Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas

Jeongwook Lee, Joon Jin Song, Yongku Kim and Jung In Seo
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Jeongwook Lee: Department of Statistics, Daejeon University, Daejeon 34519, Korea
Joon Jin Song: Department of Statistical Science, Baylor University, Waco, TX 76798, USA
Yongku Kim: Department of Statistics, Kyungpook National University, Daegu 41566, Korea
Jung In Seo: Division of Convergence Education, Halla University, Wonju, Gangwon-do 26404, Korea

Mathematics, 2020, vol. 8, issue 10, 1-16

Abstract: 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.

Keywords: C- and D-vine copulas; confidence interval; exponentiated Gumbel distribution; pivotal quantity; record values (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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