15 Time series

 

This chapter covers

  • Creating a time series
  • Decomposing a time series into components
  • Developing predictive models
  • Forecasting future values

How fast is global warming occurring, and what will the impact be in 10 years? With the exception of repeated measures ANOVA in section 9.6, each of the preceding chapters has focused on cross-sectional data. In a cross-sectional dataset, variables are measured at a single point in time. In contrast, longitudinal data involves measuring variables repeatedly over time. By following a phenomenon over time, it’s possible to learn a great deal about it.

In this chapter, we’ll examine observations that have been recorded at regularly spaced time intervals for a given span of time. We can arrange observations such as these into a time series of the form Y1, Y2, Y3, ... , Yt, ..., YT, where Yt represents the value of Y at time t and T is the total number of observations in the series.

Consider two very different time series displayed in figure 15.1. The series on the left contains the quarterly earnings (dollars) per Johnson & Johnson share between 1960 and 1980. There are 84 observations: 1 for each quarter over 21 years. The series on the right describes the monthly mean relative sunspot numbers from 1749 to 1983 recorded by the Swiss Federal Observatory and the Tokyo Astronomical Observatory. The sunspots time series is much longer, with 2,820 observations—1 per month for 235 years.

15.1 Creating a time-series object in R

15.2 Smoothing and seasonal decomposition

15.2.1 Smoothing with simple moving averages

15.2.2 Seasonal decomposition

15.3 Exponential forecasting models

15.3.1 Simple exponential smoothing

15.3.2 Holt and Holt–Winters exponential smoothing

15.3.3 The ets() function and automated forecasting

15.4 ARIMA forecasting models

15.4.1 Prerequisite concepts

15.4.2 ARMA and ARIMA models

15.4.3 Automated ARIMA forecasting