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Sign Invariance in Goodness‐of‐Fit Tests for Time Series
Author(s) -
Anderson T. W.,
Stephens M. A.
Publication year - 2000
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 - 10.1111/1467-9892.00194
Subject(s) - mathematics , goodness of fit , series (stratigraphy) , sign (mathematics) , statistics , stationary process , distribution (mathematics) , mathematical analysis , paleontology , biology
A goodness‐of‐fit test for a stationary stochastic process may be based on a functional of the difference between the sample standardized spectral distribution and a hypothesized standardized spectral distribution. Theorems are given to show that under certain conditions the distribution of such a functional based on observations from a process { y t } indexed by a parameter θ is the same for θ=θ 0 and for θ=−θ 0 . The results are illustrated by three examples of time series processes.