Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas

Recently, the area of sea ice is rapidly decreasing due to global warming, and since the Arctic sea ice has a great impact on climate change, interest in this is increasing very much all over the world. In fact, the area of sea ice reached a record low in September 2012 after satellite observations...

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Main Authors: Jeongwook Lee, Joon Jin Song, Yongku Kim, Jung In Seo
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/8/10/1678
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author Jeongwook Lee
Joon Jin Song
Yongku Kim
Jung In Seo
author_facet Jeongwook Lee
Joon Jin Song
Yongku Kim
Jung In Seo
author_sort Jeongwook Lee
collection DOAJ
description Recently, the area of sea ice is rapidly decreasing due to global warming, and since the Arctic sea ice has a great impact on climate change, interest in this is increasing very much all over the world. In fact, the area of sea ice reached a record low in September 2012 after satellite observations began in late 1979. In addition, in early 2018, the glacier on the northern coast of Greenland began to collapse. If we are interested in record values of sea ice area, modeling relationships of these values and predicting future record values can be a very important issue because the record values that consist of larger or smaller values than the preceding observations are very closely related to each other. The relationship between the record values can be modeled based on the pivotal quantity and canonical and drawable vine copulas, and the relationship is called a dependence structure. In addition, predictions for future record values can be solved in a very concise way based on the pivotal quantity. To accomplish that, this article proposes an approach to model the dependence structure between record values based on the canonical and drawable vine. To do this, unknown parameters of a probability distribution need to be estimated first, and the pivotal-based method is provided. In the pivotal-based estimation, a new algorithm to deal with a nuisance parameter is proposed. This method allows one to reduce computational complexity when constructing exact confidence intervals of functions with unknown parameters. This method not only reduces computational complexity when constructing exact confidence intervals of functions with unknown parameters, but is also very useful for obtaining the replicated data needed to model the dependence structure based on canonical and drawable vine. In addition, prediction methods for future record values are proposed with the pivotal quantity, and we compared them with a time series forecasting method in real data analysis. The validity of the proposed methods was examined through Monte Carlo simulations and analysis for Arctic sea ice data.
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spelling doaj.art-c828cbe4044f45fbbe5df0ee32ec63a92023-11-20T15:46:44ZengMDPI AGMathematics2227-73902020-10-01810167810.3390/math8101678Estimation and Prediction of Record Values Using Pivotal Quantities and CopulasJeongwook Lee0Joon Jin Song1Yongku Kim2Jung In Seo3Department of Statistics, Daejeon University, Daejeon 34519, KoreaDepartment of Statistical Science, Baylor University, Waco, TX 76798, USADepartment of Statistics, Kyungpook National University, Daegu 41566, KoreaDivision of Convergence Education, Halla University, Wonju, Gangwon-do 26404, KoreaRecently, the area of sea ice is rapidly decreasing due to global warming, and since the Arctic sea ice has a great impact on climate change, interest in this is increasing very much all over the world. In fact, the area of sea ice reached a record low in September 2012 after satellite observations began in late 1979. In addition, in early 2018, the glacier on the northern coast of Greenland began to collapse. If we are interested in record values of sea ice area, modeling relationships of these values and predicting future record values can be a very important issue because the record values that consist of larger or smaller values than the preceding observations are very closely related to each other. The relationship between the record values can be modeled based on the pivotal quantity and canonical and drawable vine copulas, and the relationship is called a dependence structure. In addition, predictions for future record values can be solved in a very concise way based on the pivotal quantity. To accomplish that, this article proposes an approach to model the dependence structure between record values based on the canonical and drawable vine. To do this, unknown parameters of a probability distribution need to be estimated first, and the pivotal-based method is provided. In the pivotal-based estimation, a new algorithm to deal with a nuisance parameter is proposed. This method allows one to reduce computational complexity when constructing exact confidence intervals of functions with unknown parameters. This method not only reduces computational complexity when constructing exact confidence intervals of functions with unknown parameters, but is also very useful for obtaining the replicated data needed to model the dependence structure based on canonical and drawable vine. In addition, prediction methods for future record values are proposed with the pivotal quantity, and we compared them with a time series forecasting method in real data analysis. The validity of the proposed methods was examined through Monte Carlo simulations and analysis for Arctic sea ice data.https://www.mdpi.com/2227-7390/8/10/1678C- and D-vine copulasconfidence intervalexponentiated Gumbel distributionpivotal quantityrecord values
spellingShingle Jeongwook Lee
Joon Jin Song
Yongku Kim
Jung In Seo
Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas
Mathematics
C- and D-vine copulas
confidence interval
exponentiated Gumbel distribution
pivotal quantity
record values
title Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas
title_full Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas
title_fullStr Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas
title_full_unstemmed Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas
title_short Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas
title_sort estimation and prediction of record values using pivotal quantities and copulas
topic C- and D-vine copulas
confidence interval
exponentiated Gumbel distribution
pivotal quantity
record values
url https://www.mdpi.com/2227-7390/8/10/1678
work_keys_str_mv AT jeongwooklee estimationandpredictionofrecordvaluesusingpivotalquantitiesandcopulas
AT joonjinsong estimationandpredictionofrecordvaluesusingpivotalquantitiesandcopulas
AT yongkukim estimationandpredictionofrecordvaluesusingpivotalquantitiesandcopulas
AT junginseo estimationandpredictionofrecordvaluesusingpivotalquantitiesandcopulas