- Autoregressive fractionally integrated moving average
statistics, autoregressive fractionally integrated moving average models are time seriesmodels that generalize ARIMA("autoregressive integrated moving average") models by allowing non-integer values of the differencing parameterand are useful in modeling time series with long memory.
ARIMAmodel, the "integrated" part of the model includes the differencing operator, in terms of the backspace operator "B", as an integer power of (1 − "B"). For example :where:In a "fractional" model, the power is allowed to be fractional, with the meaning of the term identified using the following formal expansion:
* C. W. J. Granger and R. Joyeux. "An introduction to long-memory time series and fractional differencing", Journal of Time Series Analysis, 1980.
* J. R. M. Hosking. "Fractional differencing", Biometrika 68(1):165-176, 1981.
* P. M. Robinson. "Time Series With Long Memory", Oxford University Press 2003.
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