Topics
4. Time Series
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AustraliaVIC
VCE 12 General 2023

4.01 Time series data

Lesson
Worksheet
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Lesson

Introduction

Time series data refers to bivariate data where the explanatory variable, or independent variable, is time. This can be time in hours, days, months, weeks, quarters or any unit of time that is collected at regular intervals. Time is always plotted on the horizontal axis.

Some examples of time series data include:

  • fuel prices - they tend to rise and fall in a cyclical pattern according to the day of the week

  • air-conditioner sales - they do not remain constant all year as sales increase and decrease according to the time of year

  • ocean tides - their height is cyclical over a 24 hour period

Time series data

A time series graph is a bit like a scattergraph however the points are connected in sequential order by lines.

Trend - by looking at the graph we can see overall whether the response variable is increasing (positive trend), decreasing (negative trend), or stable (not increasing or decreasing).

The image shows an increasing trend in a time series graph. Ask your teacher for more information.
This graph shows an increasing trend - note the ‘peaks’ and ‘troughs’ are steadily getting higher.
The image shows a decreasing trend in a time series graph. Ask your teacher for more information.
This graph shows a decreasing trend - note the ‘peaks’ and ‘troughs’ are steadily getting lower.
The image shows a stable trend in a time series graph. Ask your teacher for more information.
This graph shows a stable trend - note the ‘peaks’ and ‘troughs’ are at a similar level.
The image shows a seasonality in a time series graph. Ask your teacher for more information.

Seasonality - by following the rise and fall, or cyclical nature of the data, we can determine how many seasons or time periods constitute one cycle of the data. To determine how many seasons in a cycle we count the number of points from peak to peak or trough to trough.

This graph shows how to count the number of points in a cycle.

Note: To be seasonal, each cycle must have the same number of points. If there is a repeating pattern but the number of data points is different for each cycle, then we say it is cyclical rather than seasonal. In the above example each cycle has 4 points so we say it is seasonal and there are 4 seasons per cycle.

Irregular Fluctuations-once we've observed trend and seasonality, we can determine whether the data for some seasons or for entire cycles has irregular fluctuations.

A time series graph with an outlier. Ask your teacher for more information.

Outliers-once we've observed trend and seasonality, we can determine outliers, which are data points that do not follow the pattern of the rest of the data.

Below is an example of a time series graph that shows house and apartment prices in Melbourne.

A time series graph titled 5 year Metro Melbourne Median Price Trends. Ask your teacher for more information.

The overall trend is increasing. There is not enough detail to see the seasonality of the data or count how many cycles in one season. There are some clear fluctuations.

  • We can see prices flattening out leading up to the Global Financial Crisis (GFC), and then house prices took a bit of a dive from September 2008 to March 2009. Recovery was fast and house prices rose rapidly.

  • There was with a big jump in December 2010.

  • Almost a year later in September 2011, prices seem to be falling. At this time, investors may have been wondering whether they were in a pricing bubble which means prices are well above the normal market value. When the bubble bursts, prices drop rapidly and this causes a lot of uncertainty in the market.

  • In this case, if we were to allocate numerical values to the time periods, t=1 would be Sept 06, t=2 would be Dec 06 etc.

Examples

Example 1

Consider the following set of Time Series data:

Time Period123456789101112
Data510181112071322101525
a

Plot a time series graph for the data.

Worked Solution
Create a strategy

Graph the data with the time period on the x-axis and the data on the y-axis. Plot the points and connect them with straight lines.

Apply the idea
2
4
6
8
10
12
\text{Time period}
5
10
15
20
\text{Data}
b

State the number of seasons per cycle.

Worked Solution
Create a strategy

Count the points in each cycle from trough to trough.

Apply the idea
2
4
6
8
10
12
\text{Time period}
5
10
15
20
\text{Data}

We can start counting from the first trough and stop before the next troungh. We can see on the graph that there are 3 seasons in each cycle of this data.

c

Identify the underlying trend as increasing, decreasing, or constant.

Worked Solution
Create a strategy

Check whether the peaks and troughs are increasing, decreasing, or constant.

Apply the idea

The peaks and troughs are generally increasing, so the underlying trend of the time series graph is increasing.

d

State the time period that appears to be an outlier, if there is one.

Worked Solution
Create a strategy

Look for a data point that does not follow the pattern of the rest of the data.

Apply the idea

When the time period is 4, the trough is lower then the previous trough at time period 1. So at this point, the trough has decreased which does not follow the increasing trend of the rest of the data.

So there is an outlier at time period 4.

Idea summary

Characteristics of time series graphs:

  • Time is always plotted on the horizontal axis.

  • Trend - by looking at the graph we can see overall whether the data is increasing (positive trend), decreasing (negative trend), or stable (not increasing or decreasing).

  • Seasonality - by counting the number of points from peak to peak or trough to trough we can determine how many seasons or time periods constitute one cycle of the data.

  • Outliers - once we've observed trend and seasonality, we can determine outliers, which are data points that do not follow the pattern of the rest of the data.

Outcomes

U3.AoS1.13

time series data and its analysis

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