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Time‐varying coefficient models are important tools in time series analysis due to their flexibility to fit non‐stationary data. To improve the accuracy of these models, it is important to identify covariates with null, constant and time‐varying effects and to estimate their coefficients. This article proposes a combination of the local linear smoothing method and the adaptive group lasso penalty approach to achieve covariate identification and coefficient estimation. The penalty term consists of two parts. The first term penalizes the norm of the coefficient function, which is used to select relevant variables. The second term penalizes the norm of the derivative function, which assesses the constancy of the coefficient functions. The asymptotic properties of the proposed methodology are established. Performance of the proposed method is demonstrated using simulated data along with an application to the analysis of the air quality and health data in Hong Kong. [ABSTRACT FROM AUTHOR]