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Non‐parametric testing for seasonally and periodically integrated processes
Author(s) -
Castro Tomás del Barrio,
Osborn Denise R.
Publication year - 2012
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/j.1467-9892.2011.00775.x
Subject(s) - mathematics , cointegration , econometrics , parametric statistics , multivariate statistics , monte carlo method , statistics , variance (accounting) , series (stratigraphy) , bivariate analysis , economics , accounting , paleontology , biology
This article obtains the asymptotic distributions of the seasonal variance ratio tests proposed by A.M.R. Taylor (2005, Journal of Econometrics 124, 33) when these tests are applied to a periodically integrated process [ PI (1)]. In contrast to the situation where the process is seasonally integrated [ SI (1)], all test statistics in the PI (1) case are driven by a single stochastic trend and hence follow the distribution obtained by Breitung (2002, Journal of Econometrics 108, 343) for the original (non‐seasonal) variance ratio test. The multivariate non‐parametric cointegration test of Breitung (2002 Journal of Econometrics 108, 343 ) is also investigated to distinguish between PI and SI processes. A Monte Carlo analysis shows how these results apply in finite samples for both SI and PI processes and an empirical application investigates seasonally unadjusted quarterly US industrial production series.