Open AccessA new procedure for unit root to long-memory process change-point monitoring
Author(s) -
Zhanshou Chen,
AUTHOR_ID,
Muci Peng,
Xi Li,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022360
Subject(s) - unit root , statistic , mathematics , consistency (knowledge bases) , long memory , limiting , root (linguistics) , sieve (category theory) , process (computing) , statistics , computer science , algorithm , econometrics , discrete mathematics , engineering , volatility (finance) , mechanical engineering , linguistics , philosophy , operating system
In this paper, we propose a Dickey-Fuller difference statistic to sequentially detect the change-point that shift from an unit root process to a long-memory process. The limiting distribution of monitoring statistic under the unit root process null hypothesis as well as its consistency under the alternative hypothesis are proved. Simulations indicate that the new method can control the empirical size well even for the heavy-tailed unit root process when using the sieve bootstrap method computing its critical values. In particular, it performs significantly better than the available method in the literature under the alternative hypothesis. Finally, we illustrate the new monitoring procedure by a set of foreign exchange rate data.