Linganisha mbinu

	TBATS	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Uchanganuzi wa STL: Uchanganuzi wa Mwenendo wa Msimu kwa kutumia Loess
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Process / pipeline
Mwaka wa asili	2011	2015	1990
Mwanzilishi	De Livera, Hyndman & Snyder	Box & Jenkins (Box-Jenkins methodology)	Cleveland, Cleveland, McRae & Terpenning
Aina	Exponential smoothing state space model	Univariate time-series model	nonparametric iterative smoother
Chanzo asilia	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	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.
Majina mbadala	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-Trend Decomposition using Loess, STL filtering, Loess-based seasonal decomposition, Mevsimsel-Trend Ayrıştırma (STL)
Zinazohusiana	3	5	3
Muhtasari	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).	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.