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Penalized regression methods have for quite some time been a popular choice for addressing challenges in high dimensional data analysis. Despite their popularity, their application to time series data has been limited. This paper concerns bridge penalized methods in a linear regression time series model. We first prove consistency, sparsity and asymptotic normality of bridge estimators under a general mixing model. Next, as a special case of mixing errors, we consider bridge regression with autoregressive and moving average (ARMA) error models and develop a computational algorithm that can simultaneously select important predictors and the orders of ARMA models. Simulated and real data examples demonstrate the effective performance of the proposed algorithm and the improvement over ordinary bridge regression. [ABSTRACT FROM AUTHOR]

Profile monitoring is a vast area of research underneath the statistical process monitoring (SPM). Several methods for univariate and multivariate process control are found in literature to monitor the profile data, including parametric, nonparametric, and some semiparametric methods. The main idea behind monitoring the linear profiles in mixed effects is to model the possible individual differences between similar set of profiles for future monitoring. In this paper, nonparametric and semiparametric approaches are proposed to model the profile data in a linear mixed effect setting by considering the residuals from a parametric model. A simulation study was carried out to compare the efficiency of the proposed methods. At first step, the residuals from a parametric linear mixed model are obtained. A nonparametric approach (NPR) is then used to model these residuals. Finally, a semiparametric method (MMRRPM) is proposed as a convex combination of the parametric (P) and nonparametric estimations based on the residuals (NPR) to model the profile data in mix effects. Two Hoteling's T2 statistics were computed for each technique based on fitted values and the estimated random effects. The results show that the proposed methods are most effective to monitor the autocorrelated profile data compared with the state‐of‐the‐art. [ABSTRACT FROM AUTHOR]