Pub Date : 2020-07-25DOI: 10.19139/soic-2310-5070-977
Rosinah M Mukhodobwane, C. Sigauke, Wilbert Chagwiza, W. Garira
Volatility modelling is a key factor in equity markets for risk and portfolio management. This paper focuses on the use of a univariate generalized autoregressive conditional heteroscedasticity (GARCH) models for modelling volatility of the BRICS (Brazil, Russia, India, China and South Africa) stock markets. The study extends the literature by conducting the volatility modelling under the assumptions of seven error distributions that include the normal, skewed-normal, Student’s t, skewed-Student’s t, generalized error distribution (GED), skewed-GED and the generalized hyperbolic (GHYP) distribution. It was observed that using an ARMA(1, 1)-GARCH(1, 1) model, volatilities of the Brazilian Bovespa and the Russian IMOEX markets can both be well characterized (or described) by a heavy-tailed Student’s t distribution, while the Indian NIFTY market’s volatility is best characterized by the generalized hyperbolic (GHYP) distribution. Also, the Chinese SHCOMP and South African JALSH markets’ volatilities are best described by the skew-GED and skew-Student’s t distribution, respectively. The study further observed that the persistence of volatility in the BRICS markets does not follow the same hierarchical pattern under the error distributions, except under the skew-Student’s t and GHYP distributions where the pattern is the same. Under these two assumptions, i.e. the skew-Student’s t and GHYP, in a descending hierarchical order of magnitudes, volatility with persistence is highest in the Chinese market, followed by the South African market, then the Russian, Indian and Brazilian markets, respectively. However, under each of the five non-Gaussian error distributions, the Chinese market is the most volatile, while the least volatile is the Brazilian market.
{"title":"Volatility Modelling of the BRICS Stock Markets","authors":"Rosinah M Mukhodobwane, C. Sigauke, Wilbert Chagwiza, W. Garira","doi":"10.19139/soic-2310-5070-977","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-977","url":null,"abstract":"Volatility modelling is a key factor in equity markets for risk and portfolio management. This paper focuses on the use of a univariate generalized autoregressive conditional heteroscedasticity (GARCH) models for modelling volatility of the BRICS (Brazil, Russia, India, China and South Africa) stock markets. The study extends the literature by conducting the volatility modelling under the assumptions of seven error distributions that include the normal, skewed-normal, Student’s t, skewed-Student’s t, generalized error distribution (GED), skewed-GED and the generalized hyperbolic (GHYP) distribution. It was observed that using an ARMA(1, 1)-GARCH(1, 1) model, volatilities of the Brazilian Bovespa and the Russian IMOEX markets can both be well characterized (or described) by a heavy-tailed Student’s t distribution, while the Indian NIFTY market’s volatility is best characterized by the generalized hyperbolic (GHYP) distribution. Also, the Chinese SHCOMP and South African JALSH markets’ volatilities are best described by the skew-GED and skew-Student’s t distribution, respectively. The study further observed that the persistence of volatility in the BRICS markets does not follow the same hierarchical pattern under the error distributions, except under the skew-Student’s t and GHYP distributions where the pattern is the same. Under these two assumptions, i.e. the skew-Student’s t and GHYP, in a descending hierarchical order of magnitudes, volatility with persistence is highest in the Chinese market, followed by the South African market, then the Russian, Indian and Brazilian markets, respectively. However, under each of the five non-Gaussian error distributions, the Chinese market is the most volatile, while the least volatile is the Brazilian market.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"749-772"},"PeriodicalIF":0.0,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49626119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-22DOI: 10.19139/soic-2310-5070-998
M. Luz, M. Moklyachuk
We introduce stochastic sequences $zeta(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequences $zeta(k)$ based on their observations at points $ k<0$. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of functionals. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of sequences are not exactly known while some sets of admissible spectral densities are given.
{"title":"Minimax-robust forecasting of sequences with periodically stationary long memory multiple seasonal increments","authors":"M. Luz, M. Moklyachuk","doi":"10.19139/soic-2310-5070-998","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-998","url":null,"abstract":"We introduce stochastic sequences $zeta(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequences $zeta(k)$ based on their observations at points $ k<0$. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of functionals. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of sequences are not exactly known while some sets of admissible spectral densities are given.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"684-721"},"PeriodicalIF":0.0,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46159516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.19139/soic-2310-5070-784
N. V. Tan
In this paper, we study the density of the solution to a class of stochastic functional differential equations driven by fractional Brownian motion. Based on the techniques of Malliavin calculus, we prove the smoothness and establish upper and lower Gaussian estimates for the density.
{"title":"Smoothness and Gaussian Density Estimates for Stochastic Functional Differential Equations with Fractional Noise","authors":"N. V. Tan","doi":"10.19139/soic-2310-5070-784","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-784","url":null,"abstract":"In this paper, we study the density of the solution to a class of stochastic functional differential equations driven by fractional Brownian motion. Based on the techniques of Malliavin calculus, we prove the smoothness and establish upper and lower Gaussian estimates for the density.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"822-833"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48962611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.19139/SOIC-2310-5070-812
Abbas Eftekharian, M. Razmkhah, J. Ahmadi
A flexible ranked set sampling scheme including some various existing sampling methods is proposed. This scheme may be used to minimize the error of ranking and the cost of sampling. Based on the data obtained from this scheme, the maximum likelihood estimation as well as the Fisher information are studied for the scale family of distributions. The existence and uniqueness of the maximum likelihood estimator of the scale parameter of the exponential and normal distributions are investigated. Moreover, the optimal scheme is derived via simulation and numerical computations.
{"title":"A flexible ranked set sampling schemes: Statistical analysis on scale parameter","authors":"Abbas Eftekharian, M. Razmkhah, J. Ahmadi","doi":"10.19139/SOIC-2310-5070-812","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-812","url":null,"abstract":"A flexible ranked set sampling scheme including some various existing sampling methods is proposed. This scheme may be used to minimize the error of ranking and the cost of sampling. Based on the data obtained from this scheme, the maximum likelihood estimation as well as the Fisher information are studied for the scale family of distributions. The existence and uniqueness of the maximum likelihood estimator of the scale parameter of the exponential and normal distributions are investigated. Moreover, the optimal scheme is derived via simulation and numerical computations.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"9 1","pages":"189-203"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46451456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.19139/soic-2310-5070-760
N. Dung, Trinh Nhu Quynh
In this paper, we study the distribution of the integrated Jacobi diffusion processes with Brownian noise and fractional Brownian noise. Based on techniques of Malliavin calculus, we develop a unified method to obtain explicit estimates for the tail distribution of these integrated diffusions.
{"title":"Tail distribution of the integrated Jacobi diffusion process","authors":"N. Dung, Trinh Nhu Quynh","doi":"10.19139/soic-2310-5070-760","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-760","url":null,"abstract":"In this paper, we study the distribution of the integrated Jacobi diffusion processes with Brownian noise and fractional Brownian noise. Based on techniques of Malliavin calculus, we develop a unified method to obtain explicit estimates for the tail distribution of these integrated diffusions.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"790-800"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44125055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.19139/SOIC-2310-5070-781
A. Sadeghpour, A. Nezakati, M. Salehi
In this paper, point and interval estimation of stress-strength reliability based on lower record ranked set sampling (RRSS) scheme under the proportional reversed hazard rate model are considered. Maximum likelihood, uniformly minimum variance unbiased estimator, and Bayesian estimators of R are derived. Also, we compared this point estimators with their counterparts obtained by well-known sampling scheme in record values known as inverse sampling scheme. Various confidence intervals for the parameter R are constructed, and compared based on the simulation study. Moreover, the RRSS scheme is compared with ordinary records in case of interval estimations. We observed that our proposed point and interval estimations perform well in the estimation of R based on RRSS. We also proved that all calculations do not depend on the baseline distribution in the proportional reversed hazard rate model. Finally, a data set has been analyzed for illustrative purposes.
{"title":"Comparison of two sampling schemes in estimating the stress-strength reliability under the proportional reversed hazard rate model","authors":"A. Sadeghpour, A. Nezakati, M. Salehi","doi":"10.19139/SOIC-2310-5070-781","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-781","url":null,"abstract":"In this paper, point and interval estimation of stress-strength reliability based on lower record ranked set sampling (RRSS) scheme under the proportional reversed hazard rate model are considered. Maximum likelihood, uniformly minimum variance unbiased estimator, and Bayesian estimators of R are derived. Also, we compared this point estimators with their counterparts obtained by well-known sampling scheme in record values known as inverse sampling scheme. Various confidence intervals for the parameter R are constructed, and compared based on the simulation study. Moreover, the RRSS scheme is compared with ordinary records in case of interval estimations. We observed that our proposed point and interval estimations perform well in the estimation of R based on RRSS. We also proved that all calculations do not depend on the baseline distribution in the proportional reversed hazard rate model. Finally, a data set has been analyzed for illustrative purposes.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"9 1","pages":"82-98"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44624134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-23DOI: 10.19139/SOIC-2310-5070-887
Lazhar Benkhelifa
A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.
{"title":"The Weibull Birnbaum-Saunders Distribution And Its Applications","authors":"Lazhar Benkhelifa","doi":"10.19139/SOIC-2310-5070-887","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-887","url":null,"abstract":"A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"9 1","pages":"61-81"},"PeriodicalIF":0.0,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47643536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-19DOI: 10.19139/soic-2310-5070-915
O. Kostyukova, T. Tchemisova
In this paper, we consider a special class of conic optimization problems, consisting of set-semidefinite (or Ksemidefinite) programming problems, where the set K is a polyhedral convex cone. For these problems, we introduce the concept of immobile indices and study the properties of the set of normalized immobile indices and the feasible set. This study provides the main result of the paper, which is to formulate and prove the new first-order optimality conditions in the form of a criterion. The optimality conditions are explicit and do not use any constraint qualifications. For the case of a linear cost function, we reformulate the K-semidefinite problem in a regularized form and construct its dual. We show that the pair of the primal and dual regularized problems satisfies the strong duality relation which means that the duality gap is vanishing.
{"title":"CQ-free optimality conditions and strong dual formulations for a special conic optimization problem","authors":"O. Kostyukova, T. Tchemisova","doi":"10.19139/soic-2310-5070-915","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-915","url":null,"abstract":"In this paper, we consider a special class of conic optimization problems, consisting of set-semidefinite (or Ksemidefinite) programming problems, where the set K is a polyhedral convex cone. For these problems, we introduce the concept of immobile indices and study the properties of the set of normalized immobile indices and the feasible set. This study provides the main result of the paper, which is to formulate and prove the new first-order optimality conditions in the form of a criterion. The optimality conditions are explicit and do not use any constraint qualifications. For the case of a linear cost function, we reformulate the K-semidefinite problem in a regularized form and construct its dual. We show that the pair of the primal and dual regularized problems satisfies the strong duality relation which means that the duality gap is vanishing.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"668-683"},"PeriodicalIF":0.0,"publicationDate":"2020-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44745776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-18DOI: 10.19139/SOIC-2310-5070-611
S. Ashour, A. El-sheikh, A. Elshahhat
In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.
{"title":"Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals","authors":"S. Ashour, A. El-sheikh, A. Elshahhat","doi":"10.19139/SOIC-2310-5070-611","DOIUrl":"https://doi.org/10.19139/SOIC-2310-5070-611","url":null,"abstract":"In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86821463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-14DOI: 10.19139/soic-2310-5070-890
T. Khodamoradi, M. Salahi, A. Najafi
In this paper, first, we discuss some drawbacks of the cardinality constrained mean-variance (CCMV) portfolio optimization with short selling and risk-neutral interest rate when the lower and upper bounds of the assets contributions are − 1 K and 1 K (K denotes the number of assets in portfolio). Second, we present an improved variant using absolute returns instead of the returns to include short selling in the model. Finally, some numerical results are provided using the data set of the S&P 500 index, Information Technology, and the MIBTEL index in terms of returns and Sharpe ratios to compare the proposed models with those in the literature.
{"title":"A Note on CCMV Portfolio Optimization Model with Short Selling and Risk-neutral Interest Rate","authors":"T. Khodamoradi, M. Salahi, A. Najafi","doi":"10.19139/soic-2310-5070-890","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-890","url":null,"abstract":"In this paper, first, we discuss some drawbacks of the cardinality constrained mean-variance (CCMV) portfolio optimization with short selling and risk-neutral interest rate when the lower and upper bounds of the assets contributions are − 1 K and 1 K (K denotes the number of assets in portfolio). Second, we present an improved variant using absolute returns instead of the returns to include short selling in the model. Finally, some numerical results are provided using the data set of the S&P 500 index, Information Technology, and the MIBTEL index in terms of returns and Sharpe ratios to compare the proposed models with those in the literature.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"740-748"},"PeriodicalIF":0.0,"publicationDate":"2020-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47013731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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