Time-Series Decomposition

A time series is ordered in time, so its level and repeating patterns can change. Decomposition is a way to describe that structure. In an additive view, observed value equals trend plus seasonal component plus remainder. Trend captures slower movement, seasonality describes variation repeating at a chosen period, and the remainder holds what the two fitted components do not explain. A multiplicative view can be more appropriate when seasonal amplitude grows with the series level, but it requires care with zero or negative values. The choice is a modeling assumption, not a property revealed with certainty by one plot. For monthly observations with a yearly cycle, the candidate period is twelve observations; for daily observations with a weekly cycle, it is seven. Sparse data, a structural break or changing seasonality can make components unstable. Plot the original series as well as the decomposed pieces so the smoothing does not hide an important event. Classical seasonal decomposition commonly estimates trend with moving averages and then averages seasonal positions. The statsmodels documentation calls its seasonal_decompose a moving-average method and notes that it needs two complete cycles. STL, seasonal-trend decomposition using LOESS, uses local smoothing to estimate trend and seasonal components; its robust fitting option can reduce the influence of large residual outliers. Different smoothing choices can produce different trends or leave different patterns in the remainder. None of these methods proves why sales, traffic or demand changed. Be especially careful when decomposition is used before forecasting. A centered moving average for a historical point can use observations that occurred later. If those later observations lie in a test period, fitting the component before the train-test split leaks future information. Fit transformations on available history at each forecast origin and evaluate forward in time. Decomposition can guide feature design or model choice, but compare forecasts on genuinely later data and inspect the residuals for remaining structure.