Порівняння методів

	Тест Люнга-Бокса Q для автокореляції	Модель ARIMA (Авторегресійна інтегрована ковзна середня)	Тест Бройша-Годфрі LM на автокореляцію	Тест Дарбіна-Вотсона на автокореляцію
Галузь	Економетрика	Економетрика	Економетрика	Економетрика
Родина	Hypothesis test	Regression model	Regression model	Regression model
Рік появи	1978	2015	1978	1950
Автор методу	Greta Ljung & George Box	Box & Jenkins (Box-Jenkins methodology)	Trevor Breusch & Leslie Godfrey	James Durbin & Geoffrey Watson
Тип	Portmanteau goodness-of-fit test	Univariate time-series model	Lagrange-multiplier test for serial correlation	Test for first-order residual autocorrelation
Основоположне джерело	Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303.	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	Godfrey, L. G. (1978). Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables. Econometrica, 46(6), 1293–1301.	Durbin, J., & Watson, G. S. (1950). Testing for serial correlation in least squares regression: I. Biometrika, 37(3/4), 409–428.
Інші назви	Ljung-Box Q Test, Modified Box-Pierce Test, Portmanteau Test for Autocorrelation, Otokorelasyon Portmanteau Testi	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	BG test, LM test for autocorrelation, Breusch-Godfrey serial correlation test, Breusch-Godfrey otokorelasyon testi	DW test, Durbin-Watson statistic, Durbin-Watson otokorelasyon testi
Пов'язані	3	5	3	4
Підсумок	The Ljung-Box Q test is a diagnostic portmanteau test proposed by Ljung and Box (1978) to assess whether a group of autocorrelations in a time series residual sequence is jointly zero. It is widely used to evaluate the adequacy of fitted time series models — especially ARIMA models — by testing whether remaining residuals exhibit any systematic pattern. The test is applicable in econometrics, finance, and any field that relies on temporal data modeling.	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).	The Breusch-Godfrey test is a Lagrange-multiplier test for serial correlation in regression residuals, developed independently by Trevor Breusch (1978) and Leslie Godfrey (1978). Unlike the Durbin-Watson test, it detects autocorrelation up to any chosen order p, remains valid when the model includes lagged dependent variables, and produces a definite chi-square p-value rather than an inconclusive region — making it the modern standard for autocorrelation testing.	The Durbin-Watson test, developed by James Durbin and Geoffrey Watson in 1950–1951, detects first-order serial correlation in the residuals of a linear regression. Its statistic ranges from 0 to 4, with a value near 2 indicating no autocorrelation, values toward 0 indicating positive autocorrelation, and values toward 4 indicating negative autocorrelation. It remains one of the most reported regression diagnostics despite well-known limitations.