Time Series and Its Components

Time Series and Its Components

A time series is a set of observations recorded at successive intervals of time.

Components of a Time Series

Any time series may contain some or all of the following components:

1.    Trend Component (T)

2.    Cyclical Component (C)

3.    Seasonal Component (S)

4.    Irregular Component (I)

These components may get combined usually as below:

If time series is represented as y_t, then 

y_t =  T X C X S X I

or

y_t =  T + C + S + I

Trend Component (T)

The trend component is the long-term pattern of a time series.  It can be positive or negative, as it depends on whether the series exhibits an increasing or decreasing long-term pattern. 

If a time series does not have either increasing or decreasing pattern, then the series is stationary as per its mean.

Cyclical Component (C)

Any pattern showing an up and down movement around a given trend line is identified as a cyclical pattern. The duration of its cycle depends on the type of business or industry being studied.

Seasonal Component (S)

Seasonality occurs when the time series exhibits regular fluctuations during the same month (or months) every year, or during the same quarter every year. For instance, retail sales peak during the month of Christmas.

Irregular Component (I)

This component is the most unpredictable component and is even called residual or random component. Every time series has some unpredictable component that makes it a random variable or stochastic variable. In prediction, the objective is to model all the components to the point that the only component that remains unexplained is this random component.