  An emerging number of modern applications involve forecasting time series
data that exhibit both short-time dynamics and long-time seasonality.
Specifically, time series with multiple seasonality is a difficult task with
comparatively fewer discussions. In this paper, we propose a two-stage method
for time series with multiple seasonality, which does not require
pre-determined seasonality periods. In the first stage, we generalize the
classical seasonal autoregressive moving average (ARMA) model in multiple
seasonality regime. In the second stage, we utilize an appropriate criterion
for lag order selection. Simulation and empirical studies show the excellent
predictive performance of our method, especially compared to a recently popular
`Facebook Prophet' model for time series.
