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.
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Given that we are successively computing the derivative of an activation function by use of the chain rule, the gradient gets smaller and smaller the further away a weight is from the output layer see Fig. In RNNs, this problem, routinely called the problem of gradient vanishing, is amplified by the sequential data processing of the network. Specifically, the gradient signal vanishes not only across layers but also across time steps. In consequence, RNNs face difficulties in modeling long-term dependencies, and much research has sought ways to overcome this issue Schaefer et al.
The problem of gradient vanishing also implies that the magnitude of weight adjustments during training decreases for those weights.
Effectively, weights in early layers learn much slower than those in late hidden layers closer to the output Nielsen Note that the recursive application of the chain rule in neural network training may also cause a problem closely related to that of gradient vanishing. This problem is called gradient explosion and it occurs when recursively multiplying weight matrices with several entries above one in the backward pass of network training.
Remedies of this problem, which help to stabilize and accelerate neural network training, include gradient clipping and batch normalization Goodfellow et al. Twenty years after its invention, LSTM and its variants have turned out to become a state-of-the-art neural network architecture for sequential data.
The following discussion of the LSTM cell follows Graves as it seems to be one of the most popular LSTM architectures in recent research and is also available in the widely used Python library Keras Chollet et al. The central feature that allows LSTM to overcome the vanishing gradient problem is an additional pathway called the cell state.
The cell state is a stream of information that is passed on through time. Its gradient does not vanish and enforces a constant error flow through time Hochreiter a. The cell state allows the LSTM to remember dependencies through time and facilitates bridging long time lags Hochreiter and Schmidhuber Figure 2 depicts a single LSTM cell with all but the cell state pathway grayed out.
Note that the cell state contains no activation functions but only linear operations. The following discussion details how the cell state is maintained, updated, or read. A single LSTM unit a memory block according to Olah with all but the cell state pathway grayed out. The LSTM cell contains a number of gate structures that allow accessing the cell. It takes the weighted current and recurrent inputs and maps them to the interval [0, 1]. As shown in Fig. The objective of this gate is to protect the information of the cell state, which has accumulated over previous time steps, from irrelevant updates.
Therefore, the input gate selectively updates the cell state with new information Hochreiter and Schmidhuber It is not exactly the parts that got remembered that get updated, and not exactly the ones that were forgotten either. As in a FNN, predictions are computed from the hidden state by applying an output activation in the final layer. The different gates and activations work together to save, keep, and produce information for the task at hand. This architecture is an augmented version of the original LSTM architecture and the setup most common in the literature Greff et al.
Figure 7 , which depicts a sequence of LSTM cells through time, conveys how information can be propagated through time via the cell state. There exist a few variants of the LSTM cell with fewer or additional components. For example, one modification concerns the use of peephole connections , which allow the cell state to control the gates and have been shown to increase LSTM resilience toward spikes in time series Gers and Schmidhuber Greff et al.
They start from an LSTM cell with all gates and all possible peephole connections and selectively remove one component, always testing the resulting architecture on data from several domains.
Forex Prediction Lstm - Forex Ea Generator 6 Tutorial
The empirical results suggest that the forget gate and the output activation function seem particularly important, while none out of the investigated modifications of the above LSTM cell significantly improves performance Greff et al. In view of these findings, we focus on the LSTM as described above. They also use gates but simplify the handling of the cell state.
It decides how much of the recurrent information is kept:. A reset gate controls to which extent the recurrent hidden state is allowed to feed into the current activation:. The new activation can be computed as. Therefore, we consider both types of RNNs in our empirical evaluation. Financial markets are a well-studied subject. Starting with seminal work of Fama , a large body of literature has examined the informational efficiency of financial markets.
Empirical findings do not offer a clear result. It might be because of such contradictions that a statistical modeling of market prices, volatility, and other characteristics continues to be a popular topic in the forecasting and machine learning literature. The range of forecasting methods that has been considered is very broad and comprises econometric models such as ARIMA, GARCH, and their derivatives, and various machine learning and computational intelligence approaches such as support vector machines, ensemble models and fuzzy system.
Survey papers such as Cavalcante et al. Past price movements and transformation of these methods, for example, in the form a technical indicators Lo et al. More recently, research has started to examine auxiliary data sources such as financial news Feuerriegel and Prendinger ; Zhang et al.
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In this paper, we focus on artificial neural networks. Neural networks have been a popular instrument for financial forecasting for decades and represent the backbone of modern modeling approaches in the scope of deep learning. With regard to their applications in finance, feedforward neural networks FNN have received much recognition and have been used by several studies to predict price movements Hsu et al.
From a methodological point of view, RNNs are better suited to process sequential data i. Therefore, we focus the reminder of the literature review to studies that employed RNNs for financial forecasting and summarize corresponding studies in Table 1.
To depict the state of the art in the field, we consider the type of RNN as well as benchmark methods, the type of features used for forecasting, the target variable, and whether a study employed a trading strategy. In addition to reporting statistical measures of forecast accuracy such as the mean-squared error, a trading strategy facilitates examining the monetary implications of trading model forecasts.
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The last column of Table 1 sketches the main focus of a paper such as testing the EMH or the merit of a specific modeling approach such as ensemble forecasting. Table 1 suggests that there is no unified experimental framework. Notable differences across the financial time series considered in previous work exemplify this variation. About half of the studies adopt a univariate approach and use either historic prices, returns, or transformations of these as input to forecasting models. Other studies derive additional features from the time series, for example, in the form of a technical indicator, or consider external sources such as prices from other financial instruments.
Evaluation practices display a similar variance with roughly 50 percent of papers performing a trading evaluation and the rest focusing exclusively on forecast accuracy. In terms of neural network architectures, studies examining RNNs in the s can be seen as forerunners, with comparatively little research on the applications of RNNs available at that time. One of the earliest studies includes Kamijo and Tanigawa who use an RNN in the scope of technical stock analysis.
Interestingly, Table 1 also identifies some earlier studies that examine the foreign exchange market. Giles et al. These studies predate the publication of the seminal LSTM paper by Hochreiter and Schmidhuber and use relatively short input sequences of length smaller than 10 as features. Xiong et al. Shen et al. An interesting finding of Table 1 concerns the foreign exchange market. To the best of our knowledge, the studies of Kiani and Kastens and Hussain et al.
This observation inspires the focal paper.
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To set observed results into context, we contrast the performance of RNNs with that of a FNN and a naive benchmark model. Dollar USD. The selection of data follows previous work in the field Kuan and Liu ; Tenti ; Giles et al.
1 Introduction
The data set consists of 12, rows representing daily bilateral exchange rates from January 4, until August 25, However, the time series are not of the same length. The exchange rates and the corresponding daily returns are also plotted in Fig. From the return plots in the middle column, we observe that the transformation from prices to returns removes trends, but the return series still exhibit non-stationarity.
In particular, the histograms, kernel density estimators, and rug plots indicate leptokurtic distributions, and the large kurtosis values in Table 2 support this observation. Prices, 1-day returns, and a combination of histograms, KDE, and rug plots of the one-day percentage returns for the four foreign exchange rate time series.
In order to prepare the data for analysis, we divide each time series into study periods, scale the training data, and create input sequences and target variable values. Exchange rates represent the price of one unit of currency denominated in another currency, whereby we consider the USD as denominator. The one-day percentage return can then be calculated as the percentage change of the price from time t to the following trading day:. Before model training, we scale the returns to the interval [ l , u ] using min-max scaling. To avoid data leakage, we perform the scaling for each study period individually, which ensures that the scaler is fitted to the training data and has no access to the trading or test data.
The approach of using lagged returns, and more generally past realizations of the price signal, as input for a RNN follows the recent work of Fischer and Krauss , who find it to deliver highly accurate forecasts. Using multiple features would also facilitate the constructions of more advanced network designs. One could, for example, envision crafting time point embeddings that mimic the word embeddings, which are employed in natural language processing. Footnote 1. We leave the design of corresponding deep learning-based forecasting models and their empirical evaluation for future research.
We formulate the prediction task as a binary classification problem. The focus on directional forecasts is motivated by recent literature Takeuchi ; Fischer and Krauss Previous studies found foreign exchange rates to exhibit long-term memory van de Gucht et al.
This suggests the suitability of GRUs and LSTMs with their ability to store long-term information, provided they receive input sequences of sufficient length. On the contrary, a FNN, which we also consider as benchmark, regards the observations as distinct features. To test the predictive performance of different forecasting models, we employ a sliding-window evaluation, which is commonly used in previous literature Krauss et al.
This approach forms several overlapping study periods, each of which contains a training and a test window. In each study period, models are estimated on the training data and generate predictions for the test data, which facilitate model assessment. Subsequently, the study period is shifted by the length of one test period as depicted in Fig. Such evaluation is efficient in the sense that much data are used for model training while at the same time predictions can be generated for nearly the whole time series.
Only the observations in the first training window cannot be used for prediction. Sliding window evaluation: Models are trained in isolation inside each study period, which consists of a training set and a trading test set. The models are trained only on the training set, predictions are made on the test set, which is out of sample for each study period. Then, all windows are shifted by the length of the test set to create a new study period with training set and out-of-sample test set from Giles et al. The models are trained to minimize the cross-entropy between predictions and actual target values.
That way, the training process can be interpreted as a maximum likelihood optimization, since the binary cross-entropy is equal to the negative log-likelihood of the targets given the data.