## 2.1ts objects

A time series can be thought of as a list of numbers, along with some information about what times those numbers were recorded. This information can be stored as a ts object in R.

Suppose you have annual observations for the last few years:

Year Observation
2012 123
2013 39
2014 78
2015 52
2016 110

We turn this into a ts object using the ts() function:

y <- ts(c(123,39,78,52,110), start=2012)

If you have annual data, with one observation per year, you only need to provide the starting year (or the ending year).

For observations that are more frequent than once per year, you simply add a frequency argument. For example, if your monthly data is already stored as a numerical vector z, then it can be converted to a ts object like this:

y <- ts(z, start=2003, frequency=12)

Almost all of the data used in this book is already stored as ts objects. But if you want to work with your own data, you will need to use the ts() function before proceeding with the analysis.

### Frequency of a time series

The “frequency” is the number of observations before the seasonal pattern repeats.1 When using the ts() function in R, the following choices should be used.

Data frequency
Annual 1
Quarterly 4
Monthly 12
Weekly 52

Actually, there are not $$52$$ weeks in a year, but $$365.25/7 = 52.18$$ on average, allowing for a leap year every fourth year. But most functions which use ts objects require integer frequency.

If the frequency of observations is greater than once per week, then there is usually more than one way of handling the frequency. For example, data with daily observations might have a weekly seasonality (frequency$$=7$$) or an annual seasonality (frequency$$=365.25$$). Similarly, data that are observed every minute might have an hourly seasonality (frequency$$=60$$), a daily seasonality (frequency$$=24\times60=1440$$), a weekly seasonality (frequency$$=24\times60\times7=10080$$) and an annual seasonality (frequency$$=24\times60\times365.25=525960$$). If you want to use a ts object, then you need to decide which of these is the most important.

In chapter 11 we will look at handling these types of multiple seasonality, without having to choose just one of the frequencies.

1. This is the opposite of the definition of frequency in physics, or in Fourier analysis, where this would be called the “period”.