Time Series Models

In this chapter, we consider time series models. A time series is an ordered sequence of numbers with respect to time. In climatology, you encounter time-series data in a format given by . . . {h}Tt=1 = {h1,h2,. . . ,hT} (10.1) . . . where the time t is over a given season, month, week, or day and T is the time series length. The aim is to understand the underlying physical processes that produced the series. A trend is an example. Often by simply looking at a time series plot, you can pick out a trend that tells you that the process generating the data is changing. A single time series gives you a sample from the process. Yet under the ergodic hypothesis, a single time series of infinite length contains the same information (loosely speaking) as the collection of all possible series of finite length. In this case, you can use your series to learn about the nature of the process. This is analogous to spatial interpolation encountered in Chapter 9, where the variogram was computed under the assumption that the rainfall field is stationary. Here we consider a selection of techniques and models for time series data. We begin by showing you how to overlay plots as a tool for exploratory analysis. This is done to compare the variation between two series qualitatively. We demonstrate large variation in hurricane counts arising from a constant rate process. We then show techniques for smoothing. We continue with a change-point model and techniques for decomposing a continuous-valued series. We conclude with a unique way to create a network graph from a time series of counts and suggest a new definition of a climate anomaly. A plot showing your variables on a common time axis is an informative exploratory graph. Values from two different series are scaled to have the same relative range so the covariation in the variables can be compared visually. Here you do this with hurricane counts and sea-surface temperature (SST). Begin by loading annual.RData. These data were assembled in Chapter 6.