1. TOPIC 15
Time Series

2. Types of Time Series A TIME SERIES is a set of reading taken at TIME
INTERVALS. A TIME SERIES is often used to monitor
progress and to show the TREND (increase and
decreases) so that future performance can be predicted. A
LINE GRAPH is used to display a TIME SERIES.
1. SECULAR VARIATION – This is the general direction of the data over a long period of time, eg, the cost of a litre of petrol is an UPWARD moving SECULAR VARIATION while the winning time in the Olympic 100m final is a DOWNWARD moving SECULAR VARIATION.
2. SEASONAL VARIATIONS – This is the pattern which occurs in data during corresponding months in successive years, eg, electricity bills or a shop’s monthly sales figures.

3. Types of Time Series
3. CYCLICAL VARIATION – This is a long oscillation about the TREND LINE which take several years, eg, periods of prosperity and recession.
4. IRREGULAR (OR RANDOM) VARIATION – This type of variation is caused by sudden unpredictable events, eg, a stock market crash.
MOVING AVERAGES can be used to ‘smooth out’ the first
three types of variations and establish whether the TREND
is UPWARDS, DOWNWARDS or FLAT.
The TREND LINE drawn through the MOVING
AVERAGES can then be used to make predictions about
time points beyond those for which we have data.

4. Time Series
Example 1
Additional Maths: Exercise 17.1, Page 375, Number 8
Answer 1
(a) (i) Seasonal
(ii) Secular
(iii) Irregular
(b) (i) See graph paper
(ii) A 5-point moving average appears best because we have 3 sets of 5 pieces of data.