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 2001.

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

Temperature in Sydney

This time series shows the mean daily maximum temperature in Sydney each month between January 2005 and April 2009.

Temperature is highly seasonal and the seasonal pattern of a summer peak between December and April each year is clear.

Southern Oscillation

The Southern Oscillation Index is defined as the barometric pressure difference between Tahiti and the Darwin Islands at sea level. The southern oscillation is a predictor of El Nino which in turn is thought to be a driver of world-wide weather. Specifically, repeated southern oscillation values less than -1 typically defines an El Nino. The time series plot shows the index between January 1984 and December 1987.

There is a lot of random variation in this time series, but the index remains low for much of 1987 and is relatively high in 1988 and 1989. These periodic highs and lows indicate autocorrelation.

Annual barley yields

The final example shows annual barley yields per acre in England & Wales from 1884 to 1939.

This time series is dominated by random fluctuations — the yields seems to vary unpredictably.