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Looking to make some money? Your email address. Apply for similar jobs. Set your budget and timeframe. 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.
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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.
For the recurrent neural networks, activation functions in the recurrent layers are applied as described in Sect. More precisely, we follow Chollet et al.
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One drawback of neural networks is their vulnerability to overfitting Srivastava et al. We employ two regularization techniques:. To that end, a dropout layer randomly masks the connections between some neurons during model training. We use dropout on the non-recurrent connections after all hidden layers as in Zaremba et al. For example, a dropout rate of 25 percent implies that each neuron in the previous layer is dropped with probability 25 percent; on average, a quarter of the neurons of that layer are masked. The validation set error enables us to stop network training conditional on the validation loss.
Neural networks and their underlying training algorithms exhibit several hyperparameters that affect model quality and forecast accuracy. Examples include the number of hidden layers and their number of neurons, the dropout rate or other regularization parameters, as well as algorithmic hyperparameters such as the learning rate, the number of epochs, the size of mini-batches, etc.
Goodfellow et al. Hyperparameter tuning is typically performed by means of empirical experimentation, which incurs a high computational cost because of the large space of candidate hyperparameter settings. We employ random search Bengio for hyperparameter tuning considering the following search space:.
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We set up a supervised training experiment in accordance with Fischer and Krauss and Shen et al. This meant constructing overlapping study periods consisting of training observations and trading observations as depicted in Fig. We then built models with fixed hyperparameters for all time series with the insights from manual tuning.
All models had the following topology:. The other models use different layers but possess the same structure—with the exception that the FNN layers do not pass on sequences and thus the data dimensions between the first and third hidden layers in the FNN are 1, 50 rather than , 50 like in the three recurrent networks. All models were trained using minibatch sizes of 32 samples and the Adam Kingma and Ba optimizer with default parameters, training for a maximum of epochs with early stopping after 10 periods without improvement in validation loss.
We consider three measures of forecast accuracy: logarithmic loss Log loss as this loss function is minimized during network training; predictive accuracy Acc. In addition to assessing classification performance, we employ a basic trading model to shed light on the economic implications of trading on model forecasts.
The position is held for one day. As each test set consist of trading days roughly one year , the annualized net returns of this strategy in study period S are approximated by. As a measure of risk, the standard deviation SD of the series of realized trading strategy returns is considered, and the Sharpe ratio SR is computed as a measure of risk-adjusted returns. The results of this benchmark can be found in Table 3 , both per time series as well as aggregated across time series. The naive benchmarks give accurate direction predictions about half of the time. If the trading strategy defined in Sect.
Recall that the empirical results are obtained from the window-based cross-validation approach depicted in Fig. Table 4 suggests three conclusions. Second, economic measures of forecast performance paint a different picture.
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None of the models is able to produce a large positive return. This is an interesting result in that several previous forecast comparisons observe a different result. We discuss the ramifications of our results in Sect. Third, the deep learning models perform better than the benchmark in terms of accuracy and area under the ROC curve. However, the net returns resulting from applying the selected trading strategy are smaller in most cases. The paper has reported results from an empirical comparison of different deep learning frameworks for exchange rate prediction.
We have found further support for previous findings that exchange rates are highly non-stationary Kayacan et al. Even training in a rolling window setting cannot always ensure that training and trading set follow the same distribution. Another observation concerns the leptokurtic distribution of returns. For example, the average kurtosis of the exchange rate returns examined in this study is 8. This resulted in many instances of returns close to zero and few, but relatively large deviations and could have lead to the models exhibiting low confidence in their predictions.
The results, in term of predictive accuracy, are in line with previous work on LSTMs for financial time series forecasting Fischer and Krauss However, our results exhibit a large discrepancy between the training loss performance and economic performance of the models. This becomes especially apparent in Fig. The observed gap between statistical and economic results agrees with Leitch and Tanner who find that only a weak relationship exists between statistical and economic measures of forecasting performance.
A similar problem might exist between the log loss minimized during training and the trading strategy returns in this study. Arguably, this finding was to be expected and might not come as surprise.
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However, evidence of the merit of deep learning in the scope of exchange rate forecasting was sparse so that expanding the knowledge base with original empirical results is useful. One may take this finding as evidence for the adequacy of using FNNs as benchmark in this study and, more generally, paying much attention to FNNs in previous work on FX markets and financial markets as a whole. As any empirical study, the paper exhibits limitations which could be addressed in future research.
Hussain et al.
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Augmenting the input structure of RNN-based forecasting model by incorporating additional predictors might be another way to overcome the low confidence issue. Moreover, the focus of this study was on deep neural networks.
Many other powerful machine learning algorithms exist. Comparing RNN-based approaches to alternatives such as, e. Another avenue for future research concerns the employed trading strategy. Employing a more advanced trading rule might help to overcome the discrepancy between statistical and economic results. One example of such a trading strategy is the work of Fischer and Krauss who construct a strategy only trading a number of top and bottom pairs from a large set of binary predictions on stock performance.
This particular strategy would, of course, require training on many more time series.
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