Methoden vergleichen

	TBATS	ARIMA-Modell (Autoregressive Integrated Moving Average)	SARIMA (Seasonal Autoregressive Integrated Moving Average)	STL-Zerlegung: Saisonale-Trend-Zerlegung mittels Loess
Fachgebiet	Ökonometrie	Ökonometrie	Ökonometrie	Ökonometrie
Familie	Regression model	Regression model	Regression model	Process / pipeline
Entstehungsjahr	2011	2015	2015	1990
Urheber	De Livera, Hyndman & Snyder	Box & Jenkins (Box-Jenkins methodology)	Box & Jenkins (seasonal extension of ARIMA)	Cleveland, Cleveland, McRae & Terpenning
Typ	Exponential smoothing state space model	Univariate time-series model	Seasonal time-series model	nonparametric iterative smoother
Wegweisende Quelle	De Livera, A. M., Hyndman, R. J. & Snyder, R. D. (2011). Forecasting Time Series with Complex Seasonal Patterns Using Exponential Smoothing. Journal of the American Statistical Association, 106(496), 1513-1527.	Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	Box, G.E.P., Jenkins, G.M., Reinsel, G.C. & Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6(1), 3–73.
Aliasnamen	trigonometric exponential smoothing, multiple seasonal exponential smoothing, complex seasonal exponential smoothing, TBATS — Çoklu Mevsimsel Üstel Düzleştirme	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	seasonal ARIMA, Box-Jenkins seasonal model, SARIMA — Mevsimsel ARIMA	Seasonal-Trend Decomposition using Loess, STL filtering, Loess-based seasonal decomposition, Mevsimsel-Trend Ayrıştırma (STL)
Verwandt	3	5	5	3
Zusammenfassung	TBATS is an innovations state space forecasting model, introduced by De Livera, Hyndman and Snyder (2011), that combines a Box-Cox transformation, ARMA errors and trigonometric (Fourier) seasonal terms. It is built to handle continuous time series with several nested seasonal cycles at once — for example hourly data that also repeats daily, weekly and yearly.	ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015).	SARIMA is a seasonal extension of the Box-Jenkins ARIMA model that adds seasonal differencing and seasonal autoregressive and moving-average terms. Developed within the Box, Jenkins, Reinsel and Ljung framework (5th edition, 2015), it forecasts series whose pattern repeats on a yearly, monthly, or weekly period.	STL Decomposition, introduced by Cleveland, Cleveland, McRae, and Terpenning (1990), is a nonparametric procedure that separates a time series into three additive components — trend, seasonal, and remainder — using iterative locally weighted regression (loess). Widely used in economics, meteorology, and data science, it handles time series of any periodicity and is robust to the presence of outliers, making it a highly flexible alternative to classical decomposition methods.