Linganisha mbinu

	Kipimo cha Uunganishaji wa Johansen na Kielelezo cha Mfumo wa Kurekebisha Makosa	Mifumo ya Kumbukumbu-Ndefu (ARFIMA, FIGARCH)
Nyanja	Fedha	Fedha
Familia	Regression model	Regression model
Mwaka wa asili	1991	1980
Mwanzilishi	Søren Johansen	Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH)
Aina	Multivariate cointegration / vector error correction model	Fractionally integrated time series model
Chanzo asilia	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.
Majina mbadala	Johansen test, VECM, vector error correction model, multivariate cointegration	ARFIMA, FIGARCH, fractionally integrated models, fractional integration
Zinazohusiana	3	4
Muhtasari	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.