The more commonly used models for time series decomposition are

The more commonly used models for time series decomposition are: additive model, multiplicative model.

A time usually consists of long-term trends, seasonal variations, cyclical fluctuations, irregular fluctuations of several parts, the long-term trend refers to the phenomenon in a longer period of time to continue to develop and change a tendency or state. Seasonal fluctuations are regular changes in the level of development of the phenomenon caused by seasonal changes, cyclic fluctuations refer to a period of time, not a strict rule of cyclic continuous changes.

Irregular fluctuations refer to the impact on the time series due to a multitude of contingent factors Decomposition models are subdivided into additive and multiplicative models. Additive refers to the composition of the time series components are independent of each other, the four components have the same measure. The multiplicative model output part and the trend term have the same magnitude, the seasonal term and the cyclic term are proportional numbers, and the irregular variation term is a sequence of independent random variables, obeying a normal distribution.

Seasonally adjusted data may be useful if seasonally induced changes are not a major consideration. For example, monthly unemployment data are usually seasonally adjusted to highlight changes due to the underlying state of the economy rather than seasonal variations. The increase in unemployment due to school dropouts looking for work is seasonally variable, while the increase in unemployment due to recessions is non-seasonal.

Most economic analysts who study unemployment data are more interested in non-seasonal changes. As a result, employment data and many other economic series are usually seasonally adjusted. Seasonally adjusted series contain trend cycles and residuals. As such, they are not "smooth" and "down" or "up" can be misleading.