The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with ...non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.
We introduce a new wavelet based procedure for detecting outliers in financial discrete time series. The procedure focuses on the analysis of residuals obtained from a model fit, and applied to the ...Generalized Autoregressive Conditional Heteroskedasticity (GARCH) like model, but not limited to these models. We apply the Maximal-Overlap Discrete Wavelet Transform (MODWT) to the residuals and compare their wavelet coefficients against quantile thresholds to detect outliers. Our methodology has several advantages over existing methods that make use of the standard Discrete Wavelet Transform (DWT). The series sample size does not need to be a power of 2 and the transform can explore any wavelet filter and be run up to the desired level. Simulated wavelet quantiles from a Normal and Student t-distribution are used as threshold for the maximum of the absolute value of wavelet coefficients. The performance of the procedure is illustrated and applied to two real series: the closed price of the Saudi Stock market and the S&P 500 index respectively. The efficiency of the proposed method is demonstrated and can be considered as a distinct important addition to the existing methods
Understanding natural processes often involves intricate nonlinear dynamics. Nonlinear evolution equations are crucial for examining the behavior and possible solutions of specific nonlinear systems. ...The Vakhnenko equation is a typical example, considering that this equation demonstrates kink and lump soliton solutions. These solitons are possible waves with several intriguing features and have been characterized in other naturalistic nonlinear systems. The solution of nonlinear equations demands advanced analytical techniques. This work ultimately sought to find and study the kink and lump soliton solutions using the Riccati–Bernoulli sub-ode method for the Vakhnenko equation (VE). The results obtained in this work are lump and kink soliton solutions presented in hyperbolic trigonometric and rational functions. This work reveals the effectiveness and future of our method for solving complex solitary wave problems.
The purpose of this study is to develop new iterative oscillation criteria for second-order half-linear advanced dynamic equations. These findings improve and extend recently established criteria for ...the same equation by several authors as well as encompass the existing classical criteria for associated ordinary dynamic equations. Some examples are given to show that the outcomes are accurate, practical, and adaptable.
This study investigates the problem of outlier detection based on discrete wavelet transform in the context of time series data where the identification and treatment of outliers constitute an ...important component. An outlier is defined as a data point that deviates so much from the rest of observations within a data sample. In this work we focus on the application of the traditional method suggested by Tukey (1977) for detecting outliers in the closed price series of the Saudi Arabia stock market (Tadawul) between Oct. 2011 and Dec. 2019. The method is applied to the details obtained from the MODWT (Maximal-Overlap Discrete Wavelet Transform) of the original series. The result show that the suggested methodology was successful in detecting all of the outliers in the series. The findings of this study suggest that we can model and forecast the volatility of returns from the reconstructed series without outliers using GARCH models. The estimated GARCH volatility model was compared to other asymmetric GARCH models using standard forecast error metrics. It is found that the performance of the standard GARCH model were as good as that of the gjrGARCH model over the out-of-sample forecasts for returns among other GARCH specifications.
Artificial intelligence (AI) based business process optimization has a significant impact on a country’s economic development. We argue that the use of artificial neural networks in business ...processes will help optimize these processes ensuring the necessary level in the functioning and compliance with the foundations of sustainable development. In this paper, we proposed a mathematical model using AI to detect outliers in the daily return of Saudi stock market (Tadawul). An outlier is defined as a data point that deviates too much from the rest of the observations in a data sample. Based on the Engle and Granger Causality test, we selected inflation rate, repo rate, and oil prices as input variables. In order to build the mathematical model, we first used the Tukey method to detect outliers in the stock return data from Tadawul that are collected during the period from October 2011 to December 2019. In this way, we categorized the stock return data into two classes, namely, outliers and nonoutliers. These data are further used to train artificial neural network in conjunction with particle swarm optimization algorithm. In order to assess the performance of the proposed model, we employed the mean squared error function. Our proposed model is signified by the mean squared error value of 0.05. The proposed model is capable of detecting outlier values directly from the inflation rate, repo rate, and oil prices. The proposed model can be helpful in developing and applying intelligent optimization techniques to solve problems in business processes.
We aim to detect outliers in the daily stock price indices from the Saudi Arabia stock exchange (Tadawul) with 2026 observations from October 2011 to December 2019 provided by the Saudi Authority for ...Statistics and the Saudi Central Bank. We apply the Multi-Layer Perceptron (MLP) algorithm for detecting outliers in stock returns. We select the inflation rate (Inflation), oil price (Loil), and repo rate (Repo) as input variables to the MLP architecture. The performance of the MLP is evaluated using standard metrics for binary classification, namely the false positive rate (FP rate), false negative rate (FN rate), F-measure, Matthews correlation coefficient (MCC), accuracy (ACC), and area under the ROC curve (AUC). The results demonstrate the efficiency and good performance of the MLP algorithm based on different criteria tests.
This study investigates the problem of outlier detection based on discrete wavelet transform in the context of time series data where the identification and treatment of outliers constitute an ...important component. An outlier is defined as a data point that deviates so much from the rest of observations within a data sample. In this work we focus on the application of the traditional method suggested by Tukey (1977) for detecting outliers in the closed price series of the Saudi Arabia stock market (Tadawul) between Oct. 2011 and Dec. 2019. The method is applied to the details obtained from the MODWT (Maximal-Overlap Discrete Wavelet Transform) of the original series. The result show that the suggested methodology was successful in detecting all of the outliers in the series. The findings of this study suggest that we can model and forecast the volatility of returns from the reconstructed series without outliers using GARCH models. The estimated GARCH volatility model was compared to other asymmetric GARCH models using standard forecast error metrics. It is found that the performance of the standard GARCH model were as good as that of the gjrGARCH model over the out-of-sample forecasts for returns among other GARCH specifications.
The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with ...non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.
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