## Time Series

time series graph is a line graph of repeated measurements taken over regular time intervals.

Time is always shown on the horizontal axis.

On time series graphs data points are drawn at regular intervals and the points joined, usually with straight lines.

Time series graphs help to show trends or patterns.

### Types of Time Series

Polar Cream Ltd, an ice cream company, shows its sales over the past three years, taken every three months, on the time series graph below. (Quarter 1 is for January, February and March)

Long Term Trend

From the graph for Polar Cream sales there would appear to be a trend in the long term to higher sales as the peaks and troughs seem to be increasing each year.

Seasonal Variation

As would be expected ice cream sales are higher in summer and lower in winter. This effect is known as seasonal variation and can be seen on the graph. Other examples of time series with seasonal variation include electricity usage and weather statistics.

Cyclical Variation

Sometimes, time series show a recurring pattern that is not related to seasonal factors.
e.g. If elections are held every 5 years in a country, then the existing government may allow wages to increase the year before the election to make the people more likely to vote for them! This will produce peaks in wage increases in a 5 year cycle.

Spikes

Using the example of the Polar Cream sales, there may be an exceptionally warm winter which produces unusually high sales. These unusual values on a time series are called spikes.

### Drawing Time Series Graphs

Graphs can be drawn to illustrate a set of time series data. Time is always plotted on an even scale along the horizontal axis. The variable being measured is plotted on the vertical axis.

Example

The table shows the sales of a company in millions of dollars.

 Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Sales\$m 12 3 9 24 33 48 27 15 36 57 51 24 45 63 57

Showing this on a time series graph:

The features of this graph are its cyclical nature and an apparent upward long term trend.

### Moving Averages

To clarify the long term trend, a technique called smoothing can be used where an averaging of groups of values is used.

The average can be either a moving mean or a moving median.

This is best done on a spreadsheet.

Moving mean

From the smoothed graph the upward trend of increasing sales can be clearly seen.

Moving median

The procedure for smoothing using a moving median is the same as moving mean except the median of the sets of 5 values are taken. i.e. The first value above would be the median of 12, 3, 9, 24, 33 which is 12.