Seasonal Decomposition for Geographical Time Series using Nonparametric Regression

A time series often contains various systematic effects such as trends and seasonality. These different components can be determined and separated by decomposition methods. In this thesis, we discuss time series decomposition process using nonparametric regression. A method based on both loess and harmonic regression is suggested and an optimal model selection method is discussed. We then compare the process with seasonal-trend decomposition by loess STL (Cleveland, 1979). While STL works well when that proper parameters are used, the method we introduce is also competitive: it makes parameter choice more automatic and less complex. The decomposition process often requires that time series be evenly spaced; any missing value is therefore necessarily estimated. For time series with seasonality, it is preferable to use the seasonal information to estimate missing observations. The seasonal adjustment algorithm (McLeod et al., 1983) can be used for monthly time series. In this thesis, we examine the algorithm and revise it to cover daily data cases.