विधियों की तुलना करें

	दीर्घ-स्मृति मॉडल (ARFIMA, FIGARCH)	ऑटोरेग्रेसिव इंटीग्रेटेड मूविंग एवरेज (ARIMA) मॉडल	उच्च-आवृत्ति डेटा और बाज़ार सूक्ष्म संरचना विश्लेषण	साधारण न्यूनतम वर्ग (OLS) समाश्रयण
क्षेत्र	वित्त	अर्थमिति	वित्त	अर्थमिति
परिवार	Regression model	Regression model	Regression model	Regression model
उद्भव वर्ष	1980	2015	2007	2019
प्रवर्तक	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)	Box & Jenkins (Box-Jenkins methodology)	Hasbrouck (2007); Aït-Sahalia & Jacod (2014)	Wooldridge (textbook treatment); classical least squares
प्रकार	Fractionally integrated time series model	Univariate time-series model	Market microstructure / high-frequency econometrics	Linear regression
मौलिक स्रोत	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	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
उपनाम	ARFIMA, FIGARCH, fractionally integrated models, fractional integration	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	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
संबंधित	4	5	5	5
सारांश	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).	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).