An Intelligent Approach for Predicting Stock Market Movements in Emerging Markets Using Optimized Technical Indicators and Neural Networks

2.1 Stocks Analyzed

To reduce potential biases in the results and increase the reliability of our findings, we carefully selected a time frame for our analysis that ranged from December 12, 2009, to January 1, 2020. The rationale for this time frame is twofold. First, it allows us to exclude economic changes caused by atypical phenomena during global pandemics (Almehmadi, 2021; Verma et al., 2022), which could significantly impact the results. By focusing on the period preceding these unprecedented events, we hope to maintain the stability of our analysis and isolate the impact of other economic factors. In financial stock analysis, the utilization of pre-pandemic data assumes paramount significance, particularly concerning the introduction of innovative methodologies for indicator selection. Antecedent data are a fundamental, extensive, and stable cornerstone, facilitating the training and validation processes intrinsic to machine learning methodologies. By encompassing periods antedating the pandemic, datasets encapsulate diverse market conditions, spanning from periods of stability to instances of heightened volatility alongside various economic cycles. This diversity enables models to discern a broad spectrum of patterns and relationships within the data, augmenting their adaptability and predictive capacity. Furthermore, pre-pandemic data aids in constructing models capable of distinguishing between typical market fluctuations and extraordinary occurrences such as pandemic-induced disruptions. This differentiation is critical in averting models from succumbing to biases due to pandemic-specific irregularities, ensuring their resilience and applicability across diverse market landscapes. Thus, the incorporation of pre-pandemic data reinforces the credibility, generalizability, and effectiveness of feature selection.

In addition, our focus on BlackRock’s ETFs involved a meticulous selection of three funds: ECH, EWZ, and iShares Core S&P 500 ETF (IVV). This intentional choice represents emerging and developed markets, offering a nuanced analysis of predictive features and model performance. Enriching our analysis, we explore the sectoral distribution within each ETF, contributing to a comprehensive understanding of how different economic activities influence their performance. This sectoral consideration enhances the depth of our study, uncovering insights into the interconnectedness of sectors within emerging and developed markets and providing a more holistic view of the factors influencing ETF trends. (Table 2 for the sector distribution in this analysis.)

Table 1 shows these ETFs’ main market exposure areas, while Figure 2 depicts their Opening price during the considered period.

Figure 2

Behavior of Open values for ECH, EWZ, and IVV.

The data that can be obtained from Yahoo Finance for each period are the opening price Open, the highest price High, the lowest price Low, the closing price Close, the number of transactions Volume, the adjusted close price for splits, the dividends yield, and capital gain distributions Adjusted close. Table 2 presents the data summarized for the opening price.

We use a classification strategy to predict a qualitative variable Γ such that

The response variable Γ corresponds to the class label of the day. Figure 3 portrays the sum of variable Γ during the considered period for each ETF.

Figure 3

The Γ Cumulative Movement for ECH, EWZ, and IVV.

2.2 Methodological Approach Based on Data Mining

The CRISP-DM specifies the stages in which the datasets are processed (Shearer, 2000). CRISP-DM covers six stages: understanding the data and the domain of the problem, the data preparation, the construction of the model, the evaluation of the proposed model, and, finally, the presentation of the results.

Data preparation is the main stage in any data mining methodological approach. In this stage, the raw data are cleaned, merged, scaled, and feature-engineered to enhance the quality of the information, improving the machine learning algorithm’s behavior (Jamshed et al., 2019; Sun et al., 2017). The data preparation stage converts inconsistent and incomplete real-world data into a readable format. In this work, the data preparation stage was primarily based on the following activities.

2.3 Technical Indicators

This study employed the Pandas Technical Analysis Library (Pandas TA) to compute a comprehensive set of technical indicators. Pandas TA, an extension of the widely-used Pandas package, provides a versatile toolkit encompassing customizable technical indicators, utility functions, and candlestick patterns. Through the application of Pandas TA, we expanded our feature set by an additional 210 indicators from the six fundamental attributes sourced from the Yahoo Finance database, including Open, High, Low, Close, Adjusted Close, and Volume, complementing the previously acquired features. Consequently, our dataset now comprises a total of 216 daily features. This amalgamation equips our analytical framework with a rich and diverse set of features, facilitating a nuanced exploration of market trends and enhancing the depth of our predictive model.

2.4 Class Assignment

For each day t , we obtained the Γ function previously defined. Observe that G a m m a ( t ) indicates the delta sign of the ETF Open price. Hence, we employ a binary classification strategy to identify whether this happens, so each day’s class corresponds to its Γ evaluation. In order to apply the class assignment, the order of the dataset gets decreased by one.

2.5 Data Normalization

Since the scales of the features computed earlier fluctuate significantly, we use a min–max approach to convert the data linearly. Every feature’s minimum values are converted to 0; afterward, the maximum values are transformed to a 1, and finally, all other values are adjusted to a decimal between 0 and 1. The formula, for each value, is given as follows:

If normalization is performed, we avoid diluting the effectiveness of an equally important feature (on a lower scale) because other features have values on a larger scale.

2.6 Data Cleaning

The process of preparing raw data for analysis by removing incomplete data is known as data cleaning, and this prepares the data for the data mining process, which needs valuable information. As in the previous step, missing or non-available data are unavoidable when technical features are calculated. For example, when calculating SMA, it is necessary to select a range of days before the day we are calculating; hence, for the initial days of the dataset, the SMA cannot be obtained; thus, the data for those will be missing. To handle this issue, we proceeded to drop each day containing unavailable data, so the database spanned from 01/01/2009 to 01/01/2020.

2.7 MLP for Predictive Analysis

An MLP was used to predict the qualitative variable Γ . An MLP can be implemented as a linear and binary classifier since it finds the most appropriate boundary between the two classes. Hence, it may discern the structural differences between two given classes, identify the linear space separating each one, and determine the likelihood of a given data point belonging to a class.

An MLP is a neural network connecting multiple neurons or perceptrons, partitioned into the input, hidden, and output layers. The nodes form a directed acyclic graph, meaning the paths connect nodes in layers from one layer to the next, as shown in Figure 4. Apart from the input ones, each neuron has a nonlinear activation function, a bias, and connecting weights, which the MLP trains by back-propagation in a supervised learning fashion (Ecer et al., 2020) so that the error value can be updated in a much more successful way. The MLP used in this work is depicted in Figure 4. We use this MLP to evaluate the performance of the different subsets of technical features obtained by several feature selection approaches described below.

Figure 4

The input layer cardinality of the MLP corresponds to the number of input features; there would be 216 nodes if all features are considered. The hidden layer contains (input features + classes)/2 = 109 nodes. Finally, the output layer contains only one node.

The configuration parameters for the MPL are delineated in the following excerpt:

hidden_layer_sizes = int((X.shape[1] + len(np.unique(y)))/2)

MLPClassifier(hidden_layer_sizes=hidden_layer_sizes, activation=’logistic’,

solver=’lbfgs’, batch_size=’auto’, learning_rate=’adaptive’,

learning_rate_init=0.03, max_iter=5000, momentum=0.2,

random_state=np.random.get_state()[1][0], early_stopping=False)

# cross-validate  knn  on  our  training  sample  with  nof_folds=10

cv_generator = StratifiedKFold(n_splits=10, shuffle=False)

2.8 Statistical Measures for Feature Selection

As mentioned earlier, in this work, we use an approach based on exploratory analysis and reduction of the input space to improve the accuracy of multiclass classification in machine learning. This feature selection effectively reduces dimensionality, limiting the number of variables that characterize the data. This reduction is performed by selecting the subset of features that provide more information, dropping the redundant ones to obtain a significant quantity of information from a lower-dimensional space (Reddy et al., 2020). In the machine learning paradigm, a narrower input space implies a computationally efficient modeled structure since it is desirable to have input data with few variables that produce small models that generalize well. The above is especially valid for linear models with related degrees of freedom and number of inputs.

We selected features after the data cleaning and scaling stages and before the predictive model’s training phase to reduce the input space. The techniques for selecting the most relevant characteristics used in this work are described below.

2.9 Low Variance

Low variance feature removal is a basic and straightforward approach to feature selection. The low variance technique removes all characteristics whose variance does not reach the established threshold. This feature selection algorithm only works with features, not class outputs, making it an unsupervised technique. If a feature’s variance is close to zero, then a feature is approximately constant and will not improve the model’s performance. In that case, it should be removed. The expression defines the variance as follows:

where p is the probability of X = P ( X ) .

2.10 Chi-Squared

In this method, each feature is evaluated against the classes. For each pair of features, Chi-squared values are calculated; a larger Chi-squared value commonly indicates a greater interdependence between the two attributes. This method identifies the features that are more likely to be independent of the class and thus unrelated to the classification. Since this approach is commonly used with categorical attributes, it is needed first to discretize the numeric attributes at different intervals. The next expression is used to calculate the Chi-squared statistic:

where f 0 is the observed frequency (the observed counts in the cells), and f e is the expected frequency if no relationship existed between the variables.

2.11 Least Absolute Shrinkage and Sselection Operator (LASSO)

The LASSO is a regularization technique. Regularization is one technique to address the issue of overfitting by providing new information and, as a result, modifying the model’s parameter values to induce a penalty, as can be seen in the following expressions:

where y i ˆ = y 0 + ∑ j = 1 m X i j w j . The residual sum of squares and an additional penalty for feature weights minimize the above loss function. The greater the chosen value for λ , the greater the penalty on feature weights, and the more they get removed.

2.12 Tree-based Feature Selection

The extra trees classifier is a meta-method that fits several randomized decision trees on various dataset subsamples and averages their results to enhance the prediction accuracy and counter over-fitting. Those randomized decision trees are extremely randomized trees created by heavily randomizing cut point and attribute selection while splitting a tree node.

2.13 Pearson’s Correlation

Pearson’s correlation coefficient calculates the linear relationship between two random variables. Its values range between − 1 and 1; if the coefficient value is 0, then the two random variables do not have a linear relationship. If the coefficient value is negative, the correlation is negative, and when the value is positive, the correlation between the two random variables is positive. This coefficient is given as follows:

where σ is the standard deviation of the sample.

2.14 Principal Feature Analysis

The principal feature analysis method selects the principal features by adopting the structure of the principal components of the feature set, which retain the majority of the information, both in terms of maximum variability of the features in lower-dimensional space and minimization of the reconstruction error. This technique constructs the covariance matrix of all features and computes the eigenvectors of the matrix by applying a principal component analysis. Afterward, a vector is associated with each feature, and a k -means algorithm clusters the set of vectors. The vectors closest to the centroids are identified as the principal vectors; hence, the features associated with those vectors are deemed the principal features. The principal features can be considered the most dominant characteristics in each cluster and retain the least redundant information in other clusters. An in-depth description of this technique can be found in the study by Lu et al. (2007).

2.15 Mean Absolute Difference (MAD)

The MAD, as can be seen in equation, as the variance, is also a scaled variant. This implies that the greater the MAD, the greater the discriminating power.

where N corresponds to the total of data. With this technique, we rank the features from more discriminant to less discriminant. The value of MAD is not affected by extremely high or shallow values and nonormality.

2.16 Dispersion Ratio (DR)

For a given (positive) feature X i on N patterns, the arithmetic mean x ¯ and the geometric mean x ¯ g are given as follows:

Since x ¯ ≥ x ¯ g , with equality holding if and only if X i , 1 = X i , 2 = … = X i , N , the DR is

The DR can be used as a dispersion measure. When all the feature samples have (roughly) the same value, DR is close to 1, indicating a low-relevance feature. Conversely, a higher value of DR implies a higher dispersion, thus a more relevant feature (Ferreira and Figueiredo, 2012).

2.17 Cross-validation as Sampling Method

Cross-validation is a model validation approach for determining how well a model’s results generalize to a new dataset. Cross-validation aims to reduce overfitting and underfitting by defining a dataset to evaluate the model in the training phase.

This procedure splits the dataset into k partitions, alternating them with training and testing the model, as described in Algorithm 1. In our model, we partitioned the dataset into ten partitions. We chose one partition for testing and the remaining nine for training, then proceeded to the next partition for testing. We used the other nine for training, repeating this process for all partitions and averaging the accuracy.

2.18 Description of the Experiment’s Methodology

The described Algorithm 2 provides a comprehensive methodology for conducting feature selection experiments and evaluating trends in ETFs. The algorithm begins with the input of raw datasets for ETFs. In the first step, feature calculation and preprocessing are executed individually for each ETF. This involves the calculation of technical indicators, class assignments, data normalization, and cleaning. Following this preprocessing, the algorithm proceeds to feature selection.

Statistical measures are used to identify salient features during the feature selection step. The algorithm, in particular, computes the first quartile of the most important features for each statistical measure and ETF. Sets of selected features are then calculated based on their appearance in at least a specified number of subsets.

Moving on to the final step, model evaluation, the algorithm employs an MLP in a K -fold cross-validation setup instead of the well-known technique of splitting the dataset into train, test, and validation partitions; in this work, we use K = 10 . The MLP is fed with the chosen features for each subset of selected features, and the model’s accuracy is assessed for each cross-validation partition. A central tendency measure, a i ¯ , is computed to represent the average accuracy across the cross-validation folds.

In summary, this algorithm provides a systematic and iterative approach to feature selection and evaluation that is specifically designed to identify the most salient extracted features of each ETF in the dataset.

3.1 Practical Implications for Investors in Emerging Markets

Our model possesses the potential to aid investors in market timing and risk management within emerging markets. Through the analysis of predictive indicators, investors can ascertain the optimal timing for entering or exiting positions in ETFs, effectively maximizing returns and minimizing losses. By comprehending market dynamics through our model, investors can promptly adjust their positions in response to changing market conditions, mitigating risks associated with market fluctuations and diminishing exposure to volatility. While our model provides valuable insights for investors operating in emerging markets, it is imperative to acknowledge its limitations and the inherent uncertainties of financial markets. Investors can optimize their investment outcomes by integrating our model into a broader investment framework and adopting a proactive and adaptable approach.