Time Series Forecasting

In this course, forecasting refers to forecasting for business using data from a time series.

A time series is any variable – for example, sales, visitors or service usage – that is measured over time in sequential order.

The following hypothetical time series contains data about a country’s yearly electricity production. (In practice, it would be bigger and more complex.)

Forecasting is the act of predicting how a given time series will continue into the future over a certain horizon. With the time series above, you would try to forecast the country’s electricity production for the years beyond 2017.

Forecasting requires careful analysis of the time series to extract meaningful patterns.

Time series components

Analysing a time series involves studying the following four components:

Level

The level is the baseline value of the time series. All time series have a level.

Trend

A time series may have a long-term direction that it is moving in (upwards or downwards). This is its trend.

If you were to graph the electricity production time series above, you would see an upward trend.

The trend can be a linear change (additive) or an exponential one (multiplicative).

Seasonality

A time series may have a variation in its value that follows a consistent pattern over consecutive, fixed-length intervals. For example, internet traffic load will be higher during the day and lower at nights.

This variation may be modelled as a relatively constant amount, independent of the time series’ level (additive seasonality), or as a relatively constant proportion of the level (multiplicative seasonality).

Seasonality can be hourly, daily, weekly, monthly, quarterly or yearly. For example, international air travel volume has yearly seasonality (more travel during summer and less during winter). Some time series have multiple seasonalities (such as day vs night and weekday vs weekend).

Error

Other than the level, trend, and seasonality of a time series, there remains some variation not yet accounted for, which we call the error term.

Like seasonality, error may be modelled as an additive process (independent of the series level), or multiplicative process (proportional to the series level).

Stationary vs non-stationary time series

A stationary time series is one that ‘does not go anywhere’ during the period of interest. Its statistical properties – such as variance and mean – remain constant, regardless of the time of recording.

If a time series has a trend and/or seasonality, it is said to be non-stationary.

Forecasting tasks

Most time series forecasting tasks can be categorised as one of the three types below, addressing different components of a time series.

• Level forecasting – Predicting the future value of the level in a stationary time series, assuming that the variable remains constant over time.
• Trend forecasting – Predicting the future value of a variable based on past trends in a non-stationary time series. It assumes that the variable will change over time, but at a consistent rate.
• Seasonality forecasting – Predicting the future value of a variable based on seasonal patterns in a non-stationary time series. It assumes that the variable will follow a regular pattern over the course of a certain time period.

Specific forecasting models may combine these task types, depending on what’s required.

Share your thoughts

Consider the forecasting tasks that might be needed in your own work, or at your own organisation. What are the business metrics that need to be forecasted, and what types of forecasts are they – level, trend or seasonality? (You don’t need to share anything confidential or that identifies your work.)