Journal
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume 51, Issue 20, Pages 7208-7224Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2021.1871628
Keywords
Adaptive LASSO; AIC; BIC; autoregressive and moving-average; consistency; asymptotic normal
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The study proposes a two-step model selection procedure for ARMA models, suitable for time series contaminated with nonlinear trends. The method is able to effectively identify the true model and maintains asymptotic properties as sample size increases.
A two-step model selection procedure is proposed for autoregressive and moving-average (ARMA) model class. It is an adaptive least absolute shrinkage and selection operator (adLASSO) type model selection method that simultaneously chooses both the orders and significant lagged variables when the autoregressive and moving-average (ARMA) time series is contaminated with a nonlinear trend. The adLASSO is applied not to the observations, but to the detrended residuals. The proposed two-step adLASSO model selection procedure under some conditions can identify the true model with probability approaching one as the sample size increases, and the asymptotic properties of estimators are not affected by the replacement of observations with detrended residuals. The simulation studies show that the proposed method performs well with sample size as small as 50. The application of the method is illustrated by the annual varve thickness data collected from a location in Massachusetts.
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