Time series

Figure 15.1 Time series plots for (a) Johnson & Johnson quarterly earnings per share (in dollars) from 1960 to 1980, and (b) the monthly mean relative sunspot numbers recorded from 1749 to 1983

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 observa- tions—1 per month for 235 years.

Studies of time-series data involve two fundamental questions: what happened (description), and what will happen next (forecasting)? For the Johnson & Johnson data, you might ask

■Is the price of Johnson & Johnson shares changing over time?

■Are there quarterly effects, with share prices rising and falling in a regular fashion throughout the year?

■Can you forecast what future share prices will be and, if so, to what degree of accuracy?

For the sunspot data, you might ask

■What statistical models best describe sunspot activity?

■Do some models fit the data better than others?

■Are the number of sunspots at a given time predictable and, if so, to what degree?

The ability to accurately predict stock prices has relevance for my (hopefully) early retirement to a tropical island, whereas the ability to predict sunspot activity has relevance for my cell phone reception on said island.

Predicting future values of a time series, or forecasting, is a fundamental human activity, and studies of time series data have important real-world applications. Economists use time-series data in an attempt to understand and predict what will happen in

financial markets. City planners use time-series data to predict future transportation demands. Climate scientists use time-series data to study global climate change. Corporations use time series to predict product demand and future sales. Healthcare officials use time-series data to study the spread of disease and to predict the number of future cases in a given region. Seismologists study times-series data in order to predict earthquakes. In each case, the study of historical time series is an indispensable part of the process. Because different approaches may work best with different types of time series, we’ll investigate many examples in this chapter.

There is a wide range of methods for describing time-series data and forecasting future values. If you work with time-series data, you’ll find that R has some of the most comprehensive analytic capabilities available anywhere. This chapter explores some of the most common descriptive and forecasting approaches and the R functions used to perform them. The functions are listed in table 15.1 in their order of appearance in the chapter.

Table 15.1 Functions for time-series analysis

and information about its periodicity (for example, monthly, quarterly, or annual data). Once the data are in a time-series object, you can use numerous functions to manipulate, model, and plot the data.

A vector of numbers, or a column in a data frame, can be saved as a time-series object using the ts() function. The format is

myseries <- ts(data, start=, end=, frequency=)

where myseries is the time-series object, data is a numeric vector containing the observations, start specifies the series start time, end specifies the end time (optional), and frequency indicates the number of observations per unit time (for example, frequency=1 for annual data, frequency=12 for monthly data, and frequency=4 for quarterly data).

An example is given in the following listing. The data consist of monthly sales figures for two years, starting in January 2003.

Listing 15.1 Creating a time-series object

> sales <- c(18, 33, 41, 7, 34, 35, 24, 25, 24, 21, 25, 20, 22, 31, 40, 29, 25, 21, 22, 54, 31, 25, 26, 35)

>end(tsales)

[1] 2004 12

>frequency(tsales)

Subsets the object d

[1] 12

> tsales.subset <- window(tsales, start=c(2003, 5), end=c(2004, 6)) > tsales.subset

In this listing, the ts() function is used to create the time-series object b. Once it’s created, you can print and plot it; the plot is given in figure 15.2. You can modify the plot using the techniques described in chapter 3. For example, plot(tsales, type="o", pch=19) would create a time-series plot with connected, solid-filled circles.