Linganisha mbinu

	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Kipimo cha Mapumziko Mengi ya Bai-Perron	Mfumo wa SARIMA
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Hypothesis test	Regression model
Mwaka wa asili	1970	1998	1970 (first edition); 1976 (revised)
Mwanzilishi	George Box and Gwilym Jenkins	Jushan Bai & Pierre Perron	Box, Jenkins, and Reinsel
Aina	Time series forecasting model	Sequential hypothesis test for multiple structural breaks	Seasonal time series model
Chanzo asilia	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Bai, J., & Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66(1), 47–78.	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
Majina mbadala	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	Bai-Perron Multiple Break Test, Multiple Structural Change Test, Sequential Structural Break Test, Çoklu Yapısal Kırılma Testi	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
Zinazohusiana	6	2	5
Muhtasari	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.	The Bai-Perron test, introduced by Jushan Bai and Pierre Perron in their landmark 1998 Econometrica paper, is a least-squares-based procedure for detecting, estimating, and testing the number of structural breaks in a linear regression model estimated on time-series data. Unlike single-break tests, it simultaneously identifies multiple change-points in a sample, providing economists and empirical researchers with a rigorous, data-driven way to locate parameter instability across time.	SARIMA extends ARIMA by adding seasonal autoregressive and moving-average operators to capture repeating patterns at fixed intervals — such as monthly, quarterly, or annual cycles. Denoted SARIMA(p,d,q)(P,D,Q)s, it is the standard workhorse for univariate seasonal time series forecasting in econometrics, economics, and official statistics.