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On the nearly nonstationary seasonal time series
Author(s) -
Chan Ngai Hang
Publication year - 1989
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315523
Subject(s) - series (stratigraphy) , context (archaeology) , econometrics , mathematics , statistical physics , time series , diffusion , asymptotic analysis , order of integration (calculus) , statistics , geology , mathematical analysis , physics , paleontology , thermodynamics
A time series is said to be nearly nonstationary if some of its characteristic roots are close to the unit circle. For a seasonal time series, such a notion of near‐nonstationarity is studied in a double‐array setting. This approach not only furnishes a natural transition between stationarity and nonstationarity, but also unifies the corresponding asymptotic theories in a seasonal‐time‐series context. The general theory is expressed in terms of functionals of independent diffusion processes. The asymptotic results have applications to estimation and testing in a nearly nonstationary situation and serve as a useful alternative to the common practice of seasonal adjustment.