Seasonal patterns

Many time series change in cycles, with increases and decreases that cannot be explained by a smooth trend line.

Some cycles are seasonal. For example, hotel occupancy is consistently highest every summer, so monthly figures have a pattern that repeats each year. Similar annual patterns can be observed in temperatures, unemployment rates, airline passengers and many other monthly and weekly time series. Daily data can have a similar pattern that repeats each week — for example, cinema attendance peaks on Friday and Saturday. Demand for electricity also has an hourly cycle within each day.

Seasonal patterns are distinguished by a period that repeats exactly — for example, monthly data has a period of exactly 12 months.

Seasonal patterns are not usually referred to as 'cyclical'. Seasonal patterns will be dealt with in the next section.

Cyclical patterns

Other cycles do not repeat regularly. The period of the cycles may be fairly regular, such as sun-spot activity which has a cycle of approximately 11 years. The cycles are not all exactly the same length however.

Many business indicators also vary in cycles, though their periods are usually less regular. The 'business cycle' can be anywhere between 3 and 10 years, making it very difficult to predict.

The AR(1) method can be used to obtain forecasts for cyclical data with irregular cycle lengths.

We will not distinguish cyclical patterns and other forms of autocorrelation here.

In the following sections of this chapter, we will use the term cyclical patterns to refer to all forms of autocorrelation.

Unemployment rate in the USA

The time series plot below shows the monthly civilian unemployment rate in the USA between 1970 and 1999.

Although the data are monthly, the data do not have an obvious annual seasonal pattern. The major cycles have a much longer and less regular period.

Click the crosses to read the exact unemployment rate in any month.

An AR(1) method could be used to forecast the unemployment rate in the future.