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Decomposition forecasting methods are highly sophisticated and capable of finding multiple, subtle patterns. They work very well for daily forecasts. These methods, additive and multiplicative, decompose historical data into many different patterns that can simultaneously include annual seasonality, day-of-the-week patterns, fixed-date and floating holiday impacts among others.
Decomposition is popular among forecasters because it is easy to understand (and explain to others). While complex ARIMA models are often popular among statisticians, they are not as well accepted among forecasting practitioners. For seasonal (monthly, weekly, or quarterly) data, decomposition methods are often as accurate as the ARIMA methods and they provide additional information about the trend and cycle which may not be available in ARIMA methods.
Decomposition has one disadvantage: the cycle component must be input by the forecaster since it is not estimated by the algorithm. You can get around this by ignoring the cycle, or by assuming a constant value. Some forecasters consider this a strength because it allows the forecaster to enter information about the current business cycle into the forecast.
While decomposition is primarily useful for studying time series data, and exploring the historical changes over time, it can also be used in forecasting. Assuming an additive decomposition, the decomposed time series can be written as
yt=S^t+A^t
where A^t=T^t+E^t is the seasonally adjusted component. Or if a multiplicative decomposition has been used, we can write
yt=S^tA^t,
where A^t=T^tE^t. To forecast a decomposed time series, we separately forecast the seasonal component, S^t, and the seasonally adjusted component A^t. It is usually assumed that the seasonal component is unchanging, or changing extremely slowly, and so it is forecast by simply taking the last year of the estimated component. In other words, a seasonal naïve method is used for the seasonal component. To forecast the seasonally adjusted component, any non-seasonal forecasting method may be used.
