多变量线性回归中的同步模型变化检测在印尼经济增长数据中的应用

IF 1.2 Q2 MATHEMATICS, APPLIED
W. Somayasa, Muhammad Kabil Djafar, Norma Muhtar, D. K. Sutiari
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引用次数: 0

摘要

本文利用递归残差偏和过程的 Kolmogorov-Smirnov 函数,研究了多元线性回归中的渐近模型变化检测。我们通过建立观测值递归残差偏和过程序列的函数中心极限定理,来近似确定拒绝区域和检验的幂函数。当假定模型为真时,极限过程由标准多元布朗运动给出,不依赖于回归函数。然而,当假定模型不成立时(某些模型会发生变化),极限过程则由确定性趋势向量加上标准多元布朗运动来表示。通过蒙特卡罗模拟研究了有限样本量拒绝区域和检验的功率。仿真研究表明,所提出的检验方法是一致的,即当假设不成立时,其检验功率大于检验规模。我们还展示了所提检验方法在印尼经济增长数据中的应用,其中我们检验了三变量低阶多项式模型的适当性。检验结果表明,印尼经济增长既不是同时恒定的,也不是线性的。该检验成功地检测到了模型中出现的变化,而这种变化主要是由 2020 年的 COVID-19 大流行病引起的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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 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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来源期刊
Journal of Applied Mathematics
Journal of Applied Mathematics MATHEMATICS, APPLIED-
CiteScore
2.70
自引率
0.00%
发文量
58
审稿时长
3.2 months
期刊介绍: Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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