مقایسهٔ روش‌ها

	مدل‌های حافظه بلندمدت (ARFIMA, FIGARCH)	مدل آریما (میانگین متحرک یکپارچه خودرگرسیو)	رگرسیون حداقل مربعات معمولی (OLS)
حوزه	مالی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1980	2015	2019
پدیدآور	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)	Box & Jenkins (Box-Jenkins methodology)	Wooldridge (textbook treatment); classical least squares
نوع	Fractionally integrated time series model	Univariate time-series model	Linear regression
منبع بنیادین	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.	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	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
نام‌های دیگر	ARFIMA, FIGARCH, fractionally integrated models, fractional integration	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
مرتبط	4	5	5
خلاصه	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.	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).	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).