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Limiting distributions of unconditional maximum likelihood unit root test statistics in seasonal time–series models
Author(s) -
Lee Taiyeong,
Dickey David A.
Publication year - 2004
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.1467-9892.2004.01814.x
Subject(s) - mathematics , unit root , statistics , series (stratigraphy) , estimator , likelihood function , unit root test , limiting , function (biology) , maximum likelihood , seasonality , asymptotic distribution , m estimator , likelihood ratio test , econometrics , cointegration , mechanical engineering , paleontology , evolutionary biology , engineering , biology
. The likelihood function of a seasonal model, Y t = ρ Y t − d + e t as implemented in computer algorithms under the assumption of stationary initial conditions is a function of ρ which is zero at the point ρ = 1. It is a smooth function for ρ in the above seasonal model with a well‐defined maximum regardless of the data‐generating mechanism. Gonzalez‐Farias (PhD Thesis, North Carolina State University, 1992) proposed tests for unit roots based on maximizing the stationary likelihood function in nonseasonal time series. We extend it to seasonal time series. The limiting distribution of seasonal unit root test statistics based on the unconditional maximum likelihood estimators are shown. Models having a single mean, seasonal means, and a single‐trend variable across the seasons are considered.