Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth Data

In this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov–Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central lim...

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Main Authors: Wayan Somayasa, Muhammad Kabil Djafar, Norma Muhtar, Desak Ketut Sutiari
Format: Article
Language:English
Published: Wiley 2024-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2024/4499481
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author Wayan Somayasa
Muhammad Kabil Djafar
Norma Muhtar
Desak Ketut Sutiari
author_facet Wayan Somayasa
Muhammad Kabil Djafar
Norma Muhtar
Desak Ketut Sutiari
author_sort Wayan Somayasa
collection DOAJ
description In this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov–Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central limit theorem for the sequence of the partial sum processes of the recursive residuals of the observations. When the assumed model is true, the limit process is given by the standard multivariate Brownian motion which does not depend on the regression functions. However, when the assumed model is not true (some models change), the limit process is represented by a vector of deterministic trend plus the standard multivariate Brownian motion. The finite sample size rejection region and the power of the test are investigated by means of Monte Carlo simulation. The simulation study shows evidence that the proposed test is consistent in the sense that it attains the power larger than the size of the test when the hypothesis is not true. We also demonstrate the application of the proposed test method to Indonesian economic growth data in which we test the adequacy of three-variate low-order polynomial model. The test result shows that the growth of the Indonesian economy is neither simultaneously constant nor linear. The test has successfully detect the appearance of a change in the model which is mainly caused by the COVID-19 pandemic in 2020.
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spelling doaj-art-c16f4f76cef24459bd20829d019a28752025-08-20T03:23:28ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/4499481Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth DataWayan Somayasa0Muhammad Kabil Djafar1Norma Muhtar2Desak Ketut Sutiari3Department of MathematicDepartment of MathematicDepartment of MathematicDepartment of Medical Electrical EngineeringIn this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov–Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central limit theorem for the sequence of the partial sum processes of the recursive residuals of the observations. When the assumed model is true, the limit process is given by the standard multivariate Brownian motion which does not depend on the regression functions. However, when the assumed model is not true (some models change), the limit process is represented by a vector of deterministic trend plus the standard multivariate Brownian motion. The finite sample size rejection region and the power of the test are investigated by means of Monte Carlo simulation. The simulation study shows evidence that the proposed test is consistent in the sense that it attains the power larger than the size of the test when the hypothesis is not true. We also demonstrate the application of the proposed test method to Indonesian economic growth data in which we test the adequacy of three-variate low-order polynomial model. The test result shows that the growth of the Indonesian economy is neither simultaneously constant nor linear. The test has successfully detect the appearance of a change in the model which is mainly caused by the COVID-19 pandemic in 2020.http://dx.doi.org/10.1155/2024/4499481
spellingShingle Wayan Somayasa
Muhammad Kabil Djafar
Norma Muhtar
Desak Ketut Sutiari
Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth Data
Journal of Applied Mathematics
title Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth Data
title_full Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth Data
title_fullStr Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth Data
title_full_unstemmed Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth Data
title_short Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth Data
title_sort simultaneous model change detection in multivariate linear regression with application to indonesian economic growth data
url http://dx.doi.org/10.1155/2024/4499481
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