مقایسهٔ روش‌ها

	مدل‌های حافظه بلندمدت (ARFIMA, FIGARCH)	مدل GARCH (پیش‌بینی نوسانات)	تحلیل داده‌های با بسامد بالا و ریزساختار بازار	رگرسیون حداقل مربعات معمولی (OLS)
حوزه	مالی	اقتصادسنجی	مالی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	1980	1986	2007	2019
پدیدآور	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)	Tim Bollerslev	Hasbrouck (2007); Aït-Sahalia & Jacod (2014)	Wooldridge (textbook treatment); classical least squares
نوع	Fractionally integrated time series model	Conditional volatility model	Market microstructure / high-frequency econometrics	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.	Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327.	Hasbrouck, J. (2007). Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading. Oxford University Press. ISBN: 978-0195301649	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	GARCH, GARCH(1,1), conditional volatility model, GARCH Modeli (Oynaklık Tahmini)	market microstructure, high-frequency financial econometrics, tick data analysis, Yüksek Frekanslı Veri ve Piyasa Mikro Yapısı	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
مرتبط	4	5	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.	The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, introduced by Tim Bollerslev in 1986, models the time-varying conditional variance of a financial time series. It captures volatility clustering and the ARCH effect, and is the standard tool for estimating risk and volatility in return series.	Market microstructure analysis studies how prices form from tick-level trade and quote data, examining order-book dynamics, the bid-ask spread, and price discovery. The modern econometric framework was set out by Hasbrouck (2007) and extended for high-frequency data by Aït-Sahalia and Jacod (2014).	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).