Time Series

A time series is a sequence of data recorded at regular time intervals. We plot time on the x-axis and the measured quantity on the y-axis, then identify trends, cycles, and use moving averages to smooth fluctuations.

📖 Learn

Reading a Time Series Graph

Time series graphs show how a variable changes over time. Points are plotted and joined with straight lines.

Trend: overall direction — upward, downward, or roughly constant
Seasonal variation: regular pattern repeating (e.g. every year)
Random fluctuations: unpredictable ups and downs

💡 Don't confuse the trend (long-term direction) with individual fluctuations.

Moving Averages

A moving average smooths out short-term fluctuations and reveals the underlying trend.

n-point moving average: average of each group of n consecutive values
Plot the average at the MIDDLE time point of the group.

Example: data = 4, 7, 5, 8, 6, 9. 3-point moving averages:

(4+7+5)/3 = 5.33 (plotted at point 2)
(7+5+8)/3 = 6.67 (plotted at point 3)
(5+8+6)/3 = 6.33 (plotted at point 4)
(8+6+9)/3 = 7.67 (plotted at point 5)

💡 A 4-point moving average is often used with quarterly data (4 seasons). The midpoint between two 4-point averages is centred on a time point.

Trend Lines and Prediction

A trend line is drawn through the moving averages. It shows the overall direction and can be used to predict future values.

Extend the trend line to predict future data points
Predictions are more reliable for the near future
A seasonal adjustment accounts for regular deviations from the trend

💡 Extrapolation (predicting beyond the data) becomes less reliable the further you go.

✏️ Worked Examples

Example 1: 3-point moving average

Data: 5, 8, 4, 10, 6, 12, 8. Calculate all 3-point moving averages.

(5+8+4)/3 = 17/3 = 5.67

(8+4+10)/3 = 22/3 = 7.33

(4+10+6)/3 = 20/3 = 6.67

(10+6+12)/3 = 28/3 = 9.33

(6+12+8)/3 = 26/3 = 8.67

Example 2: 4-point moving average (quarterly data)

Quarterly sales: Q1=10, Q2=14, Q3=8, Q4=12, Q1=11, Q2=15. Find the 4-point moving averages.

(10+14+8+12)/4 = 44/4 = 11.0 (centred between Q2 and Q3)

(14+8+12+11)/4 = 45/4 = 11.25

(8+12+11+15)/4 = 46/4 = 11.5

Example 3: Reading a trend

Monthly temperatures (°C): 12, 14, 18, 22, 25, 24, 20, 16, 12, 10, 8, 9. Describe the trend.

Values rise from Jan to May, peak in summer, then fall through autumn and winter.

This shows a clear seasonal pattern — not a long-term upward or downward trend.

📅 Time Series

Time Series

📖 Learn

Reading a Time Series Graph

Moving Averages

Trend Lines and Prediction

✏️ Worked Examples

Example 1: 3-point moving average

Example 2: 4-point moving average (quarterly data)

Example 3: Reading a trend

🎨 Visualizer

Time Series Graph Builder

Moving Average Calculator

Ex 1 — Reading Time Series

Ex 2 — 3-Point Moving Average

Ex 3 — 4-Point Moving Average

Ex 4 — Trends and Patterns

Ex 5 — Predictions

⭐ Practice — 20 Questions

🔥 Challenge — 8 Questions