Classical Error Research Articles

The usage of the autoregressive integrated moving average model for forecasting milk production in Egypt (2022-2025).

Milk is considered one of the most important capital goods and essential sources of animal protein in the diet of the Egyptian family, as well as an effective means to improve the economic condition of farmers, considering this important view, the policymakers need accurate and advance information regarding future supply for planning on the both short and long term. The study aims to forecast the production of milk in Egypt during the period from 2022 to 2025 using the Autoregressive Integrated Moving Average (ARIMA) model using time series data of milk production (MP) (1970-2021) obtained from the Central Agency for public mobilization and statistics (CAPMS). Augmented Dickey-Fullar Unit Root test, Partial autocorrelation function (PACF), and Autocorrelation function (ACF) of the time series sequence were used to judge the stationarity of the data. After confirming the stationarity of the data, the appropriate ARIMA model was selected based on certain statistical parameters like significant coefficients, values of adjusted R-squared, Akaike information criteria (AIC), Schwarz criterion (SC), and Standard Error of Regression. After the selection of the model based on the previous parameters, the verification of the model was employed by checking the residuals of the Correlogram-Q-Statistics test. The most fitted model to predict the future levels of MP in Egypt was ARIMA (1, 1, and 3). Using the ARIMA (1, 1, 3) model, it could be forecasted that the production of milk in Egypt would show an increasing trend from 6,152.606 thousand tons in 2022 to 6,360.829 thousand tons in 2025.

Johansen’s Cointegration Analysis of Some Factors of Economic Growth and Exports of Products from the Republic of Azerbaijan to Ukraine

In the present paper, a Johansen’s cointegration analysis is carried out considering the volume of exports from Azerbaijan to Ukraine, GDP per capita of Ukraine, the openness of the economy of Ukraine and the economically active population of Azerbaijan for the period 1996-2022, also a comparative analysis of the above indicators is carried out, the characteristics of joint short-term and long-term movements are determined. In the course of research the author used the methodology of modified gravitational modeling, the econometric methodology of time series analysis, including tests for checking stationarity, the extended Dickey-Fuller test, the Granger test for the detection of causality, determining the cointegration dependence using the Johansen’s test, a Vector Error Correction Model (VECM) has been built. First, a basic modified model of gravity has been built, and the statistical adequacy of this model has been checked. A comparative analysis of two regression models was carried out after the inclusion of the trend component in one of them. The dynamic structure of regression residuals was studied and the test for heteroscedasticity and autocorrelation was carried out. It is shown that the most suitable specification for cointegration is the quadratic trend in the initial levels with a linear trend in cointegration relationships, which has led to the emergence of two cointegration vectors. As a result of the completed analysis, two cointegration relationships are obtained. The results of the impulse response functions, decomposition of dispersions and the VECM model in the form of combinations of two cointegrating vectors with the expected signs of the adjustment integers showed that the economic indicators used in the analysis for the specified period maintain cointegration in the long term with the not stable equilibrium joint movements of the factors under study.

Pareto parameter estimation by merging locally weighted median of multiple neural networks and weighted least squares

The Pareto distribution plays an important role in many data analysis tasks. An important aspect of this distribution is the estimation of its parameters. Several studies use classical methods, Bayes, and the neural network (NN) to evaluate Pareto parameters. Others have attempted to combine classical methods with a single NN-based. However, there isn’t enough research to determine the sensitivity of the single NN to the specifics of the training data due to its stochastic training algorithm in the parameter estimation field. The current research aims to prove the efficiency of the aggregation of weighted multiple NN models and weighted ordinary least-squares regression algorithm to overcome the specifics of the training data and the sensitivity to outliers, respectively. The proposed method enables a locally less accurate model to participate to a lesser extent in the overall aggregation. The proposed method was compared with prevalent methods in the area, including the ordinary least squares, weighted ordinary least squares, maximum likelihood estimation, and the Bayes’ using Monte Carlo simulations. The results verified the superiority of the proposed method in terms of regression error metrics. Moreover, it can be adapted to a variety of distributions.

Bank-Specific Decisions and Banks’ Provisioning Behaviour in Nigeria: The Role of IFRSs Adoption and Banks’ Riskiness

Goal: this study examines the relationship between bank loan loss provisioning behaviour and various bank-specific decisions on loan loss reporting. The evidence is derived from several cases of non-performing exposures of Nigerian deposit money banks. Metodology: to investigate the relationship between bank loan loss provisioning behaviour and various bank-specific decisions on loan loss reporting there was created the loan loss bank-specific decisions index (BDI) according to the International Financial Reporting Standards (IFRSs). The hypotheses are tested by using the estimates of panel corrected standard errors regression model. Findings:the results showed that discretionary adjustments to loan loss provisions (LLPV) are typical of Nigerian banks although the earnings manipulations imbedded in discretionary LLPVs (DLPV) are not factored in. However, during IFRS a reversal is evident suggesting bank-specific decisions prompting increased DLPV except for seemingly financially distressed banks. These findings also confirm the relationship between BDI components and provisioning behaviour in individual tests. The study also found out that the provisioning behaviour in Nigeria during global financial crisis was pro-cyclical (nonrational) while during the local economic recession of 2016–2017, it was counter-cyclical (rational). The latter, which happened during the IFRS period, was characterized by income smoothing while the former was addressed at the level of bank-specific decisions. Originality and contribution of the authors: the study contributes to the literature by testing a list of bank-specific factors engendering adjustments to loan loss decisions. It is unique in terms of the empirical reference to numerous bank-specific decisions as a single factor in accounting for loan losses. The paper also establishes the parochial success of institutional changes in the corporate Nigeria and offers useful suggestions for the way forward.

Analyzing the Impact of Employee Perks on Organizational Turnover in the Pharmaceutical Sector of Bangladesh

This study explores the impact of employee benefits on organizational earnings within the pharmaceutical sector in Bangladesh, an emerging economy. To conduct this investigation, researchers gathered pertinent data from the annual reports of 26 pharmaceutical companies listed on the Dhaka Stock Exchange (DSE), spanning the period 2017–2021. The primary variable under scrutiny is the employee benefits ratio (EBR), calculated by dividing the total benefits, excluding regular salaries and wages, by the total revenue. Additionally, the study examines the association between the salaries and wages ratio (SWR) and firm turnover. Focusing on these two key variables, the research also incorporates various control factors— namely, leverage, firm age, tangibility, liquidity, firm size, growth, and non-debt tax shield—to enhance the model's robustness. Organizational turnover are measured using return on assets (ROA) and return on equity (ROE) as the dependent variables. The panel-corrected standard error regression analysis reveals that the employee benefits ratio (EBR) and salaries and wages ratio (SWR) exert a significant positive influence on ROA. This implies that increased salaries and additional benefits serve as motivational factors for employees, fostering job satisfaction and enhancing performance. However, these variables do not demonstrate a significant association with ROE. Furthermore, factors such as firm age, leverage, tangibility, liquidity, and firm size exhibit a notable impact on firm performance. These findings collectively contribute to a comprehensive understanding of the relationship between employee benefits, organizational turnover and will help organizations to design their incentive programs effectively.

SUSTAINABILITY IN PROPERTY TAXATION: AN APPLICATION FOR REVENUE STABILITY AND FAIRNESS PERSPECTIVES, THE CITY OF BUFFALO, NY

The scholarly modeling of property tax has always posed a challenge, with two primary concerns to be addressed: first, maintaining sustainability in the collection, which is primarily a concern for local governments; and second, ensuring fair distribution, which is of greater concern for citizens. In today’s practices, assessment-based property tax increases unmatched expenses in bubble economies. There is a substitution problem in rapid falls, the tendency to not decrease the assessments gives way to black holes and opens the door to ghost cities. This paper proposes alternative approaches, aside from market/land value or last sold price, aimed at improving sustainability and fairness rates. The dataset examined is based on 93.7K records and 88 attributes for assessed value of properties within the City of Buffalo, the United States of America. Since the label (Total Value) is a numerical and continuous value, regression models are selected, where ensemble machine learning methods categorically work well with larger datasets, combined with weak learners, like decision trees. Stacked Ensemble led the least error for regression with 0.98 R2, followed by Gradient Boosting. Results show a 79% dominance of uncontrollable attributes, such as Land Value, Neighborhood, and Sale (last sold) Price, compared to controllable attributes, such as Total Living Area, Construction Grade, Second Story Area, and many others. This article suggests having a more balanced split between uncontrollable and controllable attributes would contribute to both sustainability and fair distribution.

Robust mitigation of EOVs using multivariate nonlinear regression within a vibration-based SHM methodology

A significant issue that has plagued data-driven Vibration-based Structural Health Monitoring (VSHM) is the mitigation of Environmental and Operational Variations (EOVs). The Damage Sensitive Features (DSFs) that are obtained from the vibration response of the structure are influenced by EOVs. Regression analysis, such as multivariate nonlinear regression, can be used to create relationships between Environmental and Operational Parameters (EOPs) and the DSFs, with EOV-insensitive DSFs created by taking the regression residuals. Inherent issues, originating from nuances in their design, exist within the design of the regression models, following from the overall uncertainty and redundancy in predictors and explained variables, leading to poor performance. To overcome this, a comprehensive nonlinear stepwise regression methodology has been developed to scour the regression models of as much uncertainty as possible. The proposed methodology addresses a number of crucial ideas: removing co-nonlinear variables, identifying the most influential EOPs, facilitating the selection of compact regression bases and determining which DSFs should be regressed. Robust DSFs are created by combining non-regressed DSFs with critically thought-out regressed DSFs. Ultimately, reducing the uncertainty within the models will lead to more confidence in the decision making within a VSHM methodology.

A neural network computational structure for the fractional order breast cancer model

The current study provides the numerical performances of the fractional kind of breast cancer (FKBC) model, which are based on five different classes including cancer stem cells, healthy cells, tumor cells, excess estrogen, and immune cells. The motive to introduce the fractional order derivatives is to present more precise solutions as compared to integer order. A stochastic computing reliable scheme based on the Levenberg Marquardt backpropagation neural networks (LMBNNS) is proposed to solve three different cases of the fractional order values of the FKBC model. A designed dataset is constructed by using the Adam solver in order to reduce the mean square error by taking the data performances as 9% for both testing and validation, while 82% is used for training. The correctness of the solver is approved through the negligible absolute error and matching of the solutions for each model’s case. To validates the accuracy, and consistency of the solver, the performances based on the error histogram, transition state, and regression for solving the FKBC model.

Neural network design for cubic autocatalysis chemical processes, the flow of a Darcy‐Forchheimer viscous fluid is optimized for entropy

AbstractIn this article, neural network backpropagation (NNBP) is used to present two‐dimensional Darcy‐Forchheimer viscous fluid (DFVF) of viscous liquid against a stretching sheet under the influence of heat sink/source and viscous dissipation. Mathematical modelling and numerical simulation are also discussed. Thermal polymer processing, engineering processes, and industrial processes all benefit from the dynamic entropy generation phenomenon. Scientists are primarily interested in finding ways to decrease entropy formation to polish up the thermal performance of industrial systems. In this continuation, the optimal frame for the Darcy‐Forchheimer flow with a curved surface has been developed. Non‐linear partial systems are converted to dimensionless differential systems through the employment of the appropriate variables. Utilizing tools from the bvp4c method, the problem's highly nonlinear equations are numerically solved. These ODEs are solved by applying the bvp4c solution approach to produce the reference dataset for NNBP. Using this reference dataset in MATLAB, the graphs for the solution and error analysis for changing various parameters are analyzed. The performance of NNBP is validated using mean squared error data, regression analysis, and error histogram. The DFVF solution is examined using the testing, validation, and training procedures. Examined through influential variables the effects of fluid flow, thermal field, Bejan number, and concentration.

Investigation of the influence of various factors on the wear of rod depth pumps

In the article, the influence of various factors on the wear of rod depth pumps is investigated. The method of variance analysis of mathematical statistics is applied here. The main factors selected are: the diameter of the pump, the percentage of sand, the amount of water, the amount of oil, the lifting height of the liquid. The task of the study is to find the degree of influence of the selected factors, while it is assumed that the pump supply coefficient decreases only to 0.6. In this case, the main values are in the following numbers of levels: pump diameter, mm; 32; 43; 44; 56; 70; percentage of sand, %; 0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; 0.9; 1; the amount of water, m3/day; 10; 20; 30; 40; 50; the amount of oil, m3/day 0.5; 1; 1.5; 2; 2.5; 3; 3.5; 4; 4.5; 5; liquid lifting height, m; 200, 400, 600, 800, 1000 m. In the article, the variable X=Snt, its average value and the concepts of variances are explained. Various numbers of degrees of freedom are presented. Here the smallest value is 8 and the largest value is 81. Table 2 presents the variability abilities, the number of degrees of freedom, the sum of squares and the variance estimation. Here, the largest variance value is 0.560 and the smallest was 0.065. The exact value of the residual mean squares was 0.084. In the case of, the amou interactions of all the analyzed factors, the amount of water in the product, its lifting heightnt of water and the diameter of the pump matter.

Cognitive inflexibility and heightened error monitoring are related to lower sexual functioning

Sexual functioning is an important predictor of well-being and relationship satisfaction. Previous research indicates that several aspects of cognitive function are related to sex-related behaviors and functioning among individuals with sex-related disorders, neurological disorders, and in older adults; however, this has been relatively underexamined in younger populations. To examine this, the present study assessed whether behavioral and/or neurophysiological measures of cognitive function are associated with sexual functioning in a community sample of young 489 adults (64 % female) ages 18–30. Cognitive flexibility (n = 460) and inhibition (n = 466) were measured using neuropsychological assessment (D-KEFS), and conflict monitoring and error monitoring were measured by event-related potentials (conflict N2: n = 394; error-related negativity: n = 389). After separately testing relations between the different measures of cognitive function and sexual functioning, we assessed whether results (1) remained after covarying for externalizing and internalizing dimensions (PID-5; n = 489) or (2) varied by gender. Finally, we tested whether any aspects of cognitive function were unique predictors of sexual functioning. Cognitive flexibility and error monitoring (i.e., error-related negativity) were both significantly related to sexual functioning among males and females, such that poorer cognitive flexibility and heightened error monitoring were related to lower sexual functioning. No significant effects emerged for inhibition or conflict monitoring. In a multiple regression model, cognitive flexibility and error monitoring each accounted for a unique portion of variance in sexual functioning beyond other aspects of cognitive function and psychopathology-related traits. Results suggest that cognitive function is a meaningful correlate of sexual functioning in young adulthood, which should be considered further in future research.

<b>The Impact of Human Resource Accounting on Profitability: A Study of Listed Textile Firms on PSX</b>

Organizations spend a considerable amount of money on their employees; however, the accounting treatment and disclosures of this amount still needs to be standardized. This study aims to assess how the number of employees and staff cost affects the financial outcomes of textile enterprises listed on the Pakistan Stock Exchange. The purpose is to assist organizations in understanding the impact and worth of their human capital investment in accomplishing long-term goals. The study utilized an ex post facto analysis methodology and obtained data from the financial statements of 73 organizations over a five-year period from 2017 to 2021. Panel regression analysis was performed using E-views software. The Breusch-Pagan test is employed to measure the heteroscedasticity of regression errors, and then the Hausman test is utilized to determine the best approach between a fixed effect and a random effect. The findings revealed that staff cost positively affects financial performance, whereas the number of employees significantly negatively affects financial performance. Therefore, the study recommends investing in employees to boost the firm’s profitability. Also, accounting standards and disclosures should be incorporated into human resource accounting.

On the Selection of Item Scores or Composite Scores for Clinical Prediction

Recent shifts to prioritize prediction, rather than explanation, in psychological science have increased applications of predictive modeling methods. However, composite predictors, such as sum scores, are still commonly used in practice. The motivations behind composite test scores are largely intertwined with reducing the influence of measurement error in answering explanatory questions. But this may be detrimental for predictive aims. The present paper examines the impact of utilizing composite or item-level predictors in linear regression. A mathematical examination of the bias-variance decomposition of prediction error in the presence of measurement error is provided. It is shown that prediction bias, which may be exacerbated by composite scoring, drives prediction error for linear regression. This may be particularly salient when composite scores are comprised of heterogeneous items such as in clinical scales where items correspond to symptoms. With sufficiently large training samples, the increased prediction variance associated with item scores becomes negligible even when composite scores are sufficient. Practical implications of predictor scoring are examined in an empirical example predicting suicidal ideation from various depression scales. Results show that item scores can markedly improve prediction particularly for symptom-based scales. Cross-validation methods can be used to empirically justify predictor scoring decisions.

About time: neurocognitive correlates of stimulus-bound and other time setting errors in the Clock Drawing Test.

Previous findings suggest that time setting errors (TSEs) in the Clock Drawing Test (CDT) may be related mainly to impairments in semantic and executive function. Recent attempts to dissociate the classic stimulus-bound error (setting the time to "10 to 11" instead of "10 past 11") from other TSEs, did not support hypotheses regarding this error being primarily executive in nature or different from other time setting errors in terms of neurocognitive correlates. This study aimed to further investigate the cognitive correlates of stimulus-bound errors and other TSEs, in order to trace possible underlying cognitive deficits. We examined cognitive test performance of participants with preliminary diagnoses associated with mild cognitive impairment. Among 490 participants, we identified clocks with stimulus-bound errors (n = 78), other TSEs (n = 41), other errors not related to time settings (n = 176), or errorless clocks (n = 195). No differences were found on any dependent measure between the stimulus-bound and the other TSErs groups. Group comparisons suggested TSEs in general, to be associated with lower performance on various cognitive measures, especially on semantic and working memory measures. Regression analysis further highlighted semantic and verbal working memory difficulties as being the most prominent deficits associated with these errors. TSEs in the CDT may indicate underlying deficits in semantic function and working memory. In addition, results support previous findings related to the diagnostic value of TSEs in detecting cognitive impairment.

Efficient estimation of state of charge of lithium-ion batteries

The promotion of electric vehicles can help reduce carbon emissions and mitigate the greenhouse effect. Lithium-ion batteries are one of the main power sources for electric vehicles, whose state of charge is a key parameter of the battery management system to ensure the safe operation of electric vehicles. The complex structure of the battery makes the state of charge unable to be directly measured, so this paper establishes a mathematical model to estimate the state of charge based on four parameters (voltage, current, wavelength and light intensity), aiming to provide a high-precision model for state of charge measurement and establish a mathematical model which can help guide actual production. These four parameters can be measured by voltmeters, ammeters, and optical fibers. In this paper, the least squares method is used to perform global linear regression and global quadratic regression of experimental data, and a data pre-treatment is proposed to improve the behavior of the linear equation system. Also, the ridge regression method is used to achieve an effective solution of the ill-conditioned linear equation system. Then, the piecewise linear regression is introduced to optimize the global regression model, and effectively reduces the regression error by capturing the local features of the data. In order to meet the actual engineering requirements, constraints satisfying segmental continuity are added in the piecewise linear regression model. Finally, the regression results are compared with the results obtained by the Machine Learning method. Besides, the proposed methods outperform the Machine Learning method with a sufficient number of segments. The state of charge estimation model established in this paper has high approximation accuracy, strong interpretability, low operational complexity, and has certain engineering application value.

Obstructive and restrictive spirometry from school age to adulthood: three birth cohort studies

Spirometric obstruction and restriction are two patterns of impaired lung function which are predictive of poor health. We investigated the development of these phenotypes and their transitions through childhood to early adulthood. In this study, we analysed pooled data from three UK population-based birth cohorts established between 1989 and 1995. We applied descriptive statistics, regression modelling and data-driven modelling to data from three population-based birth cohorts with at least three spirometry measures from childhood to adulthood (mid-school: 8-10 years, n=8404; adolescence: 15-18, n=5764; and early adulthood: 20-26, n=4680). Participants were assigned to normal, restrictive, and obstructive spirometry based on adjusted regression residuals. We considered two transitions: from 8-10 to 15-18 and from 15-18 to 20-26 years. Obstructive phenotype was observed in ∼10%, and restrictive in ∼9%. A substantial proportion of children with impaired lung function in school age (between one third in obstructive and a half in restricted phenotype) improved and achieved normal and stable lung function to early adulthood. Of those with normal lung function in school-age, <5% declined to adulthood. Underweight restrictive and obese obstructive participants were less likely to transit to normal. Maternal smoking during pregnancy and current asthma diagnosis increased the risk of persistent obstruction and worsening. Significant associate of worsening in restrictive phenotypes was lower BMI at the first lung function assessment. Data-driven methodologies identified similar risk factors for obstructive and restrictive clusters. The worsening and improvement in obstructive and restrictive spirometry were observed at all ages. Maintaining optimal weight during childhood and reducing maternal smoking during pregnancy may reduce spirometry obstruction and restriction and improve lung function. MRC Grant MR/S025340/1.

Potential bioremediation of lead and phenol by sunflower seed husk and rice straw-based biochar hybridized with bacterial consortium: a kinetic study

Environmental pollution is a global phenomenon and troublesome fact that poses a grave risk to all living entities. Via coupling carbonaceous feedstocks with outstanding microbial activity, kinetic experiments were established using the consortium of Proteus mirabilis and Raoultella planticola, biochar-derived sunflower seed husk (SHB) and rice straw (RSB), and their composites, which investigated at 30 °C (150 rpm) to eliminate 700 mg L−1 lead (120 h) and phenol (168 h) from synthetic wastewater. The derived biochars physicochemical properties of were studied. According to adsorption capacity (qe), consortium-SHB composites and consortium-RSB composites removed lead completely (70 mg g−1) within 48 h and 66 h, respectively. Besides, phenol was remediated entirely after 42 h and 48 h by both composite systems (69.90 mg g−1), respectively, comparing with bacterial consortium only or parent SHB and RSB. Moreover, four kinetic models were studied to describe the bioremediation process. Fractional power and Elovich models could be recommended for describing the adsorption kinetics for lead and phenol removal by the studied biomaterials with high correlation coefficient (R2 ≥ 0.91 for Pb2+ and ≥ 0.93 for phenol) and lower residual root mean square error (RMSE) and chi-square (X2). Overall, bacterial consortium-biochar composites exhibited greater remediation of lead and phenol than the sum of each single bacterial consortium and biochar systems; reflecting synergistic interaction of adsorptive capability of biochar and metabolic performance of bacterial consortium, as denoted by scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). The current study addressed the successful design of employing functional remediating consortium immobilized on waste biomass-derived biochar as a conducive alternative eco-sorbent and economic platform to detoxify organic and inorganic pollutants.

Characteristics of Inter-System Bias between BDS-2 and BDS-3 and Its Impact on BDS Orbit and Clock Solutions

The inter-system-like bias between the regional (BDS-2) and global (BDS-3) constellation of the BeiDou Navigation Satellite System (BDS) has been identified on common B1I pseudo-range observations. In this study, its characteristics are investigated with tracking data from the International GNSS Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS) network. Firstly, the satellite-specific inter-system-like bias is calculated and the dependency on satellite is observed. Clearly noticeable discrepancies on BDS-2 and BDS-3 can be identified. Hence, the constellation-specific inter-system-like bias is estimated. Biases for all receivers are quite stable, with standard derivation (STDev) less than 0.2 m in average. The bias shows clear dependence on the receiver, while the firmware and antenna have limited but not negligible impacts, particularly for Trimble NetR9 and Alloy receivers. The Trimble NetR9 with TRM59800.00 antenna shows noticeable discrepancy up to about 1.5 m with different antenna, and the bias of the Trimble Alloy 5.37 jumps about 2.4 m with respect to later firmware. In addition, clear annual variations are observed for stations ABPO and MIZU with Septentrio POLARX5 5.3.2 and ASTERX4 4.4.2 receivers, respectively. Furthermore, the impacts of the biases on the BDS orbit and clock solutions are analyzed. Once BDS-2 and BDS-3 are treated as two independent systems, the root mean square (RMS) of code and carrier phase residuals can be reduced by around 9.3 cm and 0.23 mm, respectively, while the three-dimensional orbit consistency is improved by 6.8%, mainly in the tracking direction. Satellite laser ranging (SLR) shows marginal impacts on IGSO and MEO satellites. However, the SLR residual of C01 shifts −13.2 cm, resulting in a smaller RMS value. In addition, the RMS of linear clock fitting is reduced from 0.050 ns to 0.038 ns for BDS-3 MEO satellites in average.

Changepoint detection with the use of the RESPERM method – a Monte Carlo study

RESPERM (residuals permutation-based method) is a single changepoint detection method based on regression residuals permutation, which can be applied to many physiological situations where the regression slope can change suddenly at a given point. This article presents the results of a Monte Carlo study on the properties of the RESPERM method for single changepoint detection in a linear regression model. We compared our method with a well-known segmented method for detection breakpoint in linear models. The Monte Carlo study showed that when the input data are very noisy, the RESPERM method outperforms the segmented approach in terms of variance, and in the case of bias, the results of the two methods are comparable.

Validity Testing of Classical Asset Allocation Models: An Empirical Study

This paper uses a 20 years of daily total return data for the S&amp;P 500 Index (ticker symbol SPX) and 10 stocks, make all the necessary calculations to plot a portfolio area that gather an efficient boundary, a minimum risk or variance boundary, and a minimum return boundary together for a given set of constraints. Analyze all the outcomes in order to compare the various restrictions for each optimization issue (MM and IM), as well as the two solutions to the same optimization problem. The Excel solver was the primary tool utilized during calculation to resolve optimization issues for each point on the minimal risk or variance border. Also, this paper use an Excel solution table to calculate a large number of multipoints on any desired boundary. Through calculation and research, we found that, Markowitz model makes full use of covariance matrix to generate excellent portfolio. However, the results are numerically unstable. At the same time, the hypothesis of normality, stationarity and mean square error are verified. The exponential model simplifies the Markowitz model and produces more robust results. However, it introduces additional assumptions about the independence, normality, and homoscedasticity of the regression residuals, which are also invalid. The reduction (CDaR) model is hypothesis-free. The numerical stability can be obtained by transforming the nonlinear optimization problem into a linear programming problem.