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Fractionally Differenced and Fractionally Integrated Processes

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Stochastic Processes and Long Range Dependence

Abstract

The adjective “fractional” appears frequently in the names of processes related to long-range dependence; two immediate examples are the fractional Brownian motion of Example 3.5.1 and the fractional Gaussian noise introduced in Section 5.1

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Bibliography

  • R. Baillie, T. Bollerslev, H. Mikkelsen, Fractionally integrated generalized autoregressive conditional heteroscedasticity. J. Econ. 74, 3–30 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • T. Bollerslev, Generalized autoregressive conditional heteroskedasticity. J. Econ. 31, 307–327 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • P. Brockwell, R. Davis, Time Series: Theory and Methods (Springer, New York, 1987)

    Book  MATH  Google Scholar 

  • N. Crato, P. Rothman, Fractional integration analysis of long-run behavior for US macroeconomic time series. Econ. Lett. 45, 287–291 (1994)

    Article  MATH  Google Scholar 

  • R. Douc, F. Roueff, P. Soullier, On the existence of some ARCH() processes. Stoch. Process. Appl. 118, 755–761 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • R. Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987–1008 (1982)

    Google Scholar 

  • W. Feller, An Introduction to Probability Theory and Its Applications, vol. 2, 2nd edn. (Wiley, New York, 1971)

    Google Scholar 

  • L. Gil-Alana, A fractionally integrated model for the Spanish real GDP. Econ. Bull. 3, 1–6 (2004)

    Google Scholar 

  • C. Granger, R. Joyeux, An introduction to long-memory time series and fractional differencing. J. Time Series Anal. 1, 15–30 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  • M. Hauser, R. Kunst, Fractionally integrated models with ARCH errors: with an application to the Swiss 1-month Euromarket interest rate. Rev. Quant. Finan. Acc. 10, 95–113 (1998)

    Article  Google Scholar 

  • J. Hosking, Fractional differencing. Biometrika 68, 165–176 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  • P. Zaffaroni, Stationarity and memory of ARCH() models. Econ. Theory 20, 147–160 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Samorodnitsky, G. (2016). Fractionally Differenced and Fractionally Integrated Processes. In: Stochastic Processes and Long Range Dependence. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-45575-4_7

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