Yes, seasonal trend decomposition using LOESS (STL) is a method for decomposing a time series into its trend, seasonal, and remainder components. The trend component represents the long-term movement in the data, while the seasonal component represents the periodic fluctuations in the data. The remainder component represents the residual variation in the data after the trend and seasonal components have been removed.
STL works by applying LOESS smoothing to the time series data to estimate the trend and seasonal components. Once these components have been estimated, they can be subtracted from the original time series to obtain the remainder component. This allows for the removal of both trend and seasonality from the time series.
Seasonal-Trend decomposition using LOESS (STL) is a time series decomposition technique that separates a time series into three components: trend, seasonal, and remainder. The trend component captures the long-term changes in the data, the seasonal component captures the repetitive patterns that occur within a year, and the remainder component represents the random variation or noise in the data.
The STL method uses a non-parametric technique called LOESS (Locally Estimated Scatterplot Smoothing) to estimate the trend and seasonal components of the time series. LOESS uses a moving window to estimate the local polynomial that fits the data, with the window size varying depending on the density of the data points. This allows LOESS to capture complex nonlinear relationships in the data, including seasonal patterns.
Therefore, STL does remove both trend and seasonality from a time series by decomposing the time series into these two components, leaving only the remainder component which represents the random variation or noise in the data. The remainder component is often easier to model and analyze than the original time series since it has had the trend and seasonal components removed. However, it is important to note that the accuracy of the decomposition can be influenced by the choice of parameters, such as the window size used in the LOESS smoothing, and may require some tuning based on the specific characteristics of the data.
Like what has been already nicely explained, it is mathematically considered as fitting a model "Y=season+trend+error/Remainder". But there are always caveats when it comes to modeling. Here is a post that explained a little bit more, with some examples: https://stats.stackexchange.com/questions/563477/end-of-a-time-series-have-to-be-corrected-before-decomposition-if-partial-peri. Basically, "the notional of seasonal variation is always intrinsically ambiguous: whether the temporal variation should be considered Seasonal, Trend, or Remainder is, to a degree, a matter of opinion and determined by choice of model and model parameters. This is true in STL as well as any seasonal variational approach." Translated differently, time series decomposition is more of an art than a science; the models/algorithms can't tell whether the results make sense or not and the interpretations need to be informed by domain expertise.
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