The classical decomposition of a time series can help to get an overview on the tendencies (trend component), periodic patterns (seasonal component) and quality of the model (random component). In addition it helps to identify outliers in a time series.
To forecast a time series it is often useful to have a decomposition and to forecast each of the components in the decomposition seperately. A seasonal component would just be repeated constantly (naive forecast), meanwhile you could use exponential smoothing methods to forecast the trend and random component.
On the other hand the classical decomposition shows some disadvantages: We saw in this post that the trend and therefore also the random component cannot be determined at the beginning and at the end of a time series. Also we saw in that post that it relies on the assumption that we have a stable period with a pretty constant pattern. In reality this is often not the case: e.g. 100 years ago the energy consumption was high in winter was high due to heaters, now in summer it is equally high due to air condition.
To overcome these bounderies other decomposition methods have been developed, see for instance the Seasonal and Trend Determination using LOESS (1990). I will describe it in a new post.
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