Basic Data Analysis for Time Series with R

12 FITTING FOURIER SERIES

12.1 INTRODUCTION: MORE COMPLEX PERIODIC MODELS

In Chapter 10, a simple periodic model was fitted to the New York City temperature data and a number of more complex data sets were introduced. In the case of more complex models, a model must usually be selected from a collection of candidate models. In this chapter, more complex models are selected that are simple extensions of the previous periodic model, now that model selection tools are available and can address some of these issues. In each case, a collection of candidate models are proposed and a “best” model from the candidates is selected. As much as possible, likelihood ratio tests, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC) will be demonstrated, however, given these are all real data sets and the proposed models are probably only crude approximations of reality, BIC is presented only for comparison purposes and will never be used to select the best model.

A second, and perhaps the main, purpose of this chapter will be to introduce an additional complication. Due to this complication, all the results in this chapter should be viewed as tentative. The first fully legitimate model selection will occur in the next chapter, where fitting models to the signal is combined with modeling the error structure.

12.2 MORE COMPLEX PERIODIC BEHAVIOR: ACCIDENTAL DEATHS

12.2.1 Fourier Series Structure

Sometimes, data is known, or at least expected, to display periodic ...