mid This performance data was generated using a test set comprising the other 20% of the trends observed over this time period. 8

9 Some observations from these plots that are worth highlighting: Each model produces a gain in profit over a wide range of decision thresholds, with gains as high as ~1000 pips for the logistic regression model over thresholds between roughly 0.5 and (Recall that we can think of pips as being roughly equivalent to dollars, so this represents a possible total improvement of $1000 in profitability over the 127 trends in the test set.) It is perhaps somewhat surprising that the random forest model produces some negative incremental profit (i.e. it performs worse than the baseline strategy) while the decision tree which we presumed to have less predictive power and a greater tendency to overfit the training data delivers negative gains only at very low decision thresholds. Both the random forest and logistic regression models appear to show the broad pattern that we might expect for gains vs. decision thresholds: namely, that gains are highest for thresholds at or slightly above 0.5, but much lower for very low or very high decision thresholds. (The latter fact is somewhat intuitive in the sense that very low or very high decision thresholds suggest that we may exit the trend very early or very late, and thereby fail to capture the profit that is available near the turning point of the trend.) It is unclear to me why the decision tree results don t show a similar parabolic pattern, though it s possible that since the decision tree has lower predictive power and perhaps more susceptibility to noise in the training data, it generates the most incremental profit using high decision thresholds that demand a high level of confidence before making a decision to exit the trend. One important caveat coming along with these results is the fact that even though my predictive models do appear to deliver improved profitability in many cases, the baseline profit level may be negative meaning that even the gain from adding prediction may only bring a trader back to break-even or slightly above. (In my testing, baseline profit on the test set typically ranged between roughly -700 and +400 pips, depending on which trends were randomly selected for training vs. test.) This is important to bear in mind for potential applications, as even significant gains from prediction may not be especially valuable in a real-world sense if they mainly help a trader reduce losses rather than extending profits. Challenges and error analysis As I explored the performance of my models, the biggest problem that arose consistently was the high level of volatility in the data. Although currency prices often show strong trending behavior, they can also be subject to sudden swings known to traders as whipsaws. These types of price swings greatly increase the challenge of learning a model that will be robust and generalize well to unseen data. One obvious way that this lack of robustness manifested itself was in the model selection process that I ran to find parameter values and a subset of features that produced the best profitability gains. As described in the previous section, I used grid search, forward variable selection, and 5-fold cross-validation on the training set to run this model selection process. Unfortunately, the results of the process did not generalize well: in most cases, the subset of features chosen as the components of the best model for each combination of parameter values actually produced a model that performed worse on the held-out test set than a model built from *all* features using the same parameter values. (A subset of my results from running model selection for logistic regression are shown in the table on the following page.) In a similar vein, I observed that when I built the three types of different predictive models with different random seeds (leading to different mixes of trends in the training and test sets), there was sometimes wide variance in model performance. For example, in some cases, all three of the models (decision tree, random forest, logistic regression) actually delivered negative profit gains across almost all decision thresholds, simply because the models did not generalize well from training to test data. These results suggest that the volatility of the price data can create clear risks to using these predictive models in practice at least without much more training data to help ensure that the model has seen many examples of possible whipsaws or other unexpected movements that may radically disrupt a trend. 9

10 A concerning result: despite running model selection to try to find the best subset of features to optimize performance on unseen data, the feature subsets found using 5-fold cross-validation on the training set usually delivered *worse* performance on the held-out test set than a model built with all features. Beyond volatility, I also encountered more narrow cases of errors that I tried to address through feature engineering. Some examples include: Trends that begin with a massive price movement often lead to losses, since they reach their turning point right at the beginning of the trend. I added several features describing the candlestick that triggered the trend to my training data in an attempt to help the algorithms learn how to respond most profitably (or at least with minimal losses) in this scenario. One possible signal that a trend is ending is that the price will test a high or low level that was reached in a previous candlestick. My algorithm appeared to get confused about these test candles sometimes, since they represented two different candles with almost the same close price that might be considered the true turning point. I added some features identifying the characteristics of these test levels in order to help the algorithm distinguish price tests from other types of peaks. Conclusions and future work My primary conclusions from this project are that supervised learning models do have some capability to help currency traders, businesspeople, or other forex market participants find the turning points of trends but there is also significant risk that remains when using these models, due mainly to the volatility of realworld price movements in many currency pairs. I plan to continue exploring several broad paths that I think may help me achieve more consistent positive results: Experimenting with further feature engineering to see if other technical indicators (or perhaps interaction terms between existing features) might improve predictive accuracy. Looking at a wider range of currency pairs, since not all pairs may have the same volatility as EUR/USD, which I used for training and testing in this project. (Though there is an accompanying downside that less liquid pairs may have higher transaction costs or fewer trends.) Looking at a wider range of candlestick intervals and historical data ranges, since longer candles appear to have somewhat less volatility and more training data may improve generalization. 10

11 Appendix 1: References Cao, Ding-Zhou, Pang, Su-Lin, and Bai, Yuan-Huai, Forecasting Exchange Rate Using Support Vector Machines. Proceedings of the Fourth International Conference on Machine Learning and Cybernetics 2005, Nassirtoussi, Arman Khadjeh et al., Text mining of news-headlines for FOREX market prediction: A Multi-layer Dimension Reduction Algorithm with semantics and sentiment. Expert Systems with Applications 42, Neely, C.J., and Weller, P.A., Intraday technical trading in the foreign exchange market. Journal of International Money and Finance 22, Olson, Dennis, Have trading rule profits in the currency markets declined over time? Journal of Banking and Finance 28, Rehman, Mehreen, Khan, Gul Muhammad, and Mahmud, Sahibzada Ali, Foreign Currency Exchange Rates Prediction using CGP and Recurrent Neural Network. IERI Procedia 10, Schulmeister, Stephan, The interaction between technical currency trading and exchange rate fluctuations. Finance Research Letters 3, Talebi, Hossein, Hoang, Winsor, and Gavrilova, Marina L., Multi-Scale Foreign Exchange Rates Ensemble for Classification of Trends in Forex Market. International Conference on Computational Science 29,

12 Appendix 2: Description of Project Scope Some of the code on which my project is based was written by me (as a hobby) before I enrolled in CS 221, since currency market trends (and financial markets and trading more generally) have long been a personal interest of mine. In accordance with the requirement given on the project page, I am outlining which portion of the project relied on existing code, and which portion was developed specifically for CS 221. Capabilities that I used from pre-existing (C#) code: o Downloading raw historical price data from the FXCM API o Organizing the raw price data into the data objects described in the body of the paper above (such as candlesticks, price trends, and price movement legs) o Calculating the values of technical indicators for each candlestick o Processing a text-based configuration file to specify the currency pairs and candlestick length(s) for which we want to download historical prices and construct all of these objects/values Capabilities that I developed specifically for this CS 221 project: o Writing code in C# to calculate and output to file the oracle and baseline values for each price trend observed in the historical data o Selecting and defining the set of more than 50 features (both real-valued and discretevalued) that I wanted to incorporate into my predictive model o Writing code in C# to calculate the values of each of these features for every individual candlestick within each price trend o Writing code in C# to output the calculated feature values to a file for later loading in a separate programming environment for model building o Writing code in R to perform pre-training transformations on the feature data and randomly select training/test sets on the level of trends o Writing code in R to implement 3 types of model construction (decision tree, random forest, logistic regression) and produce per-candlestick predictions (in the form of both classes and probabilities) o Writing code in both R and Python to take per-candlestick predictions over the course of a single trend and determine the profitability gain (positive or negative) for a trade over that trend, using an arbitrary decision threshold o Writing code in R to perform model selection using k-fold cross-validation over the training set, grid search over multiple values of multiple parameters, and forward variable selection over the 50+ features in the dataset o Writing code in R to plot gains vs. the baseline measurement over a range of decision thresholds 12