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Inference on a Structural Break in Trend with Fractionally Integrated Errors
Author(s) -
Chang Seong Yeon,
Perron Pierre
Publication year - 2016
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/jtsa.12176
Subject(s) - spurious relationship , mathematics , consistency (knowledge bases) , long memory , limiting , convergence (economics) , rate of convergence , inference , structural break , econometrics , series (stratigraphy) , statistics , computer science , economics , discrete mathematics , geology , mechanical engineering , computer network , channel (broadcasting) , paleontology , volatility (finance) , artificial intelligence , engineering , economic growth
Perron and Zhu (2005) established the consistency, convergence rate and limiting distributions of parameter estimates in time trends with a change in slope with or without a concurrent level change for the cases with I(1) or I(0) errors. We extend their analysis to the general case of fractionally integrated errors with memory parameter d ∗ . Our results uncover interesting features; e.g., with a level shift allowed, the convergence rate for the break date estimate is the same for all d ∗ ∈(−0.5,0.5). In other cases, it is decreasing as d ∗ increases. We also provide results about the so‐called spurious break issue.