Data Decomposition

Decomposition in Time Series Analysis

Decomposition divides Time Series data into individual components—namely, level, trend, seasonality, and noise.

• Level: Represents the series' average value.
• Trend: Indicates whether the series is ascending or descending.
• Seasonality: Represents recurring short-term cycles.
• Noise: Constitutes random fluctuations within the data.

Every Time Series data comprises at least the level and noise. However, trend and seasonality may not always be present.

Models of Time Series Decomposition

The decomposition can adopt two models: Additive and Multiplicative.

Additive Model:

• Exhibits consistent variance across the series.
• Sums predictors' effects.
• Features consistent seasonality frequency and amplitude.
• Boasts a linear trend.

Multiplicative Model:

• Sees the seasonal variation intensify with data growth.
• Integrates error, trend, and seasonality through multiplication.
• Presents a non-linear trend—either quadratic or exponential.
• Portrays changing seasonality frequency and amplitude.

Applying Decomposition to Forecasting

Decomposition is pivotal in understanding Time Series data for forecasting. Recognizing the model's complexity and its intrinsic patterns, such as alternating upward and downward trends or recurring seasonal components, aids in tailoring forecasting strategies.

The Python statsmodels library offers tools for this purpose. Its seasonal decompose function segregates the series into trend, seasonal, and residual components, with the residual being what's left post the extraction of trend and seasonality.

Limitations and Considerations

Basic decomposition isn't flawless. Moving averages can produce missing values at series ends. For instance, monthly data might exclude estimates for the initial and final six months. Plus, the assumed annually repeating seasonal pattern may falter with longer series exhibiting dynamic trends. Both Additive and Multiplicative models underline this recurring seasonal assumption.

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