On the nearly nonstationary seasonal time series

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Original languageEnglish
Pages (from-to)279-284
Journal / PublicationCanadian Journal of Statistics
Issue number3
Publication statusPublished - Sept 1989
Externally publishedYes


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. Copyright © 1989 Statistical Society of Canada

Research Area(s)

  • Brownian motions, least squares, near‐nonstationarity, seasonal differencing

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