Open AccessChange-In-Mean Problem for Long Memory Time Series Model
Author(s) -
Danya Liang,
Hao Jin
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1852/4/042009
Subject(s) - cusum , long memory , consistency (knowledge bases) , mathematics , fractional brownian motion , series (stratigraphy) , statistic , range (aeronautics) , limit (mathematics) , null hypothesis , test statistic , statistics , asymptotic distribution , brownian motion , statistical hypothesis testing , statistical physics , econometrics , mathematical analysis , discrete mathematics , volatility (finance) , paleontology , materials science , physics , estimator , composite material , biology
In this paper, we propose the ratio test to detect the mean change point in the long-range memory. We proved that the limit distribution of the cumulative sum (CUSUM) statistic under the null hypothesis is a functional of fractional Brownian motion. At the same time, the consistency under the alternative hypothesis is also obtained. Simulations demonstrate that our asymptotic results provide good size and power.