Time Series • Statistics Background for Forecasting
Time Series / Graphical Displays

Graphical Displays

Notes 3 Statistics Background for Forecasting

A graphical display is a visual presentation of time series observations. Instead of studying only a table of numbers, the analyst plots the data so that pattern, change and unusual behaviour can be seen at a glance.

Notes

Graphical Displays

Definition

A graphical display is a visual presentation of time series observations. Instead of studying only a table of numbers, the analyst plots the data so that pattern, change and unusual behaviour can be seen at a glance.

Example

A line chart of monthly electricity demand for two years shows whether demand is rising, whether summer months are regularly higher, and whether any month is unusually high or low.

Why Graphs Are Used Before Modelling

Graphs are a first step in analysis. A model chosen without looking at the series may ignore trend, seasonality or a sudden change in level. Visual inspection does not replace later numerical checks, but it guides which checks and methods are reasonable.

In simple terms: look at the series before you try to forecast it.

What Graphs Help Identify

Feature What the graph may show Simple interpretation
Trend A long-term rise, fall or stable level Sales climbing slowly over several years
Seasonality A repeating shape at a known interval Ice-cream sales peaking every summer
Variability Whether swings become larger or stay similar Later years showing bigger ups and downs
Unusual observations A spike, drop or isolated odd point One month of very high sales after a festival
Change in behaviour A break in the earlier pattern Demand shifting after a new product launch

Common Graphical Displays (Introductory)

  • Time series plot (line plot): time on the horizontal axis and the observed value on the vertical axis. This is the main display for a single series.
  • Multiple series on one time axis: two related series, such as temperature and demand, plotted together to compare movement.
  • Original vs smoothed plot: the raw series together with a smoothed line so that the underlying movement is easier to see.
  • Seasonal comparison (simple): the same months of different years compared to judge whether a yearly pattern repeats.

Histograms and box plots can summarise the size of values, but they do not keep time order. For time series work, a chronological plot remains the first and most important display.

Simple Workflow

Raw Data ↓ Plot Data ↓ Observe Pattern ↓ Identify Possible Structure ↓ Select Appropriate Analysis
Example

A shop plots 24 months of packet sales, sees a gentle rise and a dip every February, then decides that both trend and a yearly seasonal pattern should be considered before forecasting.

Exam-Oriented Key Points

  1. Graphical display means presenting the series visually so that pattern can be studied.
  2. Graphs are used before modelling because they reveal trend, seasonality, variability, unusual points and changes in behaviour.
  3. A table of numbers alone can hide time-order structure.
  4. The time series plot is the basic graphical tool at this stage.
Exam Note

Always inspect a time series graph before selecting a forecasting method.