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Table 3 Classification results with ANN/DNN classifiers using transformed data with PCs = 60

Table 3 Classification results with ANN/DNN classifiers using transformed data with PCs = 60

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Fig. 1 Histogram of SPY current return (left) and histogram of adjusted SPY current return (right) eigenproblem var(X)W=AW, where A represents the eigenvalues of var(X). It is also X)W, where var(X) is the variance-covariance matrix of the data X, needs to be created.
Fig. 1 Histogram of SPY current return (left) and histogram of adjusted SPY current return (right) eigenproblem var(X)W=AW, where A represents the eigenvalues of var(X). It is also X)W, where var(X) is the variance-covariance matrix of the data X, needs to be created.
Traditional feed-forward ANNs often utilize the backpropagation learning algorithm (Rumelhart, et al, 1986) based on an iterative process where the connection weights between the layers are adjusted repeatedly in a backwards direction, from the output layer, through the hidden layers, and then to the first hidden layer, such that the difference between the predicted class and the true class measured by the mean squared error (MSE) can be minimized during the procedure. Although other sophisticated learning algorithms have been developed over the years for specific applications, the traditional backpropagation learning is still often used to train newly developed DNNs.
Traditional feed-forward ANNs often utilize the backpropagation learning algorithm (Rumelhart, et al, 1986) based on an iterative process where the connection weights between the layers are adjusted repeatedly in a backwards direction, from the output layer, through the hidden layers, and then to the first hidden layer, such that the difference between the predicted class and the true class measured by the mean squared error (MSE) can be minimized during the procedure. Although other sophisticated learning algorithms have been developed over the years for specific applications, the traditional backpropagation learning is still often used to train newly developed DNNs.
Table 1 The ANN classification results using 12 transformed datasets Once again, the first row in Ta benchmark ANN classifier (wit vide the results from the various DNN classifiers (with the number of hid than 10). In each of the three ta increases from 12 to 28, the accuracy of the classification in the testing creases, reaching the highest va 4) when the number of hidden ues of 58.6 (in Table 2), 59.9 (in Table 3), ayers equals 28, 16, and 22, respectively. bles 2, 3 and 4 provides the classification results using the h 10 hidden layer neurons), while the remaining rows pro- den layers greater bles, it can be observed that as the number of hidden layers phase typically in- and 59.9 (in Table However, after the number of hidden layers becomes larger than 30 or 35, the accuracy o f the classification
Table 1 The ANN classification results using 12 transformed datasets Once again, the first row in Ta benchmark ANN classifier (wit vide the results from the various DNN classifiers (with the number of hid than 10). In each of the three ta increases from 12 to 28, the accuracy of the classification in the testing creases, reaching the highest va 4) when the number of hidden ues of 58.6 (in Table 2), 59.9 (in Table 3), ayers equals 28, 16, and 22, respectively. bles 2, 3 and 4 provides the classification results using the h 10 hidden layer neurons), while the remaining rows pro- den layers greater bles, it can be observed that as the number of hidden layers phase typically in- and 59.9 (in Table However, after the number of hidden layers becomes larger than 30 or 35, the accuracy o f the classification
Table 2 Classification results with ANN/DNN classifiers using entire untransformed data for the testing data stops climbing and drops or converges to values that are close to the results using the ANN classifiers (which includes 10 hidden layers), except for one case where the transformed data with PCs = 60 and the number of hidden layers = 500 is con- sidered. Note that the overfitting issue appears to be under control, in part since all the ANN and DNN classifiers are strictly trained with the same criteria, such that for each classifier the four correction percentages of the classification, corresponding to the train- ing, validation, testing, and entire data sets cannot be significantly different from each other; that is, the absolute value of the percentage difference must be within a defined threshold, for example, 5% (Zhong & Enke, 2017a, 2017b). for the testing data stops climbing and drops or converges to values that are close to the
Table 2 Classification results with ANN/DNN classifiers using entire untransformed data for the testing data stops climbing and drops or converges to values that are close to the results using the ANN classifiers (which includes 10 hidden layers), except for one case where the transformed data with PCs = 60 and the number of hidden layers = 500 is con- sidered. Note that the overfitting issue appears to be under control, in part since all the ANN and DNN classifiers are strictly trained with the same criteria, such that for each classifier the four correction percentages of the classification, corresponding to the train- ing, validation, testing, and entire data sets cannot be significantly different from each other; that is, the absolute value of the percentage difference must be within a defined threshold, for example, 5% (Zhong & Enke, 2017a, 2017b). for the testing data stops climbing and drops or converges to values that are close to the
Table 4 Classification results with ANN/DNN classifiers using transformed data with PCs = 31
Table 4 Classification results with ANN/DNN classifiers using transformed data with PCs = 31
Table 5 Comparison of classification results from DNN classifiers for three data sets simulation is conducted to see if the higher prediction accuracy from the DNN classi- fiers indicates higher profitability among the three datasets with different representa- tion. This study is based on predicting the direction of the SPDR S&P 500 ETF (ticker symbol: SPY) daily returns. Consequently, we modify the trading strategy for classifi- cation models defined by Enke & Thawornwong (2005) as follows.
Table 5 Comparison of classification results from DNN classifiers for three data sets simulation is conducted to see if the higher prediction accuracy from the DNN classi- fiers indicates higher profitability among the three datasets with different representa- tion. This study is based on predicting the direction of the SPDR S&P 500 ETF (ticker symbol: SPY) daily returns. Consequently, we modify the trading strategy for classifi- cation models defined by Enke & Thawornwong (2005) as follows.
Table 6 Simulation results with ANN/DNN classifiers using entire untransformed data 45, or 50. Table 8 shows that the Sharpe ratios that are generated by the trading strat- egies using the DNN classification over the PCA-represented data with PCs = 31 are mostly higher than the Sharpe ratios generated by the ANN-based trading strategy, except for those cases where the number of hidden layers is 12, 24, 26, 45, 50, or 1000. The Sharpe ratios and their corresponding hidden layer numbers that are rele- vant to these exceptions are highlighted in Tables 6, 7 and 8.
Table 6 Simulation results with ANN/DNN classifiers using entire untransformed data 45, or 50. Table 8 shows that the Sharpe ratios that are generated by the trading strat- egies using the DNN classification over the PCA-represented data with PCs = 31 are mostly higher than the Sharpe ratios generated by the ANN-based trading strategy, except for those cases where the number of hidden layers is 12, 24, 26, 45, 50, or 1000. The Sharpe ratios and their corresponding hidden layer numbers that are rele- vant to these exceptions are highlighted in Tables 6, 7 and 8.
Table 7 Simulation results with ANN/DNN classifiers using transformed data with PCs = 6C algorithms to the least amount of data, with both the most accurate forecasting re- sults and the highest risk-adjusted profits being desired. We have also considered this standard for this research. algorithms to the least amount of data, with both the most accurate forecasting re-
Table 7 Simulation results with ANN/DNN classifiers using transformed data with PCs = 6C algorithms to the least amount of data, with both the most accurate forecasting re- sults and the highest risk-adjusted profits being desired. We have also considered this standard for this research. algorithms to the least amount of data, with both the most accurate forecasting re-
Table 8 Simulation results with ANN/DNN classifiers using transformed data with PCs = 37
Table 8 Simulation results with ANN/DNN classifiers using transformed data with PCs = 37
Table 9 Comparison of simulation results from DNN classifiers for three data sets With additional hidden layers and more complicated learning algorithms, DNNs are rec- ognized as an important and advanced technology in the fields of computational intelligence and artificial intelligence. However, DNNs are still regarded as a black box with less clear theoretical confirmations of the learning algorithms that are used in common deep architectures, such as the stochastic gradient descent methodology. These DNN learning algorithms actually increase the computation time as a large number of hidden layers and neurons are included. This area of research needs to receive more attention and effort in the future.
Table 9 Comparison of simulation results from DNN classifiers for three data sets With additional hidden layers and more complicated learning algorithms, DNNs are rec- ognized as an important and advanced technology in the fields of computational intelligence and artificial intelligence. However, DNNs are still regarded as a black box with less clear theoretical confirmations of the learning algorithms that are used in common deep architectures, such as the stochastic gradient descent methodology. These DNN learning algorithms actually increase the computation time as a large number of hidden layers and neurons are included. This area of research needs to receive more attention and effort in the future.
Table 10 The 60 financial and economical features of the raw data
Table 10 The 60 financial and economical features of the raw data
Table 10 The 60 financial and economical features of the raw data (Continued)
Table 10 The 60 financial and economical features of the raw data (Continued)
Table 10 The 60 financial and economical features of the raw data (Continued)
Table 10 The 60 financial and economical features of the raw data (Continued)
Table 10 The 60 financial and economical features of the raw data (Continued)
Table 10 The 60 financial and economical features of the raw data (Continued)
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Computer ScienceArtificial IntelligenceMachine LearningFinancial InnovationData representation
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