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# Internal structures of time series

In this section, we will conceptually explain the following special characteristics of time series data that requires its special mathematical treatment:

• General trend
• Seasonality
• Cyclical movements
• Unexpected variations

Most time series has of one or more of the aforementioned internal structures. Based on this notion, a time series can be expressed as xt = ft + st + ct + et, which is a sum of the trend, seasonal, cyclical, and irregular components in that order. Here, t is the time index at which observations about the series have been taken at t = 1,2,3 ...N successive and equally spaced points in time.

The objective of time series analysis is to decompose a time series into its constituent characteristics ...

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