What is a time series?
A time series is a set of observations of a variable recorded at successive points or periods of time, arranged in chronological order. Examples: a company's annual sales from 2010 to 2020, monthly rainfall in a city, daily closing price of a share. Time is the independent variable and is usually plotted on the x-axis.
The four components
Changes in a time series are explained by four kinds of movement.
Secular trend (T)
The general long-term tendency of the series to rise, fall or stay steady over many years, ignoring short-term ups and downs. Example: steady growth of a country's population or of mobile phone users.
Seasonal variation (S)
Regular, periodic changes that repeat within a year (period of one year or less), caused by seasons, festivals, weather or customs. Example: sales of umbrellas rise every monsoon; sales of sweets rise around festivals.
Cyclical variation (C)
Up-and-down swings that last more than a year, linked to the business cycle with its four phases: prosperity, recession, depression and recovery. The length of a cycle is not fixed.
Irregular (random) variation (I)
Unpredictable, short-lived changes caused by accidental events such as floods, earthquakes, strikes or wars. They cannot be forecast.
Combining the components
- Additive model: Y = T + S + C + I. Components are measured in the same units as Y; S, C, I are positive or negative deviations.
- Multiplicative model: Y = T × S × C × I. Here T is in the units of Y, and S, C, I are ratios or indices around 1 (or 100%). Example: T = 500, S = 1.2, C = 0.9, I = 1 gives Y = 540.
Key points
- Time series data must be in time order.
- Seasonal: repeats within a year; cyclical: swings over more than a year.
- Irregular variations are caused by unforeseen events.
- The multiplicative model is used more often for economic data.
Common mistakes
- Calling a festival-time rise in sales "cyclical"; it is seasonal.
- Treating a single unusual event (a strike) as a trend.