Decomposition - Additive and Multiplicative

Components

Decomposition methods are used to deconstruct a time series signal into several components:

• Trend

• Seasonal

• Cyclic

• Noise (random error)

Additive Decomposition Model

Used when the amount of seasonal variation DOES NOT increase (or decrease) steadily over time.

y_t = TR_t + SN_t + CL_t + IR_t

• y_t = observed value of the time series in time period t

• TR_t = trend component

• SN_t = seasonal component

• CL_t = cyclical component

• IR_t = irregular component (noise, random error)

Multiplicative Decomposition Model

Used when the amount of seasonal variation DOES increase (or decrease) steadily over time.

As an alternative it may be possible to take the natural log of the time series and use additive decomposition.

y_t = TR_t x SN_t x CL_t x IR_t

• y_t = observed value of the time series in time period t

• TR_t = trend component

• SN_t = seasonal component

• CL_t = cyclical component

• IR_t = irregular component (noise, random error)

Decomposition using R

• See subpage Decomposition - Example 1 (R)

• See https://www.otexts.org/fpp/6 which also offers a good overview of decomposition methods.