On smoothing estimation for seasonal time series with long cycles

We consider a kernel smoothing estimator to the periodic component of seasonal time series which have quite a large periodicity relative to the length of the time series. The estimator is formulated by smoothing the commonly used seasonal-dummy estimator. It combines the neighboring seasonal-dummy estimates of the periodic function so as to reduce the variance of the estimation. We provide some theoretical justifications to the approach as well as simulation evaluations to demonstrate its effectiveness. The proposed approach is used to analyze the return rates of a German electricity price index.