Abstract
In this article, we propose a new class of flexible seasonal time series models to characterize the trend and seasonal variations. The proposed model consists of a common trend function over periods and additive individual trend (seasonal effect) functions that are specific to each season within periods. A local linear approach is developed to estimate the trend and seasonal effect functions. The consistency and asymptotic normality of the proposed estimators, together with a consistent estimator of the asymptotic variance, are obtained under the alpha-mixing conditions and without specifying the error distribution. The proposed methodologies are illustrated with a simulated example and two economic and financial time series, which exhibit nonlinear and nonstationary behavior.