Pub Date : 2020-08-18DOI: 10.5604/01.3001.0014.1785
E. Panek
In the author’s earlier papers concerning asymptotic characteristics of the optimal growth processes in non-stationary Gale economies with multilane production turnpikes, it is assumed that production technology used in time period 𝑡𝑡 may also be used in the next period. Such an assumption, relevant for short periods, is difficult to justify in the longer term. The paper contains a proof of the so called ‘weak’ effect of the multilane turnpike in a non-stationary Gale economy with changing technology, where this assumption has been suspended.
{"title":"Multilane turnpike in the non-stationary input-outputeconomy with von Neumann temporary equilibrium","authors":"E. Panek","doi":"10.5604/01.3001.0014.1785","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1785","url":null,"abstract":"In the author’s earlier papers concerning asymptotic characteristics of the optimal growth processes in non-stationary Gale economies with multilane production turnpikes, it is assumed that production technology used in time period 𝑡𝑡 may also be used in the next period. Such an assumption, relevant for short periods, is difficult to justify in the longer term. The paper contains a proof of the so called ‘weak’ effect of the multilane turnpike in a non-stationary Gale economy with changing technology, where this assumption has been suspended.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127956362","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 : 2020-03-17DOI: 10.5604/01.3001.0013.9127
V. Bystrov
The results of the study presented in this paper demonstrate that a structural model of the natural interest rate, which is consistent with the standard assumptions of the natural rate theory, admits an interpretable, observationally equivalent representation in which a redefined, ’unnatural’ equilibrium rate is different from the natural rate in the original model. The alternative representation was obtained by an invertible transformation implemented in the minimal state-space form of the natural-rate model. The identification theory for state-space models is used in the paper to prove the observational equivalence of these two representations. In the alternative representation, the equilibrium interest rate fails to meet the assumption of the natural rate theory, because it depends on past demand shocks. The alternative model, being observationally equivalent, has different implications for the conduct of monetary policy. The problem of observational equivalence arises in relation to natural-rate models because of the inherent unobservability of the natural interest rate; a potential solution to this problem could be the augmentation of the information set which is used to identify and estimate the natural rate.
{"title":"The observational equivalence of natural and unnatural rates of interest","authors":"V. Bystrov","doi":"10.5604/01.3001.0013.9127","DOIUrl":"https://doi.org/10.5604/01.3001.0013.9127","url":null,"abstract":"The results of the study presented in this paper demonstrate that a structural model of the natural interest rate, which is consistent with the standard assumptions of the natural rate theory, admits an interpretable, observationally equivalent representation in which a redefined, ’unnatural’ equilibrium rate is different from the natural rate in the original model. The alternative representation was obtained by an invertible transformation implemented in the minimal state-space form of the natural-rate model. The identification theory for state-space models is used in the paper to prove the observational equivalence of these two representations. In the alternative representation, the equilibrium interest rate fails to meet the assumption of the natural rate theory, because it depends on past demand shocks. The alternative model, being observationally equivalent, has different implications for the conduct of monetary policy. The problem of observational equivalence arises in relation to natural-rate models because of the inherent unobservability of the natural interest rate; a potential solution to this problem could be the augmentation of the information set which is used to identify and estimate the natural rate.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"312 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116597693","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 : 2020-03-17DOI: 10.5604/01.3001.0013.9131
Mariusz Łapczyński, Bartłomiej Jefmański
For quite a long time, research studies have attempted to combine various analytical tools to build predictive models. It is possible to combine tools of the same type (ensemble models, committees) or tools of different types (hybrid models). Hybrid models are used in such areas as customer relationship management (CRM), web usage mining, medical sciences, petroleum geology and anomaly detection in computer networks. Our hybrid model was created as a sequential combination of a cluster analysis and decision trees. In the first step of the procedure, objects were grouped into clusters using the k-means algorithm. The second step involved building a decision tree model with a new independent variable that indicated which cluster the objects belonged to. The analysis was based on 14 data sets collected from publicly accessible repositories. The performance of the models was assessed with the use of measures derived from the confusion matrix, including the accuracy, precision, recall, F-measure, and the lift in the first and second decile. We tried to find a relationship between the number of clusters and the quality of hybrid predictive models. According to our knowledge, similar studies have not been conducted yet. Our research demonstrates that in some cases building hybrid models can improve the performance of predictive models. It turned out that the models with the highest performance measures require building a relatively large number of clusters (from 9 to 15).
{"title":"The number of clusters in hybrid predictive models: does it really matter?","authors":"Mariusz Łapczyński, Bartłomiej Jefmański","doi":"10.5604/01.3001.0013.9131","DOIUrl":"https://doi.org/10.5604/01.3001.0013.9131","url":null,"abstract":"For quite a long time, research studies have attempted to combine various analytical tools to build predictive models. It is possible to combine tools of the same type (ensemble models, committees) or tools of different types (hybrid models). Hybrid models are used in such areas as customer relationship management (CRM), web usage mining, medical sciences, petroleum geology and anomaly detection in computer networks. Our hybrid model was created as a sequential combination of a cluster analysis and decision trees. In the first step of the procedure, objects were grouped into clusters using the k-means algorithm. The second step involved building a decision tree model with a new independent variable that indicated which cluster the objects belonged to. The analysis was based on 14 data sets collected from publicly accessible repositories. The performance of the models was assessed with the use of measures derived from the confusion matrix, including the accuracy, precision, recall, F-measure, and the lift in the first and second decile. We tried to find a relationship between the number of clusters and the quality of hybrid predictive models. According to our knowledge, similar studies have not been conducted yet. Our research demonstrates that in some cases building hybrid models can improve the performance of predictive models. It turned out that the models with the highest performance measures require building a relatively large number of clusters (from 9 to 15).\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122793060","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 : 2019-12-30DOI: 10.5604/01.3001.0013.7609
D. Witkowska, K. Kompa
Providing care for one’s relatives is always a sacrifice, which, aside from the reduction of income, often entails the worsening of one’s professional position and, consequently, a lower pension in the future. The aim of the paper is to establish if the phenomenon of the loss of income by family caregivers (care penalty) is observable in the Polish labour market, and if it is, whom it affects. The research was carried out on the basis of the data from the Polish Labour Force Survey (LFS) 2009Q1. Factors affecting employees' income were identified using regression models which contained explana-tory variables describing the employees and the structure of their families as well as the characteristics of their workplaces. The analysis was performed separately for all the respondents, according to the respondents’ sex, and for female employees aged 25–54. The parameters of the models of monthly and hourly wages which used various sets of variables reflecting the family structure were estimated using the OLS method. Introducing variables representing the structure of households made it possible to observe that both the phenomena of the loss of income by working mothers (motherhood penalty) and of the loss of income by caregivers of elderly relatives (eldercare penalty) do apply to the Polish labour market. The study also demonstrated that the reduction of caregivers' income, especially that of the caregivers of the elderly, affects mostly women aged 25-54. The results of the research indicate that a vast number of Polish families function according to the traditional model, where it is mostly women who combine the role of a caregiver with their professional career.
{"title":"Childcare and eldercare and Polish employees’ remunerations","authors":"D. Witkowska, K. Kompa","doi":"10.5604/01.3001.0013.7609","DOIUrl":"https://doi.org/10.5604/01.3001.0013.7609","url":null,"abstract":"Providing care for one’s relatives is always a sacrifice, which, aside from the reduction of income, often entails the worsening of one’s professional position and, consequently, a lower pension in the future. The aim of the paper is to establish if the phenomenon of the loss of income by family caregivers (care penalty) is observable in the Polish labour market, and if it is, whom it affects. The research was carried out on the basis of the data from the Polish Labour Force Survey (LFS) 2009Q1. Factors affecting employees' income were identified using regression models which contained explana-tory variables describing the employees and the structure of their families as well as the characteristics of their workplaces. The analysis was performed separately for all the respondents, according to the respondents’ sex, and for female employees aged 25–54. The parameters of the models of monthly and hourly wages which used various sets of variables reflecting the family structure were estimated using the OLS method. Introducing variables representing the structure of households made it possible to observe that both the phenomena of the loss of income by working mothers (motherhood penalty) and of the loss of income by caregivers of elderly relatives (eldercare penalty) do apply to the Polish labour market. The study also demonstrated that the reduction of caregivers' income, especially that of the caregivers of the elderly, affects mostly women aged 25-54. The results of the research indicate that a vast number of Polish families function according to the traditional model, where it is mostly women who combine the role of a caregiver with their professional career.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128487685","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 : 2019-05-28DOI: 10.5604/01.3001.0013.8363
D. Kacprzak
Multiple Criteria Decision Making methods, such as TOPSIS, have become very popular in recent years and are frequently applied to solve many real-life situations. However, the increasing complexity of the decision problems analysed makes it less feasible to consider all the relevant aspects of the problems by a single decision maker. As a result, many real-life problems are discussed by a group of decision makers. In such a group each decision maker can specialize in a different field and has his/her own unique characteristics, such as knowledge, skills, experience, personality, etc. This implies that each decision maker should have a different degree of influence on the final decision, i.e., the weights of decision makers should be different. The aim of this paper is to extend the fuzzy TOPSIS method to group decision making. The proposed approach uses TOPSIS twice. The first time it is used to determine the weights of decision makers which are then used to calculate the aggregated decision matrix for all the group decision matrices provided by the decision makers. Based on this aggregated matrix, the extended TOPSIS is used again, to rank the alternatives and to select the best one. A numerical example illustrates the proposed approach.
{"title":"Doubly Extended Fuzzy TOPSIS Method for Group Decision Making","authors":"D. Kacprzak","doi":"10.5604/01.3001.0013.8363","DOIUrl":"https://doi.org/10.5604/01.3001.0013.8363","url":null,"abstract":"Multiple Criteria Decision Making methods, such as TOPSIS, have become very popular in recent years and are frequently applied to solve many real-life situations. However, the increasing complexity of the decision problems analysed makes it less feasible to consider all the relevant aspects of the problems by a single decision maker. As a result, many real-life problems are discussed by a group of decision makers. In such a group each decision maker can specialize in a different field and has his/her own unique characteristics, such as knowledge, skills, experience, personality, etc. This implies that each decision maker should have a different degree of influence on the final decision, i.e., the weights of decision makers should be different. The aim of this paper is to extend the fuzzy TOPSIS method to group decision making. The proposed approach uses TOPSIS twice. The first time it is used to determine the weights of decision makers which are then used to calculate the aggregated decision matrix for all the group decision matrices provided by the decision makers. Based on this aggregated matrix, the extended TOPSIS is used again, to rank the alternatives and to select the best one. A numerical example illustrates the proposed approach.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114850553","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 : 2019-05-28DOI: 10.5604/01.3001.0013.8375
Dorota Rozmus
In the context of taxonomy methods in recent years, a lot of attention is paid to the stability of these methods, i.e. the answer to the question to what extent the structure discovered by a given method is actually present in the data? Many different ways of measuring stability have been proposed in the literature, which are mainly relating to the stability of the final grouping result. Lord et al. (2017) instead proposed a measure of stability for each observation from the data set and the measure of stability for individual groups. In their article, they suggest that an individual measure of stability may indicate noisy observation whereas the stability measure relating to particular groups may indicate clusters of noise which should be removed from the dataset. The aim of the paper is to apply the proposed individual measure of stability and a measure of stability for individual groups to answer the question to what extent Poland is matched the EU in terms of the level of sustainable development.
{"title":"Level of Sustainable Development in Poland and EU Countries – Analysis with Cluster Stability Measures","authors":"Dorota Rozmus","doi":"10.5604/01.3001.0013.8375","DOIUrl":"https://doi.org/10.5604/01.3001.0013.8375","url":null,"abstract":"In the context of taxonomy methods in recent years, a lot of attention is paid to the stability of these methods, i.e. the answer to the question to what extent the structure discovered by a given method is actually present in the data? Many different ways of measuring stability have been proposed in the literature, which are mainly relating to the stability of the final grouping result. Lord et al. (2017) instead proposed a measure of stability for each observation from the data set and the measure of stability for individual groups. In their article, they suggest that an individual measure of stability may indicate noisy observation whereas the stability measure relating to particular groups may indicate clusters of noise which should be removed from the dataset. The aim of the paper is to apply the proposed individual measure of stability and a measure of stability for individual groups to answer the question to what extent Poland is matched the EU in terms of the level of sustainable development.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"186 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133418147","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 : 2019-05-28DOI: 10.5604/01.3001.0013.8374
M. Salamaga
The purpose of the article is the multivariate analysis of export competitiveness in EU countries. It is based on the decomposition of changes in the exports of EU countries made using the model of Constant Market Share developed by Leamer and Stern (1970). The calculated effects of competitiveness, commodity composition, world trade and market distribution allow a detailed analysis of the sources of changes in export of compared countries, and in particular help to answer the question to what extent can changes in exports explain the global trade situation and to what extent do they result from proper proportion of market share, appropriate product assortment matching, or expansive exporter policy? In the comparative analysis there is used Ward's method, which allowed to indicate countries with the most similar competitive position in the spatial and commercial system in the field of goods with different shares of production factors. The presented results allow for a multidirectional comparison of the trade competitiveness of EU countries, as well as may be a source of important information on shaping the right proportions of participation and expansion of companies on foreign markets.
{"title":"Analysis of the Competitive Position of EU Countries in Foreign Trade with the Use of the CMS and Ward’s Methods","authors":"M. Salamaga","doi":"10.5604/01.3001.0013.8374","DOIUrl":"https://doi.org/10.5604/01.3001.0013.8374","url":null,"abstract":"The purpose of the article is the multivariate analysis of export competitiveness in EU countries. It is based on the decomposition of changes in the exports of EU countries made using the model of Constant Market Share developed by Leamer and Stern (1970). The calculated effects of competitiveness, commodity composition, world trade and market distribution allow a detailed analysis of the sources of changes in export of compared countries, and in particular help to answer the question to what extent can changes in exports explain the global trade situation and to what extent do they result from proper proportion of market share, appropriate product assortment matching, or expansive exporter policy? In the comparative analysis there is used Ward's method, which allowed to indicate countries with the most similar competitive position in the spatial and commercial system in the field of goods with different shares of production factors. The presented results allow for a multidirectional comparison of the trade competitiveness of EU countries, as well as may be a source of important information on shaping the right proportions of participation and expansion of companies on foreign markets.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121453708","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 : 2019-05-28DOI: 10.5604/01.3001.0013.8285
Andrzej Młodak
The paper contains a proposal of original method of assessment of information loss resulted from an application of the Statistical Disclosure Control (SDC) conducted during preparation of the resulting data to the publication and disclosure to interested users. The SDC tools enable protection of sensitive data from their disclosure – both direct and indirect. The article focuses on pseudonimised microdata, i.e. individual data without fundamental identifiers, used for scientific purposes. This control is usually to suppress, swapping or disturbing of original data. However, such intervention is connected with the loss of some information. Optimization of choice of relevant SDC method requires then a minimization of such loss (and risk of disclosure of protected data). Traditionally used methods of measurement of such loss are not rarely sensitive to dissimilarities resulting from scale and scope of values of variables and cannot be used for ordinal data. Many of them weakly take also connections between variables into account, what can be important in various analyses. Hence, this paper is aimed at presentation of a proposal (having the source in papers by Zdzisław Hellwig) concerning use of a method of normalized and easy interpretable complex measure (called also the synthetic indicator) for connected features based on benchmark and anti–benchmark of development to the assessment of information loss resulted from an application of some SDC techniques and at studying its practical utility. The measure is here constructed on the basis of distances between original data and data after application of the SDC taking measurement scales into account.
{"title":"Using the Complex Measure in an Assessment of the Information Loss Due to the Microdata Disclosure Control","authors":"Andrzej Młodak","doi":"10.5604/01.3001.0013.8285","DOIUrl":"https://doi.org/10.5604/01.3001.0013.8285","url":null,"abstract":"The paper contains a proposal of original method of assessment of information loss resulted from an application of the Statistical Disclosure Control (SDC) conducted during preparation of the resulting data to the publication and disclosure to interested users. The SDC tools enable protection of sensitive data from their disclosure – both direct and indirect. The article focuses on pseudonimised microdata, i.e. individual data without fundamental identifiers, used for scientific purposes. This control is usually to suppress, swapping or disturbing of original data. However, such intervention is connected with the loss of some information. Optimization of choice of relevant SDC method requires then a minimization of such loss (and risk of disclosure of protected data). Traditionally used methods of measurement of such loss are not rarely sensitive to dissimilarities resulting from scale and scope of values of variables and cannot be used for ordinal data. Many of them weakly take also connections between variables into account, what can be important in various analyses. Hence, this paper is aimed at presentation of a proposal (having the source in papers by Zdzisław Hellwig) concerning use of a method of normalized and easy interpretable complex measure (called also the synthetic indicator) for connected features based on benchmark and anti–benchmark of development to the assessment of information loss resulted from an application of some SDC techniques and at studying its practical utility. The measure is here constructed on the basis of distances between original data and data after application of the SDC taking measurement scales into account.","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122526266","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 : 2019-05-28DOI: 10.5604/01.3001.0013.8364
Piotr Szczepocki
The article presents a method for parametric estimation of instantaneous variance in the case of non-Gaussian Ornstein-Uhlenbeck stochastic volatility process by means of the iterated filtering and realized variance estimator. The method is applied to realized variance of S&P500 index data. Empirical application is accompanied with simulation study to examine performance of the estimation technique.
{"title":"Application of Iterated Filtering for Parametric Estimation of Instantaneous Variance in the Case of Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Processes","authors":"Piotr Szczepocki","doi":"10.5604/01.3001.0013.8364","DOIUrl":"https://doi.org/10.5604/01.3001.0013.8364","url":null,"abstract":"The article presents a method for parametric estimation of instantaneous variance in the case of non-Gaussian Ornstein-Uhlenbeck stochastic volatility process by means of the iterated filtering and realized variance estimator. The method is applied to realized variance of S&P500 index data. Empirical application is accompanied with simulation study to examine performance of the estimation technique.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121295881","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 : 2019-01-30DOI: 10.5604/01.3001.0014.0532
A. Staszewska-Bystrova
Joint prediction bands are often constructed using Bonferroni’s inequality. The drawback of such bands may be their large width and excessive coverage probability. The paper proposes two refinements to the basic Bonferroni method of constructing bootstrap prediction bands. These are based on higher order inequalities and optimization of the width of the band. The procedures are applied to the problem of predicting univariate autoregressive processes. Their properties are studied by means of Monte Carlo experiments. It is shown that the proposed methods lead, in many scenarios, to obtaining relatively narrow prediction bands with desired coverage probabilities.
{"title":"Refined Bonferroni prediction bands for autoregressive models","authors":"A. Staszewska-Bystrova","doi":"10.5604/01.3001.0014.0532","DOIUrl":"https://doi.org/10.5604/01.3001.0014.0532","url":null,"abstract":"Joint prediction bands are often constructed using Bonferroni’s inequality. The drawback of such bands may be their large width and excessive coverage probability. The paper proposes two refinements to the basic Bonferroni method of constructing bootstrap prediction bands. These are based on higher order inequalities and optimization of the width of the band. The procedures are applied to the problem of predicting univariate autoregressive processes. Their properties are studied by means of Monte Carlo experiments. It is shown that the proposed methods lead, in many scenarios, to obtaining relatively narrow prediction bands with desired coverage probabilities.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128245159","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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