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.

New company registrations in New Zealand

The time series below shows the rate of new company registrations in New Zealand (per 100,000 population) each year from 1960 to 1998.

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 2004 and December 2007.

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.

British Airways share prices

This example concerns the price of British Airways shares in the first 57 trading days of 2002 — between 2nd January and 21st March. An investor would be interested in using this time series to forecast future changes in the share price.

The 'wavy' appearance indicates autocorrelation — if the share price is high in one day, it is more likely to be high in the adjacent days too.

British Airways share volumes traded

The final example shows the number of British Airways shares that were traded in the same days as the previous time series

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