Индикатор Qv Форекс

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Forex (foreign exchange) is a special financial market that entails both high risks and high profit opportunities for traders. It is also a very simple market since traders can profit by just predicting the direction of the exchange rate between two currencies. However, incorrect predictions in Forex may cause much higher losses than in other typical financial markets. The direction prediction requirement makes the problem quite different from other typical time-series forecasting problems. In this work, we used a popular deep learning tool called “long short-term memory” (LSTM), which has been shown to be very effective in many time-series forecasting problems, to make direction predictions in Forex. We utilized two different data sets—namely, macroeconomic data and technical indicator data—since in the financial world, fundamental and technical analysis are two main techniques, and they use those two data sets, respectively. Our proposed hybrid model, which combines two separate LSTMs corresponding to these two data sets, was found to be quite successful in experiments using real data.

The foreign exchange market, known as Forex or FX, is a financial market where currencies are bought and sold simultaneously. Forex is the world’s largest financial market, with a volume of more than $5 trillion. It is a decentralized market that operates 24 h a day, except for weekends, which makes it quite different from other financial markets.

The characteristics of Forex show differences compared to other markets. These differences can bring advantages to Forex traders for more profitable trading opportunities. Some of these advantages include no commissions, no middlemen, no fixed lot size, low transaction costs, high liquidity, almost instantaneous transactions, low margins/high leverage, h operations, no insider trading, limited regulation, and online trading opportunities. Two types of techniques are used to predict future values for typical financial time series—fundamental analysis and technical analysis—and both can be used for Forex. The former uses macroeconomic factors while the latter uses historical data to forecast the future price or the direction of the price.

The main decision in Forex involves forecasting the directional movement between two currencies. Traders can profit from transactions with correct directional prediction and lose with incorrect prediction. Therefore, identifying directional movement is the problem addressed in this study.

We chose the Euro/US dollar (EUR/USD) pair for the analysis since it is the largest traded Forex currency pair in the world, accounting for more than 80% of the total Forex volume.

In recent years, deep learning tools, such as long short-term memory (LSTM), have become popular and have been found to be effective for many time-series forecasting problems. In general, such problems focus on determining the future values of time-series data with high accuracy. However, in direction prediction problems, accuracy cannot be defined as simply the difference between actual and predicted values. Therefore, a novel rule-based decision layer needs to be added after obtaining predictions from LSTMs.

In this work, we propose a hybrid model composed of a macroeconomic LSTM model and a technical LSTM model, named after the types of data they use. We first separately investigated the effects of these data on directional movement. After that, we combined the results to significantly improve prediction accuracy. The macroeconomic LSTM model utilizes several financial factors, including interest rates, Federal Reserve (FED) funds rate, inflation rates, Standard and Poor’s (S&P) , and Deutscher Aktien IndeX (DAX) market indexes. Each factor has important effects on the trend of the EUR/USD currency pair. This can be interpreted as a fundamental analysis of price data. The other model is the technical LSTM model, which takes advantage of technical analysis. Technical analysis is based on technical indicators that are mathematical functions used to predict future price action. The feature set in our model uses popular technical indicators such as moving average (MA), moving average convergence divergence (MACD), rate of change (ROC), momentum, relative strength index (RSI), Bollinger bands (BB), and the commodity channel index (CCI).

The contributions of this study are as follows:

• A popular deep learning tool called LSTM, which is frequently used to forecast values in time-series data, is adopted to predict direction in Forex data.

• Both macroeconomic and technical indicators are used as features to make predictions.

• A novel hybrid model is proposed that combines two different models with smart decision rules to increase decision accuracy by eliminating transactions with weaker confidence.

• The proposed model and baseline models are tested using recent real data to demonstrate that the proposed hybrid model outperforms the others.

The rest of this paper is organized as follows. In “Related work” section, related studies of the financial time-series prediction problem are thoroughly examined. “Forex preliminaries”–“Technical indicators” sections provide background information about Forex, LSTM, and the technical indicators. Then, “The data set” section presents the data set used in the experiments. “LSTM-based hybrid model using macroeconomic and technical indicators” section introduces the proposed algorithm to handle the directional movement prediction problem. Moreover, the preprocessing and postprocessing phases are also explained in detail. “Experiments” section presents the results of the experiments and the classification performances of the proposed model. “Discussion” and “Conclusion” sections discuss the experimental results and provide insight for future research directions.

Various forecasting methods have been considered in the finance domain, including machine learning approaches (e.g., support vector machines and neural networks) and new methods such as deep learning. Unfortunately, there are not many survey papers on these methods. Cavalcante et al. (), Bahrammirzaee (), and Saad and Wunsch () have provided overviews of the field. The most recent of these, by Cavalcante et al. (), categorized the approaches used in different financial markets. Although that study mainly introduced methods proposed for the stock market, it also discussed applications for foreign exchange markets.

There has been a great deal of work on predicting future values in stock markets using various machine learning methods. We discuss some of them below.

Selvamuthu et al. () used neural networks based on Levenberg–Marquardt, scaled conjugate gradient, and Bayesian regularization for stock market prediction based on tick data and min-interval data for an Indian company.

Patel et al. (b) developed a two-stage fusion structure to predict the future values of the stock market index for 1–10, 15, and 30 days using 10 technical indicators. In the first stage, support vector machine regression (SVR) was applied to these inputs, and the results were fed into an artificial neural network (ANN). SVR and random forest (RF) models were used in the second stage. They compared the fusion model with standalone ANN, SVR, and RF models. They reported that the fusion model significantly improved upon the standalone models.

Guresen et al. () explored several ANN models for predicting stock market indexes. These models include multilayer perceptron (MLP), dynamic artificial neural network (DAN2), and hybrid neural networks with generalized autoregressive conditional heteroscedasticity (GARCH). Applying mean-square error (MSE) and mean absolute deviation (MAD), their results showed that MLP performed slightly better than DAN2 and GARCH-MLP while GARCH-DAN2 had the worst results.

Weng et al. () developed a financial expert system using ensemble methods (i.e., neural network regressing ensemble (NNRE), support vector regression ensemble (SVRE), boosted regression tree (BRT), and random forest regression (RFR)) to predict stock prices 1 day ahead. Market prices, technical indicators, financial news, Google Trends, and the number unique visitors to Wikipedia pages were used as inputs. They also investigated the effect of PCA on performance. They reported that ensembles with PCA performed better than those without PCA. They also noted that BRT and RFR were the best while SVRE was the worst in terms of mean absolute percentage error.

Huang et al. () examined forecasting weekly stock market movement direction using SVM. They compared SVM with linear discriminant analysis, quadratic discriminant analysis, and Elman back-propagation neural networks. They also proposed a model that combined SVM with other classifiers. They used not only the NIKKEI index but also macroeconomic variables as features for the model. Their direction calculation was based on the first-order difference natural logarithmic transformation, and the directions were either increasing or decreasing. SVM outperformed the other models with an accuracy of 73% while the combined model was the best, with an accuracy of 75%.

Kara et al. () compared the performance of ANN and SVM for predicting the direction of stock price index movement. Ten technical indicators were used as inputs for the model. They found that ANN, with an accuracy of %, performed significantly better than SVM, which had an accuracy of %.

Patel et al. (a) compared the performance of four classifiers (ANN, SVM, random forest, and naive Bayes) for stock price index direction using two approaches. In the first approach, they used 10 technical indicator values as inputs with different parameter settings for classifiers. Prediction accuracy fell within the range of – In the other approach, they represented same 10 technical indicator results as directions (up and down), which were used as inputs for the classifiers. Using this approach, they enhanced accuracy by about 15% for all of the classifiers. Although their experiments concerned short-term prediction, the direction period was not explicitly explained.

Ballings et al. () evaluated ensemble methods (random forest, AdaBoost, and kernel factory) against neural networks, logistic regression, SVM, and k-nearest neighbor for predicting 1 year ahead. They used different stock market domains in their experiments. According to the median area under curve (AUC) scores, random forest showed the best performance, followed by SVM, random forest, and kernel factory.

Hu et al. () introduced an improved sine–cosine algorithm (ISCA) for optimizing the weights and biases of BPNN to predict the directions of open stock prices of the S&P and Dow Jones Industrial Average indices. Using Google Trends data in addition to the opening, high, low, and closing price, as well as trading volume, in their experiments, they obtained an % hit ratio for the S&P index and an % hit ratio for the Dow Jones Industrial Average Index.

Gui et al. () investigated SVM for predicting stock price index direction with different parameter settings. That study also compared the result for SVM with BPNN and case-based reasoning models; multiple technical indicators were used as inputs for the models. That study found that SVM outperformed the other models with an accuracy of % while the other models had accuracies of % and %, respectively.

Qiu and Song () developed a genetic algorithm (GA)—based optimized ANN to predict the direction of the next day’s price in the stock market index. GA was used to optimize the initial weights and bias of the model. Two types of input sets were generated using several technical indicators of the daily price of the Nikkei index and fed into the model. They obtained accuracies % for the first set and % for the second set.

Zhong and Enke () investigated three-dimensional reduction techniques applied to ANN for forecasting the daily direction of the S&P Index ETF (SPY). Principal component analysis (PCA), fuzzy robust principal component analysis (FRPCA), and kernel-based principal component analysis (KPCA) were used to reduce the number of features. Their experiments indicated that ANN with PCA performed slightly better than the other two techniques.

Zhong and Enke () used deep neural networks and ANNs to forecast the daily return direction of the stock market. They performed experiments on both untransformed and PCA-transformed data sets to validate the model.

In addition to classical machine learning methods, researchers have recently started to use deep learning methods to predict future stock market values. LSTM has emerged as a deep learning tool for application to time-series data, such as financial data.

Zhang et al. () proposed a state-frequency memory recurrent network, which is a modification of LSTM, to forecast stock prices. By decomposing the hidden states of memory cells into multiple frequency components, they could learn the trading patterns of those frequencies. They used state-frequency components to predict future price values through nonlinear regression. They used stock prices from several sectors and performed experiments to make forecasts for 1, 3, and 5 days. They compared the results with LSTM and autoregressive integrated moving average (ARIMA) in terms of mean-square error. They obtained errors of , , and for the different steps, which outperformed the other models.

Fulfillment et al. () studied stock market forecasting in six different domains using LSTM. He aimed to predict the next 3 h using hourly historical stock data. The model was trained to classify three classes—namely, increasing 0–1%, increasing above 1%, and not increasing (less than 0%). The accuracy results ranged from to %. That study also built a stock trading simulator to test the model on real-world stock trading activity. With that simulator, he managed to make profit in all six stock domains with an average of %.

Nelson et al. () examined LSTM for predicting min trends in stock prices using technical indicators. They used technical indicators (i.e., external technical analysis library) and the open, close, minimum, maximum, and volume as inputs for the model. They compared their model with a baseline consisting of multilayer perceptron, random forest, and pseudo-random models. The accuracy of LSTM for different stocks ranged from 53 to %. They concluded that LSTM performed significantly better than the baseline models, according to the Kruskal–Wallis test.

More recently, Fischer and Krauss () applied LSTM to the stock market. They investigated many different aspects of the stock market and found that LSTM was very successful for predicting future prices for that type of time-series data. They also compared LSTM with more traditional machine learning tools to show its superior performance.

Similarly, Di Persio and Honchar () applied LSTM and two other traditional neural network based machine learning tools to future price prediction. They also analyzed ensemble-based solutions by combining results obtained using different tools.

In addition to traditional exchanges, many studies have also investigated Forex. Some studies of Forex based on traditional machine learning tools are discussed below.

Galeshchuk and Mukherjee () investigated the performance of a convolutional neural network (CNN) for predicting the direction of change in Forex. Using the daily closing rates of EUR/USD, GBP/USD, and USD/JPY, they compared the results of CNN with their baseline models and SVM. While the baseline models and SVM had an accuracy of around 65%, their proposed CNN model had an accuracy of about 75%.

Meanwhile, Kayal () investigated the use of MLP in Forex. That work used basic technical indicators as inputs.

Ghazali et al. () also investigated the use of neural networks for Forex. They proposed a higher-order neural network called a dynamic ridge polynomial neural network (DRPNN). In their experiments, DRPNN performed better than a ridge polynomial neural network (RPNN) and a pi-sigma neural network (PSNN).

To predict exchange rates, Majhi et al. () proposed using new ANNs, referred to as a functional link artificial neural network (FLANN) and a cascaded functional link artificial neural network (CFLANN). They demonstrated that those new networks were more robust and had lower computational costs compared to an MLP trained with back-propagation.

In what is commonly called a mark-to-market approach, market prices are increasingly being used to calibrate models to quantify risk in several sectors. The net present value of a financial institution, for example, is an important input for estimating both bankruptcy risk (e.g., Kou et al. ) and the likelihood that shocks will propagate throughout the financial system (Kou et al. ). In such a context, stock price crashes not only dramatically damage the capital market but also have medium-term adverse effects on the financial sector as a whole (Wen et al. ). Credit risk is a major factor in financial shocks. Therefore, a realistic appraisal of solvency needs to be an objective for banks. At the level of the individual borrower, credit scoring is a field in which machine learning methods have been used for a long time (e.g., Shen et al. ; Wang et al. ).

Deep learning methods such as LSTM are rarely used for Forex. In one recent work, Shen et al. () proposed a modified deep belief network. They were able to show that deep learning approaches outperformed traditional methods.

Even though LSTM is starting to be used in financial markets, using it in Forex for direction forecasting between two currencies, as proposed in the present work, is a novel approach.

Forex has characteristics that are quite different from those of other financial markets (Archer ; Ozorhan et al. ). To explain Forex, we start by describing how a trade is made. Profit/loss calculations are made using the difference between the final ratio and the initial ratio of the currency pair that has been traded. If the ratio of the currency pair increases and the trader goes long, or the currency pair ratio decreases and the trader goes short, the trader will profit from that transaction when it is closed. Otherwise, the trader not profit. For example, let us assume the EUR/USD ratio was when the trader started a transaction, going long with an initial amount of $10, When the position closes (i.e., the transaction ends) with a ratio of , the trader will gain \({ * ( - ) = \$50}\). When the position closes with a ratio of , the trader will lose \( * ( - ) = \$50\). Furthermore, these calculations are based on no leverage. If the trader uses a leverage value such as 10, both the loss and the gain are multiplied by

Detailed definitions of commonly used concepts and terms in Forex can be found in Forex (), Archer () and Özorhan (). Here, we explain only the most important ones.

Base currency, which is also called the transaction currency, is the first currency in the currency pair while quote currency is the second one in the pair. To illustrate, in the EUR/USD pair, EUR is the base currency, and USD is the quote currency.

Being long (or going long) means buying the base currency or selling the quote currency in the currency pair. Being short (or going short) means selling the base currency or buying the quote currency in the currency pair. Pip is an abbreviation for “percentage of point,” defined as the smallest amount of change occurring in the currency ratio. In general, pip corresponds to the fourth decimal point (i.e., minimum as ) of that currency. Pipette is the fractional pip, which corresponds to the fifth decimal point (i.e., as ). In other words, 1 pip equals 10 pipettes.

Leverage corresponds to the use of borrowed money when making transactions. A leverage of indicates that if one opens a position with a volume of 1, the actual transaction volume will be After using leverage, one can either gain or lose times the amount of that volume. Margin refers to money borrowed by a trader that is supplied by a broker to make investments using leverage. In this way, one can multiply his/her gains or losses.

Bid price is the price at which the trader can sell the base currency. Ask price is the price at which the trader can buy the base currency. Spread is the difference between the ask and bid prices. A lower spread means the trader can profit from small price changes. Spread value is dependent on market volatility and liquidity. Stop loss is an order to sell a currency when it reaches a specified price. This order is used to prevent larger losses for the trader. Take profit is an order by the trader to close the open position (transaction) for a gain when the price reaches a predefined value. This order guarantees profit for the trader without having to worry about changes in the market price. Market order is an order that is performed instantly at the current price. Swap is a simultaneous buy and sell action for the currency at the same amount at a forward exchange rate. This protects traders from fluctuations in the interest rates of the base and quote currencies. If the base currency has a higher interest rate and the quote currency has a lower interest rate, then a positive swap will occur; in the reverse case, a negative swap will occur.

Fundamental analysis and technical analysis are the two techniques commonly used for predicting future prices in Forex. While the first is based on economic factors, the latter is related to price actions (Archer ).

Fundamental analysis focuses on the economic, social, and political factors that can cause prices to move higher, move lower, or stay the same (Archer ; Murphy ). These factors are also called macroeconomic factors. Economic data reports, interest rates, monetary policy, and international trade/investment flows are some examples (Ozorhan et al. ).

Technical analysis uses only the price to predict future price movements (Kritzer and Service ). This approach studies the effect of price movement. Technical analysis mainly uses open, high, low, close, and volume data to predict market direction or generate sell and buy signals (Archer ). It is based on the following three assumptions (Murphy ):

• Market action discounts everything.

• Price moves in trends.

• History repeats itself.

Chart analysis and price analysis using technical indicators are the two main approaches in technical analysis. While the former is used to detect patterns in price charts, the latter is used to predict future price actions (Ozorhan et al. ).

Long short-term memory (LSTM) was proposed by Hochreiter and Schmidhuber (). LSTM is a recurrent neural network architecture that was designed to overcome the vanishing gradient problem found in conventional recurrent neural networks (RNNs) (Biehl ). Errors between layers tend to vanish or blow up, which causes oscillating weights or unacceptably long convergence times. The initial LSTM structure solves this problem by introducing the constant error carousel (CEC). In this way, the architecture ensures constant error flow between the self-connected units (Hochreiter and Schmidhuber ).

The memory cell of the initial LSTM structure consists of an input gate and an output gate. While the input gate decides which information should be kept or updated in the memory cell, the output gate controls which information should be output. This standard LSTM was extended with the introduction of a new feature called the forget gate (Gers et al. ). The forget gate is responsible for resetting a memory state that contains outdated information. Furthermore, peephole connections and full back-propagation through time (BPTT) training are final features that were added to the LSTM architecture (Gers and Schmidhuber ; Greff et al. ). With these modifications, the architecture was renamed Vanilla LSTM (Greff et al. ), as shown in Fig. 1.

LSTM offers an effective and scalable model for learning problems that includes sequential data (Greff et al. ). It has been used in many different fields, including handwriting recognition (Graves et al. ; Pham et al. ) and generation (Graves ), language modeling (Zaremba et al. ) and translation (Luong et al. ), acoustic modeling of speech (Zia and Zahid ), speech synthesis (Fan et al. ), protein secondary structure prediction (Sønderby and Winther ), audio analysis (Marchi et al. ), and video data analysis (Donahue et al. ; Greff et al. ).

Forward pass

One of the two main operations of LSTM, shown in Fig. 1, is called the forward pass. In the forward pass, the calculation moves forward by updating the weights (Greff et al. ). The weights of LSTM can be categorized as follows:

• Input weights: \(W_z, W_i, W_f, W_o \, \in \, \mathbb {R^{N*M}}\)

• Recurrent weights: \(R_z, R_i, R_f, R_o \, \in \, \mathbb {R^{N*N}}\)

• Peephole weights: \(p_i, p_f, p_o \, \in \, \mathbb {R^N}\)

• Bias weights: \(b_z, b_i, b_f, b_o \, \in \, \mathbb {R^N}\),

where z is the block input, i is the input gate, f is the forget gate, o is the output gate, N is the number of LSTM blocks, and M is the number of inputs. By introducing \(x^t\) as the input vector, \(y^t\) as the block output, and \(c^t\) as the cell at time t, the formulation of the forward pass in Vanilla LSTM can be defined as below:

where \(\sigma \) is the logistic sigmoid function, g and h are hyperbolic tangent functions, and \(\odot \) is the point-wise multiplication of the two vectors.

Back-propagation through time

The other main operation is back-propagation. Back-propagation through time (BPTT) is the process of calculating the deltas of LSTM blocks and the gradient of the weights (Greff et al. ).

First, the deltas (\(\delta \)) of LSTM blocks and the inputs are calculated. In the below equations, \(\Delta ^t\) is the vector of the deltas passed down from the above layer, and T is the transposition operator. Calculation of the deltas is performed as follows:

Then, the calculation of the gradient of the weights is performed. In the below formulas, \(*\) can be any of {\({\bar{z}}, {\bar{i}}, {\bar{f}}, {\bar{o}}\)}, \(<*_1, *_2>\) corresponds to the outer product of the two vectors, and T is the vector length. The calculations are as follows:

Using Eqs. 11–23, all weights are updated.

A technical indicator is a time series that is obtained from mathematical formula(s) applied to another time series, which is typically a price (TIO ). These formulas generally use the close, open, high, low, and volume data. Technical indicators can be applied to anything that can be traded in an open market (e.g., stocks, futures, commodities, and Forex). They are empirical assistants that are widely used in practice to identify future price trends and measure volatility (Ozorhan et al. ). By analyzing historical data, they can help forecast the future prices.

According to their functionalities, technical indicators can be grouped into three categories: lagging, leading, and volatility. Lagging indicators, also referred to as trend indicators, follow the past price action. MA and MACD are the best examples of lagging indicators. Leading indicators, also known as momentum-based indicators, aim to predict future price trend directions and show rates of change in the price. ROC and RSI are the best-known examples of leading indicators. Volatility-based indicators measure volatility levels in the price. BB is the most widely used volatility-based indicator.

The technical indicators used in this study are described below.

Moving average (MA)

Moving average (MA) is a trend-following (or lagging) indicator that smooths prices by averaging them in a specified period. In this way, MA can help filter out noise. MA can not only identify the trend direction but also determine potential support and resistance levels (TIO ).

Moving average convergence divergence (MACD)

Moving average convergence divergence (MACD) is a momentum oscillator developed by Gerald Appel in the late s. It is a trend-following indicator that uses the short and long term exponential moving averages of prices (Appel ). MACD uses the short-term moving average to identify price changes quickly and the long-term moving average to emphasize trends (Ozorhan et al. ).

Rate of change (ROC)

Rate of change (ROC) is a momentum oscillator that defines the velocity of the price. This indicator measures the percentage of the direction by calculating the ratio between the current closing price and the closing price of the specified previous time (Ozorhan et al. ).

Momentum

Momentum measures the amount of change in the price during a specified period (Colby ). It is a leading indicator that either shows rises and falls in the price or remains stable when the current trend continues. Momentum is calculated based on the differences in prices for a set time interval (Murphy ).

Relative strength index (RSI)

The relative strength index (RSI) is a momentum indicator developed by J. Welles Wilder in RSI is based on the ratio between the average gain and average loss, which is called the relative strength (RS) (Ozorhan et al. ; Wilder ). RSI is an oscillator, which means its values change between 0 and It determines overbought and oversold levels in the prices.

Bollinger bands (BB)

Bollinger bands (BB) refers to a volatility-based indicator developed by John Bollinger in the s. It has three bands that provide relative definitions of high and low according to the base (Bollinger ). While the middle band is the moving average in a specific period, the upper and lower bands are calculated by the standard deviations in the price, which are placed above and below the middle band. The distance between the bands depends on the volatility of the price (Bollinger ; Ozturk et al. ).

Commodity channel index (CCI)

The commodity channel index (CCI) is a momentum-based indicator developed by Donald Lambert in CCI is based on the principle that current prices should be examined based on recent past prices, not those in the distant past, to avoid confusing present patterns (Lambert ). This indicator can be used to highlight a new trend or warn against extreme conditions. Moreover, CCI identifies overbought and oversold conditions (Özorhan ).

Interest and inflation rates are two fundamental indicators of the strength of an economy. In the case of low interest rates, individuals tend to buy investment tools that strengthen the economy. In the opposite case, the economy becomes fragile. If supply does not meet demand, inflation occurs, and interest rates also increase (IRD ).

Germany and the US are two of the world’s most powerful economies. In such economies, the stock markets have strong relationships with their currencies. DAX is the German stock index, which has a strong relationship on the price of the EUR while the S&P is one a US stock index that affects the USD. Central banks’ interest rates are also important factors determining the prices of currencies. Therefore, the interest rates determined by the Central Bank of Europe and the Fed directly affect EUR and USD prices, respectively.

In this work, to investigate the effect of macroeconomic factors on the value of the EUR/USD currency pair, we used the factors described in Table 1, as well as the close, open, high, and low values of the EUR/USD pair, which were retrieved from EUR/USD historical data (EUR ). The rest of the data were obtained from various online resources, including the ECB Statistical Data Warehouse (ECB ; EU ; Germany ), Bureau of Labor Statistics Data (), Federal Reserve Economic Data (EFFR ), and Yahoo Finance (DAX ).

The data set was created with values from the period January –January This 5-year period contains data points in which the markets were open. There were increases and decreases for the EUR/USD ratio during this period. Table 1 presents explanations for each field in the data set. Monthly inflation rates were collected from the websites of central banks, and they were repeated for all days of the corresponding month to fill the fields in our daily records.

Using LSTM, we constructed a hybrid model to forecast directional movement in the EUR/USD currency pair that uses both macroeconomic and technical indicators. This hybrid model consists of two separate LSTM models that learn different parameter settings for different input sets (Yıldırım and Toroslu ). These models are called “macroeconomic LSTM” (ME-LSTM) and “technical LSTM” (TI-LSTM); they are explained below in “Macroeconomic LSTM model” and “Technical LSTM model” sections, respectively.

The main structure of the hybrid model, as shown in Fig. 2, can be summarized as follows:

1. 1

   Preprocess the dataset.

2. 2

   Train ME-LSTM and postprocess its results.

3. 3

   Train TI-LSTM and postprocess its results.

4. 4

   Apply different strategies to combine these LSTMs and use their individual results.

Baseline LSTMs

As a baseline, ME-LSTM and TI-LSTM were tested separately. Also, by combining all of the features of these two into a single model, we generated a third baseline model: ME-TI-LSTM.

Macroeconomic LSTM model

This LSTM model (ME_LSTM) was built to investigate the effects of macroeconomic factors on the price movement of the EUR/USD pair. These factors, which are explained in detail in “The data set” section, are listed below:

• Interest rates of Germany and the EU

• FED funds rate (for the US)

• Inflation rates in the EU and the US

• Close value of the S&P market index

• Close value of the DAX market index

After the preprocessing phase, the ME_LSTM model was trained using all of these macroeconomic factors together with the closing values of the EUR/USD pair.

Technical LSTM model

This LSTM model (TI_LSTM) is formed by using technical indicators to observe their effects on the price movement of the EUR/USD pair. These technical indicators are listed below:

• MA with a period of 10

• MACD with short- and long-term periods of 12 and 26, respectively

• ROC with a period of 2

• Momentum with a period of 4

• RSI with a period of 10

• BB with period of 20

• CCI with a period of 20

After the preprocessing stage, the TI_LSTM model is trained using these seven technical indicators together with the closing values of the EUR/USD pair.

Macroeconomic and technical LSTM model

This LSTM model (ME_TI_LSTM) was formed using all of the macroeconomic and technical indicators taken together to observe the effects of the combined set of indicators. After the preprocessing stage, ME_TI_LSTM was trained using the macroeconomic and technical indicators mentioned above together with the closing values of the EUR/USD currency pair.

Proposed model: hybrid LSTM model

Our proposed model does not combine the features of the two baseline LSTMs into a single model. Instead, we propose a rule-based decision mechanism that acts as a kind of postprocessing; it is used to combine the results of the baselines into a final decision (Yıldırım and Toroslu ).

Training classifiers and labeling the data

We trained ME-LSTM, TI-LSTM, and ME-TI-LSTM using the same settings. The data set was split into the training and test sets, with ratios of 80% and 20%, respectively. The training phase was carried out with different numbers of iterations (50, , and ).

Our data points were labeled based on a histogram analysis and the entropy approach. At the end of these operations, we divided the data points into three classes by using a threshold value:

• \(Class\_inc\): Corresponds to an increase in a price that is more than a threshold value.

• \(Class\_dec\): Corresponds to a decrease in a price that is more than a threshold value.

• \(Class\_noact\): Corresponds to a price change that is less than a threshold value.

In addition to the usual classes, increase and decrease, we introduced a third class no_action, which corresponds to the changes remaining in a predefined threshold range that is sufficiently small and thus negligible. Only when a difference between two consecutive data points is greater/less than the threshold will the next data point be labeled as increase/decrease. Otherwise, we treated the next data point as unaltered. This new class enabled us to eliminate some data points for generating risky trade orders. This helped us improve our results compared to the binary classification results. This approach generates a fewer number of trades but with higher accuracy, as reported in “Experiments” section.

Histogram analysis and threshold calculation

In addition to the decrease and increase classes, we needed to determine the threshold we could use to generate a third class—namely, a no-action class—corresponding to insignificant changes in the data. Algorithm 1 was used to determine the upper bound of this threshold value. The aim was to prevent exploring all of the possible difference values and narrow the search space. In other words, we assumed that the optimal threshold value should be in the range of [0, threshold_upper_bound] instead of [0, max_of_differences].

The idea of Algorithm 1 is to determine the upper bound of the threshold based on 85% coverage of all differences. To do that, first, histogram analysis was performed on the closing prices of the EUR/USD pair to determine the distributions of price changes occurring in the data during consecutive days.

We placed the EUR/USD ratio differences between consecutive days into 10 bins (as \(number\_of\_bins\) value), which range equally between the minimum (which is 0) and maximum difference values. We determined the count of each bin and sorted them in descending order. After that, the counts of the bins were summed until the sum exceeded 85% of the whole count (the data set size). Then, the maximum difference value of the last bin added was used as the upper bound of the threshold value.

As can be seen in Algorithm 1, it has two phases. In the first phase, which simply corresponds to line 2, the whole data set is processed linearly to determine the distributions of the differences, using a simple histogram construction function. The second phase is depicted in detail, corresponding to the rest of the algorithm. To improve the threshold construction operation, an upper bound of the potential threshold was calculated as the value that is larger than 85% of the differences between two consecutive days’ closing values.

The threshold value should be determined based on entropy. Entropy is related to the distribution of the data. The following formula defines entropy where \(p_i\) corresponds to the probability of the occurrence of class i:

To get balanced distribution, we calculated the entropy of class distribution in an iterative way for each threshold value up until the maximum difference value. However, we precalculated the threshold of the upper bound value and used it instead of the maximum difference value. After limiting the iteration number to the upper bound of the threshold found in the histogram analysis, we aimed to find the final threshold \(\tau \), which maximizes entropy. Algorithm 2 shows the details of our approach.

In Algorithm 2, to find the best threshold, potential threshold values are attempted with increments of Dropping the maximum threshold value is thus very important in order to reduce the search space. The main while loop is used to try each threshold value between 0 and the \(threshold\_upper\_bound\) with increments of For each threshold value, the number of increases (labeled as 2) and decreases (labeled as 1) above the threshold value are both determined, and the rest of the changes are assumed to be \(no\_change\) (labeled 0). Then, the entropy value for this distribution is calculated. At the end of the while loop, the distribution that gives the best entropy is determined, and that distribution is used to determine the increase, decrease, and no-change classes.

In our experiments, we observed that in most cases, the threshold upper bound approach significantly reduced the search space (i.e., searching for the threshold value). In a typical case, this improvement corresponds to reducing the search space to around 20% of the original. For example, in one case, the maximum difference value was , but our approach determined the upper bound of the threshold value to be In this case, the optimum threshold value was found to be

Postprocessing

The purpose of this processing is to determine the final class decision. We combined the predictions of the ME_LSTM and TI_LSTM models with the following set of rules:

• If one model’s prediction is class_noact, then the final decision will be class_noact.

• If both models agree on the labels, we set the final decision as this label.

• If the predictions of the two models are different, we choose for the final decision the one whose prediction has higher probability. If the probability is the same, we choose the prediction of the TI_LSTM model.

This is a type of conservative approach to trading; it reduces the number of trades and favors only high-accuracy predictions.

Performance metric

Measuring the accuracy of the decisions made by these models also requires a new approach. Consider that during the testing phase of one of the LSTMs, our model predicts the class as “increase” (or “decrease”), but according to our three-class classification, it actually corresponds to a “no_act” class. In that case, we check if the actual movement is in the same direction with the prediction; that is, there was an “increase” (or “decrease”) but with less than the threshold value. If that is the case, then the prediction is correct, and we treat this test case as the correct classification.

We introduced a new performance metric to measure the success of our proposed method. We defined profit_accuracy as the accuracy that is related to the number of increases and decreases in the predicted labels. We can interpret this metric such that it gives the ratio of the number of profitable transactions over the total number of transactions, defined using Table 2. In the below formula, the following values are used:

• True_dec: the number of true predictions decreases

• True_inc: the number of true predictions increases

• False_dec_noact: the number of predictions of the no-action class decreases

• False_inc_noact: the number of predictions of the no-action class increases

• False_inc_dec: the number of predictions of the decrease class increases

• False_dec_inc: the number of predictions of the increase class decreases

Note that in the above formula, there is no case corresponding to the “True_inc_noact” and the “True_dec_noact” counts since we converted such decisions into “True_inc” and “True_dec,” respectively, as explained above.

After applying the labeling algorithm, we obtained a balanced distribution of the three classes over the data set. This algorithm calculates different threshold values for each period and forms different sets of class distributions. For predictions of different periods, the thresholds and corresponding number of data points (explicitly via training and test sets) in each class are calculated, as shown in Table 3.

This table shows that the class distributions of the training and test data have slightly different characteristics. While the class decrease has a higher ratio in the training set and a lower ratio in the test set, the class increase shows opposite behavior. Class \(no\_action\), meanwhile, is more stable in both sets. This is because a split is made between the training and test sets without shuffling the data sets to preserve the order of the data points.

We collected daily EUR/USD rates for a total of consecutive days. We used the first days of this data to train our models and the last days to test them. Our models aims to determine if there will be an “increase” or “decrease” in the next day, 3 days ahead, and 5 days ahead of the day of the prediction. If one of these is predicted, a transaction is considered to be started on the test day ending on the day of the prediction (1, 3, or 5 days ahead). Otherwise, no transaction is started. A transaction is successful and the traders profit if the prediction of the direction is correct.

Experiments on long-term real data

For time-series data, LSTM is typically used to forecast the value for the next time point. It can also forecast the values for further time points by replacing the output value with not the next time point value but the value for the chosen number of data points ahead. This way, during the test phase, the model predicts the value for that many time points ahead. However, as expected, the accuracy of the forecast usually diminishes as the distance becomes longer.

Zhang et al. () used a very similar LSTM model for stock price prediction. They defined it as an n-step prediction as follows:

This simply corresponds to mapping the history of prices from \(p_1\) to \(p_t\) into n-steps ahead. They performed experiments for 1, 3, and 5 days ahead. In their experiments, the accuracy of the prediction decreased as n became larger.

Our experiments also involved 1-day, 3-day, and 5-day predictions of the directional movement of the EUR/USD currency pair. We used individual LSTM models and the simple combined LSTM as baselines and compared them with our proposed hybrid model. We also present the number of total transactions made on test data for each experiment. Accuracy results are obtained for transactions that are made.

For each experiment, we performed 50, , , and iterations in the training phases to properly compare different models. The execution times of the experiments were almost linear with the number of iterations. For our data set, using a typical high-end laptop (MacBook Pro, GHz dual-core Intel Core i5 processor, 8 GB memory, GB disk space), the training phase for iterations took more than 7 h.

Forecasting one day ahead

Macroeconomic LSTM model results

As seen in Table 4, this model shows huge variance in the number of transactions. Meanwhile, the profit_accuracy results show small variance, with % ± 3,72% accuracy on average. Additionally, the average predicted transaction number is , which corresponds to % of the test data.

Technical LSTM model results

In these experiments, whose results are shown in Table 5, the profit_accuracy results are also close to each other, with % ± % accuracy on average. For this LSTM model, the average predicted transaction number is , which corresponds to % of the test data.

Macroeconomic and technical LSTM model results

The results for this model are shown in Table 6. The profit_accuracy results have higher variance, with % ± % accuracy on average. The average predicted transaction number is , which corresponds to % of the test data. One major difference of this model is that it is for iterations. For this test case, the accuracy significantly increased, but the number of transactions dropped even more significantly.

Hybrid LSTM model results

Table 7 summarizes the profit_accuracy values and the number of transactions for each case in this model. In some experiments, the number of transactions is quite low. In particular, for iterations, our model generated very few transactions, which corresponds to the “increase” and “decrease” predictions. Basically, the total number of decrease and increase predictions are in the range of [8, ], with an overall average of That value corresponds to a transaction ratio of \({/ = }\)%. Moreover, we obtained an average profit_accuracy in 16 cases of % ± % and % ± % for ME_LSTM- and TI_LSTM-based modified hybrid models, respectively, where and represent standard deviations.

When we analyze the results for one-day-ahead predictions, we observe that although the baseline models made more transactions ( more on average out of ), our hybrid model predicted more accurately (25,57% better on average).