  In this article, we consider flexible seasonal time series models which
consist of a common trend function over periods and additive individual trend
(seasonal effect) functions. The consistency and asymptotic normality of the
local linear estimators were obtained under the $\alpha$-mixing conditions and
without specifying the error distribution. We develop these results to
consistency and asymptotic normality of local linear estimates by using central
limit theorems for flexible seasonal time series model, which error terms are
$k$-weak dependent and $\lambda$-weak dependent random variables.
