Time Series
Trend lines, moving averages, seasonal variation, forecasting
Time Series
A time series is a set of data collected at regular intervals over time. The aim is to identify trends and seasonal patterns to make predictions.
The general long-term direction of the data (increasing, decreasing, or constant).
Regular, repeating fluctuations around the trend that occur within a fixed time period (e.g. higher ice cream sales in summer every year).
Longer-term fluctuations that do not have a fixed period (e.g. economic cycles).
Irregular, unpredictable fluctuations that cannot be explained by trend or seasonal variation.
Moving Averages
A moving average smooths out seasonal variation to reveal the underlying trend.
The average of n consecutive values. Each new average is calculated by dropping the oldest value and adding the next one.
Sales data: 10, 14, 8, 12, 11, 15, 9, 13. Calculate the first two 4-point moving averages.
For an even number of points (e.g. 4-point), the moving average falls between two time periods. To centre it, calculate the mean of two consecutive moving averages.
Seasonal Variation and Forecasting
Once the trend is established using moving averages, we can calculate the seasonal variation and use it to make forecasts.
Seasonal Effect = Actual value − Moving average (trend) value at the same time point.
- Calculate moving averages to find the trend
- Extend the trend line to the forecast period
- Calculate the average seasonal effect for each season
- Forecast = Trend value + Average seasonal effect
When asked to forecast, always add the seasonal effect to the trend — do not just extend the trend line. A positive seasonal effect means the actual value is typically above the trend; negative means below.