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Data Decomposition

Decomposition is a statistical job that involves breaking down Time Series data into many components or identifying seasonality and trend from a series of data. The following are the components’ definitions:

  • The average value in the series is called the level.
  • The growing or falling value in the series is referred to as the trend.
  • Seasonality is the series’ recurring short-term cycle.
  • The random variance in the series is referred to as noise.

These elements are combined to form time series data. Level and noise are present in all series. The seasonality and trend components are optional.

These components are either additively or multiplicatively blended in time series data.

Model of Addition– The variance of data does not change over different values of the time series in an additive model. The systematic component is the arithmetic sum of the predictors’ individual effects.

Seasonality has the same frequency and amplitude as the additive model, and the trend line is straight.

Multiplicative Model- is one in which the seasonal pattern or variation increases as the data grows. The error component is multiplied by the trend and seasonal components before being added.

The trend is a curved line, and seasonality has a rising or decreasing frequency and amplitude throughout time. Multiplicative models are non-linear, such as quadratic or exponential, and the trend is a curved line.

Decomposition in the Classical Style

For time series analysis, decomposition is utilized. And, depending on the challenge, the outcome can be utilized to inform a forecasting model. It provides a quick overview of the forecasting challenge in terms of model complexity and how to effectively capture these elements in the model.

The components of the time series data might be multiplicative or additive. There might be an upward trend followed by a downward trend, or a non-repeating cycle with seasonality components that repeat.

Decomposition aids in the analysis of facts and the exploration of various solutions to the problem.

Python has a statsmodels package that may be used to break down a sequence of data into its constituents. seasonal decompose is the function utilized (). The model must be “Additive” or “Multiplicative” for this function to work.

Trend and seasonal series are stored in an array as the function’s output. When trend and seasonal components are eliminated from the data, the residuals are what remain. In addition, the original data that was seen is saved.

Wrap up

Simple decomposition methods have certain limitations, it’s worth noting. Two of them are highlighted in this article.

To begin, there are certain drawbacks to utilizing a moving average to estimate the trend+cycle component. This strategy, in particular, generates missing values for the series’ initial few and last values. We will not have estimates for the first and last six months of monthly data. On the Trend graph above, this is illustrated.

The seasonal pattern estimation is supposed to recur every year. This can be a concern for longer series with changing trends. This assumption is seen in both decomposition charts. Take note of how the seasonal patterns, both additive and multiplicative, recur throughout time.

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