Methoden vergleichen
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| Langzeitgedächtnismodelle (ARFIMA, FIGARCH)× | ARIMA-Modell (Autoregressive Integrated Moving Average)× | Methode der kleinsten Quadrate (OLS)× | |
|---|---|---|---|
| Fachgebiet≠ | Finanzwirtschaft | Ökonometrie | Ökonometrie |
| Familie | Regression model | Regression model | Regression model |
| Entstehungsjahr≠ | 1980 | 2015 | 2019 |
| Urheber≠ | Granger & Joyeux (ARFIMA); Baillie, Bollerslev & Mikkelsen (FIGARCH) | Box & Jenkins (Box-Jenkins methodology) | Wooldridge (textbook treatment); classical least squares |
| Typ≠ | Fractionally integrated time series model | Univariate time-series model | Linear regression |
| Wegweisende Quelle≠ | 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. DOI ↗ | 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 |
| Aliasnamen≠ | 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 |
| Verwandt≠ | 4 | 5 | 5 |
| Zusammenfassung≠ | 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). |
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