DTSMA: Dominant Swarm with Adaptive T-distribution Mutation-based Slime Mould Algorithm

<abstract> <p>The slime mould algorithm (SMA) is a metaheuristic algorithm recently proposed, which is inspired by the oscillations of slime mould. Similar to other algorithms, SMA also has some disadvantages such as insufficient balance between exploration and exploitation, and easy to fall into local optimum. This paper, an improved SMA based on dominant swarm with adaptive t-distribution mutation (DTSMA) is proposed. In DTSMA, the dominant swarm is used improved the SMA's convergence speed, and the adaptive t-distribution mutation balances is used enhanced the exploration and exploitation ability. In addition, a new exploitation mechanism is hybridized to increase the diversity of populations. The performances of DTSMA are verified on CEC2019 functions and eight engineering design problems. The results show that for the CEC2019 functions, the DTSMA performances are best; for the engineering problems, DTSMA obtains better results than SMA and many algorithms in the literature when the constraints are satisfied. Furthermore, DTSMA is used to solve the inverse kinematics problem for a 7-DOF robot manipulator. The overall results show that DTSMA has a strong optimization ability. Therefore, the DTSMA is a promising metaheuristic optimization for global optimization problems.</p> </abstract>

Pengaruh Model Problem Based Learning berbantuan Mind Mapping terhadap Kemampuan Pemecahan Masalah Siswa

The purpose of this study was to determine the effect of a mind mapping-assisted problem-based learning model on the problem-solving abilities of class IX students at SMP Negeri 1 Gunungsari in the 2020/2021 school year. This type of research is a pre-experimental research using a one group pretest-posttest design. The population in this study were all grade IX students. While the sample in this study is class IX E with random cluster sampling. Based on the results of the pretest and posttest data analysis in the experimental class, it can be seen that the students' mathematical problem solving ability has increased by an average of 27%. Meanwhile, the results of the pretest and posttest data analysis in the control class increased by an average of 9%. Based on the results of hypothesis testing, it is obtained that the value of ttable with a significant level = 5% and dk = 12 from the t-distribution list obtained ttable of 1.78 and tcount of 5.40 which means tcount > ttable, then H0 is rejected so H1 is accepted. This means that there is an effect of the problem-based learning model with the aid of mind mapping on the problem-solving abilities of class IX students at SMP Negeri 1 Gunungsari for the 2020/2021 academic year.

The Risk of Miscomputing the Value at Risk / O Risco de Calcular mal o Valor em Risco

Este artigo explora como o VaR (Value at Risk), que é a métrica de risco financeiro mais popular, é comumente calculado e usado. Ainda persiste um grande mal-entendido sobre essa técnica no setor financeiro, do que ela é, para que serve, como é usada e até mesmo quem deve usá-la. Embora o VaR não seja mais uma novidade, em muitas organizações, tanto na academia quanto na indústria, ele ainda é implementado da forma como foi concebido na década de 1990 como um primeiro esforço para quantificar o risco financeiro.Dado que o VaR é fortemente apoiado pela Teoria Moderna de Portfólio (Modern Portfolio Theory -MPT), e que esta, por sua vez, foi elaborada sob a suposição de que as oscilações dos sinais financeiros se comportam sob uma Distribuição de Probabilidade Normal, é assim que ainda é calculado em muitas organizações que o aplicam para controlar o negociação de ativos financeiros à vista e derivativos. Neste artigo, o uso da distribuição t de Student em escala (Scaled t-Distribution) é discutido como a melhor opção para modelar a série temporal de retornos financeiros. Os retornos modelados com essa distribuição, por sua vez, permitem que o Value at Risk seja calculado com maior precisão. Além disso, com essa distribuição, pode-se calcular a métrica de risco criada como uma grande melhoria para o VaR: The Expected Shortfall (ES), também conhecido como VaR Condicional (CVaR).Para demonstrar que a distribuição t de Student em escala é melhor para modelar sinais financeiros nos retornos de ações e, portanto, para o cálculo de VaR e ES, três gráficos de distribuições de probabilidade diferentes são gerados e sobrepostos: A distribuição empírica, a distribuição Normal e a distribuição t de Student em escala, calculadas com a técnica de estimativa de máxima verossimilhança (Maximum Likelihood Estimation).Isso é feito para cada uma das seis ações analisadas neste estudo: O FAANG (Facebook, Apple, Amazon, Netflix, and Google), mais aquele recentemente adicionado ao SP 500: Tesla.

Model Calibration and Validation for the Fuzzy-EGARCH-ANN Model

This work shown as the fuzzy-EGARCH-ANN (fuzzy-exponential generalized autoregressive conditional heteroscedastic-artificial neural network) model does not require continuous model calibration if the corresponding DE algorithm is used appropriately, but other models such as GARCH, EGARCH, and EGARCH-ANN need continuous model calibration and validation so they fit the data and reality very well up to the desired accuracy. Also, a robust analysis of volatility forecasting of the daily S&P 500 data collected from Yahoo Finance for the daily spanning period 1/3/2006 to 20/2/2020. To our knowledge, this is the first study that focuses on the daily S&P 500 data using high-frequency data and the fuzzy-EGARCH-ANN econometric model. Finally, the research finds that the best performing model in terms of one-step-ahead forecasts based on realized volatility computed from the underlying daily data series is the fuzzy-EGARCH-ANN (1,1,2,1) model with Student’s t-distribution.

MEASURING VALUE AT RISK USING GARCH MODEL - EVIDENCE FROM THE CRYPTOCURRENCY MARKET

There is a growing interest in the activities of the crypto market by various stakeholders. These stakeholders generally include investors, entrepreneurs, governments, fund managers, climate activists, institutional managers, employees with surplus funds, and crypto miners. This study aims to investigate the accuracy of the GARCH models for measuring and estimating Value-at-risk (VaR) using the Cryptocurrency index for future investment and managerial decision making. Because of this, the present study uses the top 30 Cryptocurrencies index in terms of Market capitalization excluding stable coins to determine the best GARCH models. Many entrepreneurs, institutional managers, fund managers, and other stakeholders have recently included cryptocurrency in their investment portfolio because of the increase in transactions and high returns growth in the global financial market with its associated high returns and volatility. Information communication technology has paved the way for such activities in the global markets. The daily data frequency was applied because of the availability of the data. The empirical analysis has been carried out for the period from January 2017 to December 2020 for a total of 1461observation. The returns volatility is estimated using SGARCH and EGARCH models. The findings evidenced that, using both normal distribution and Student t distribution, EGARCH provides a better measure and estimate than SGARCH concerning high persistence and volatility. Against this background, the present study also examined Backtesting to estimate Value at Risk. Interestingly, the findings of the available study would provide industry players, practitioners, entrepreneurs, and investors the maximum edge on how to use or measure such variables against others to make investment decisions. Also, the findings would subsequently contribute more insight into academia on the study area.

Modelling the Botswana Pula/Us Dollar exchange rate using the Skewed generalized t (SGT) distributions

The economy of Botswana heavily relies on mineral exports (mainly diamond exports), which are largely dependent on the exchange rate. And, the US Dollar is one of the most important currencies in the basket of currencies to which the Botswana Pula is pegged. Therefore, this paper seeks to empirically establish the baseline characteristics of the Botswana Pula (BWP) and the US Dollar (USD) exchange rate and to identify the most plausible probability distribution from the skewed generalized t (SGT) family that can be used to model the log-returns of the daily BWP/USD exchange rates for the period January 2001 to December 2020. The SGT family is a highly versatile class of models that can capture the skewness and kleptokurticity that are inherent in financial time series. Four probability distributions are considered in this study: skewed t, skewed generalized error, generalized t and skewed generalized t. The maximum likelihood approach is used to estimate the parameters of each model. Model comparison and selection are based on the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results of the study show that the daily BWP/USD exchange rate series is nonnormal, negatively skewed heavy-tailed. It is also found that, based on the values of both the AIC and BIC, the model that gives the best fit to the data is the skewed t, which is closely followed by the skewed generalized error distribution, while the generalized t gives the worst fit. Keywords: Pula/US Dollar exchange rate, log returns, Generalized t distribution, Skewed generalized error distribution, Skewed generalized t distribution, Skewed t distribution, skewness, kurtosis, maximum likelihood

A New Generalization of the Student’s t Distribution with an Application in Quantile Regression

In this work, we present a new generalization of the student’s t distribution. The new distribution is obtained by the quotient of two independent random variables. This quotient consists of a standard Normal distribution divided by the power of a chi square distribution divided by its degrees of freedom. Thus, the new symmetric distribution has heavier tails than the student’s t distribution and extensions of the slash distribution. We develop a procedure to use quantile regression where the response variable or the residuals have high kurtosis. We give the density function expressed by an integral, we obtain some important properties and some useful procedures for making inference, such as moment and maximum likelihood estimators. By way of illustration, we carry out two applications using real data, in the first we provide maximum likelihood estimates for the parameters of the generalized student’s t distribution, student’s t, the extended slash distribution, the modified slash distribution, the slash distribution generalized student’s t test, and the double slash distribution, in the second we perform quantile regression to fit a model where the response variable presents a high kurtosis.