مقایسهٔ روش‌ها

	مدل آریما (میانگین متحرک یکپارچه خودرگرسیو)	مدل نمایی GARCH (EGARCH)	آزمون هم‌انباشتگی یوهانسن و مدل برداری تصحیح خطا	مدل‌های حافظه بلندمدت (ARFIMA, FIGARCH)
حوزه	اقتصادسنجی	اقتصادسنجی	مالی	مالی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	2015	1991	1991	1980
پدیدآور	Box & Jenkins (Box-Jenkins methodology)	Nelson	Søren Johansen	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)
نوع	Univariate time-series model	Conditional volatility model (asymmetric GARCH variant)	Multivariate cointegration / vector error correction model	Fractionally integrated time series model
منبع بنیادین	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	Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370.	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.	Granger, C. W. J. & Joyeux, R. (1980). An Introduction to Long-Memory Time Series Models and Fractional Differencing. Journal of Time Series Analysis, 1(1), 15-29.
نام‌های دیگر	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH	Johansen test, VECM, vector error correction model, multivariate cointegration	ARFIMA, FIGARCH, fractionally integrated models, fractional integration
مرتبط	5	4	3	4
خلاصه	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).	EGARCH is an asymmetric GARCH variant, introduced by Nelson in 1991, that models the leverage effect in which bad news raises volatility more than good news of the same size. It captures the negative-shock asymmetry of financial return series by modelling the logarithm of the conditional variance.	The Johansen procedure is a multivariate cointegration framework, introduced by Søren Johansen in 1991, that tests for long-run equilibrium relationships among several I(1) time series. It determines how many cointegrating vectors link the series and then builds a Vector Error Correction Model (VECM) to describe the short-run dynamics around that equilibrium.	Long-memory models are fractional-integration methods that capture genuine long memory through a hyperbolically decaying autocorrelation structure. ARFIMA, introduced by Granger and Joyeux (1980), models long memory in return series, while FIGARCH, introduced by Baillie, Bollerslev and Mikkelsen (1996), captures long memory in volatility series; the parameter d measures the degree of fractional integration.