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Long memory and fractional differencing: revisiting Clive W. J. Granger’s contributions and further developments. (English) Zbl 1380.62013

Summary: In 1980, Sir Clive W. J. Granger discovered the fractional differencing operator and its fundamental properties in discrete-time mathematics, which sparked an enormous literature concerning the fractionally integrated autoregressive moving average models. Fractionally integrated models capture a type of long memory and have useful theoretical properties, although scientists can nd them dicult to estimate or intuitively interpret. His introductory papers from 1980, oneof which with Roselyne Joyeux, show his early and deep understanding of this subject by showing that familiar short memory processes can produce long memory eects under certain conditions. Moreover, fractional dierencing advanced our understanding of cointegration and the properties of traditional Dickey-Fuller tests, and motivated the development of new unit-root tests against fractional alternatives. This article honors his signicant contributions by identifying key areas ofresearch he inspired and surveying recent developments in them.

MSC:

62-03 History of statistics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15 Inference from stochastic processes and spectral analysis
62M20 Inference from stochastic processes and prediction
62P20 Applications of statistics to economics
91B84 Economic time series analysis
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Granger, Clive W. J.
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References:

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