Time Series • Statistics Background for Forecasting
Time Series / Time Series Plots

Time Series Plots

Notes 3 Statistics Background for Forecasting

A time series plot is a graph of observations against time. Time is shown on the x-axis and the observed value is shown on the y-axis. The points are joined in chronological order so that the path of the series can be followed.

Notes

Time Series Plots

Definition

A time series plot is a graph of observations against time. Time is shown on the x-axis and the observed value is shown on the y-axis. The points are joined in chronological order so that the path of the series can be followed.

Example

Monthly shop sales from January to December are plotted with months along the x-axis and sales along the y-axis. January comes before February; the order is never shuffled by size.

Why a Line Plot Is Commonly Used

A line plot emphasises sequence. Neighbouring months or days are connected, so a rise, fall or repeating wave is easier to see than in a bar chart of unsorted values. Bars can still be used for a few discrete periods, but the standard teaching display is a line through time-ordered points.

Time (x-axis) ↓ Observed value (y-axis) ↓ Keep chronological order ↓ Join successive points ↓ Read the pattern of the line

How to Interpret the Line

Appearance Possible meaning Simple example
Rising line Values tend to increase over time Sales growing through the year
Falling line Values tend to decrease over time Demand falling after a peak season
Repeating pattern A similar shape returns at a regular interval Higher sales every December
Sudden spike or drop An unusual observation or a short shock One week of very high festival sales

A rising line does not prove that next month must be higher. It only describes what has happened so far. A spike should be studied: it may be a data error, a one-time event, or the start of a new level.

Practical Interpretation

Suppose monthly sales run roughly: low in February, higher towards December, and generally a little higher than the previous year. The plot would show a repeating yearly wave sitting on a gentle upward movement. That picture is the starting point for later smoothing, numerical summary and modelling.

The exact height of each point depends on the dataset. Students should describe the shape of their own plot rather than memorising invented numbers.

Small Educational Python Example

The following snippet only shows how a chronological plot is prepared. Run it outside the portal. The chart should show eight weeks in time order with a general rise and one small dip.

# Import libraries import pandas as pd import matplotlib.pyplot as plt # Chronological weekly index and sales weeks = pd.date_range("2026-01-06", periods=8, freq="W-MON") sales = [42, 45, 44, 50, 53, 49, 55, 58] ts = pd.Series(sales, index=weeks, name="packet_sales") # Time series plot ts.plot(marker="o", title="Weekly packet sales") plt.xlabel("Time") plt.ylabel("Packets sold") plt.tight_layout() plt.show()

Exam-Oriented Key Points

  1. In a time series plot, time is on the x-axis and the observed value is on the y-axis.
  2. Observations must stay in chronological order.
  3. Line plots are common because they show movement over time.
  4. Rising, falling, repeating and spiked shapes are interpreted from the plot, then confirmed with further analysis.