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Change‐Point Estimation of Fractionally Integrated Processes
Author(s) -
Kuan ChungMing,
Hsu ChihChiang
Publication year - 1998
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00117
Subject(s) - estimator , mathematics , spurious relationship , least squares function approximation , convergence (economics) , rate of convergence , statistics , point estimation , set (abstract data type) , econometrics , computer science , economics , computer network , channel (broadcasting) , programming language , economic growth
In this paper we analyze the least‐squares estimator of the change point for fractionally integrated processes with fractionally differencing parameter −0.5 < d < 0.5. When there is a one‐time change, we show that the least‐squares estimator is consistent and that the rate of convergence depends on d . When there is no change, we find that the least‐squares estimator converges in probability to the set {0, 1} for −0.5 < d ≤ 0 but is likely to suggest a spurious change for 0 < d < 0.5. Simulations are also used to illustrate the asymptotic analysis.