Methodology Glossary Tier 1
Time Series
Monitoring underlying change over time
A time series is a sequence of measurements taken at regular time intervals and in a
consistent way. There are two kinds of time series data:
1. Continuous, where we have an observation at every instant of time, e.g. lie
detectors, electrocardiograms.
2. Discrete, where we have an observation at (usually regularly) spaced
intervals, e.g. Economics - weekly share prices, monthly profits Meteorology daily rainfall
Time series analysis can show valuable information about the factors influencing a
variable by looking at any changes that occur over time. An important function of this
kind of analysis is to help decision making by forecasting future levels of the variable.
Time series methods can enable the separation of processes of interest from those
that are not of interest by breaking down variation in the data over time into the
following components:

Trend: a smooth, long term underlying pattern in the data.
Diagram 1
Diagram 2
Diagram 1 shows a constant series where the measurements stay roughly the same
over time. Diagram 2 shows a series with an increasing trend.
 Seasonal effect: variation which is cyclic and predictable in nature. Common
timescales for seasonal effects are monthly (e.g. sales of sandwiches fall during
months when fewer people are at work), weekly (sandwich sales may dip on a
Friday when workers may buy a different type of lunch), daily (e.g. sandwich
sales will peak at lunchtime).
Diagram 3
Diagram 4
Diagram 3 shows a seasonal series where the graph follows a pattern that repeats
itself at regular intervals. E.g. consumer spending is always greatest at Christmas.
Diagram 4 shows a seasonal series with an increasing trend. Notice that each peak
is greater than the previous peak.
 Fluctuations: These can be long-term or short-term but their cause is
different to that producing the trend, e.g. the economic cycle typical of a
developed country.
Diagram 5
Diagram 6
Diagram 5 shows a series with a sudden fluctuation where the graph takes an
unsuspected rise but quickly returns to normal. Diagram 6 shows a step series
where the graph takes a sudden rise but then stays at the new level.
 Random effects- irregular and unpredictable residual variation left after other
identifiable effects have been removed. Notice that in the diagrams above none of
the lines are perfectly smooth – this is caused by the random effects.
In this way time series analysis can divide and statistically remove the parts of the
variation other than the one of interest. For example, if the interest is in the
relationship between unemployment and Gross Domestic Product (GDP), it is
desirable to eliminate or minimise 1. the seasonal effect, 2. any long term trend not
due to economic conditions and, 3. random effects, in order to get the clearest
picture of the underlying relationship between unemployment and GDP.
Further Information
Link Office for National Statistics information on time series