Seasonal data
In cyclical time series, the peaks and troughs tend to occur at irregular intervals. We next consider more regular cycles that are strongly related to the calendar.
In monthly or quarterly data, there is often a pattern of peaks and troughs that repeats in a similar way each year. Daily data often have a similar pattern that repeats each week, and hourly data often have a daily pattern. These are called seasonal patterns.
In seasonal data, it is important that the most recent value is not interpreted in relation to the immediately preceding values. For example, a July unemployment rate may be lower than those in May and June, but this may not indicate a real improvement in the economy if July rates are always lower than those in May and June.
Seasonal patterns make it difficult to assess whether a particular month's value is unusually high or low.
Since seasonal patterns are also likely to occur in the future, it is important to use them for forecasting future values of the series.
Monthly temperatures in Boulder, Colorado
Most climatic data show a strong annual pattern. The diagram below shows the mean monthly temperature in Boulder Colorado between 1998 and 2007.
Observe that the pattern of temperatures is similar (but not identical) each year, with a pronounced peak in the summer. Click on the graph to display the actual temperature in any month.