Types of pattern

A few patterns in time series are particularly important.

Trend
This refers to long-term increases and decreases in the values. Identifying trend is important since we might use it to help forecast future values.

Seasonal variation
Seasonal variation is often evident in monthly or quarterly data and refers to a pattern that is repeated each year. For example, temperature is lowest in the winter months and highest in the summer of every year.

Cyclic variation (autocorrelation)
In some time series, successive values tend to be similar to the adjacent values but, unlike in a situation where there is trend, there is no systematic tendency to increase or decrease. The time series plot often appears to have irregular waves or cycles.
 

Random fluctuations
These are 'ups and downs' in a time series that do not correspond to trend, seasonal variation or autocorrelation.

Most time series show more than one of these patterns to some degree.

World rice production

The time series plot below shows the total world rice production each year from 1961 to 2012.

The dominant feature of this time series is the upward trend over the period.

Tourist arrivals in Fiji

This time series shows the total number of tourists arriving in Fiji each month between January 2009 and December 2012.

Tourist arrivals are highly seasonal. In most tourist destinations, there is a single peak in the summer of each year but in Fiji, the peak is in the winter months of July to September which have less rainfall and are cooler. This is a seasonal pattern.

US defence expenditure

The time series below shows the percentage of GDP in the USA that was invested in defence between 1947 and 2013.

The 'wavy' appearance indicates autocorrelation — if there is high expenditure in one year, there is usually high expenditure in the adjacent years too.

British Petroleum share volumes traded

The final example shows the number of BP shares that were traded in each of the first 60 full trading days of 2014 — between 2nd January and 19th March.

This time series is dominated by random fluctuations — the volume of shares traded seems to vary unpredictably.