The aim was to prevent exploring all of the possible difference values and narrow the search space. We determined the count of each bin and sorted them in descending order. 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.

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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. The threshold value should be determined based on entropy. Entropy is related to the distribution of the data. 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. Algorithm 2 shows the details of our approach. In Algorithm 2, to find the best threshold, potential threshold values are attempted with increments of 0. Dropping the maximum threshold value is thus very important in order to reduce the search space. 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. For example, in one case, the maximum difference value was 0. In this case, the optimum threshold value was found to be 0.

Random Decision Forest in Reinforcement learning - MQL5 Articles

The purpose of this processing is to determine the final class decision. If the predictions of the two models are different, we choose for the final decision the one whose prediction has higher probability. This is a type of conservative approach to trading; it reduces the number of trades and favors only high-accuracy predictions.

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Measuring the accuracy of the decisions made by these models also requires a new approach. 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 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:. 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. 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 used the first days of this data to train our models and the last days to test them. 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.

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Otherwise, no transaction is started. A transaction is successful and the traders profit if the prediction of the direction is correct. 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.

They defined it as an n-step prediction as follows:. They performed experiments for 1, 3, and 5 days ahead. In their experiments, the accuracy of the prediction decreased as n became larger. 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, 2. As seen in Table 4 , this model shows huge variance in the number of transactions.

Modeling and Trading the EUR/USD Exchange Rate Using Machine Learning Techniques

Additionally, the average predicted transaction number is For this LSTM model, the average predicted transaction number is The results for this model are shown in Table 6. The average predicted transaction number is 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. In some experiments, the number of transactions is quite low.

Basically, the total number of decrease and increase predictions are in the range of [8, ], with an overall average of When we analyze the results for one-day-ahead predictions, we observe that although the baseline models made more transactions Table 8 presents the results of these experiments. One significant observation concerns the huge drop in the number of transactions for iterations without any increase in accuracy. Furthermore, the variance in the number of transactions is also smaller; the average predicted transaction number is There is a drop in the number of transactions for iterations but not as much as with the macroeconomic LSTM.

The results for this model are presented in Table However, the case with iterations is quite different from the others, with only 10 transactions out of a possible generating a very high profit accuracy. On average, this value is However, all of these cases produced a very small number of transactions. When we compare the results, similar to the one-day-ahead cases, we observe that the baseline models produced more transactions more than The results of these experiments are shown in Table Table 13 shows the results of these experiments. Again, the case of iterations shows huge differences from the other cases, generating less than half the number of the lowest number of transactions generated by the others.

Table 14 shows the results of these experiments. Meanwhile, the average predicted transaction number is However, the case of iterations is not an exception, and there is huge variance among the cases. From the five-days-ahead prediction experiments, we observe that, similar to the one-day- and three-days-ahead experiments, the baseline models produced more transactions more than This extended data set has data points, which contain increases and decreases overall. Applying our labeling algorithm, we formed a data set with a balanced distribution of three classes.

Table 16 presents the statistics of the extended data set.

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Below, we report one-day-, three-days-, and five-days-ahead prediction results for our hybrid model based on the extended data. The average the number of predictions is The total number of generated transactions is in the range of [2, 83]. Some cases with iterations produced a very small number of transactions. The average number of transactions is Table 19 shows the results for the five-days-ahead prediction experiments.

Interestingly, the total numbers predictions are much closer to each other in all of the cases compared to the one-day- and three-days-ahead predictions. These numbers are in the range of [59, 84].

On average, the number of transactions is Table 20 summarizes the overall results of the experiments. However, they produced 3. In these experiments, there were huge differences in terms of the number of transactions generated by the two different LSTMs. As in the above case, this higher accuracy was obtained by reducing the number of transactions to Moreover, the hybrid model showed an exceptional accuracy performance of Also, both were higher than the five-days-ahead predictions, by 5.

The number of transactions became higher with further forecasting, for It is difficult to form a simple interpretation of these results, but, in general, we can say that with macroeconomic indicators, more transactions are generated.