Autoregressive fractionally integrated moving average

In statistics, autoregressive fractionally integrated moving average models are time series models that generalize ARIMA (autoregressive integrated moving average) models by allowing non-integer values of the differencing parameter. These models are useful in modeling time series with long memory—that is, in which deviations from the long-run mean decay more slowly than an exponential decay. The acronyms "ARFIMA" or "FARIMA" are often used, although it is also conventional to simply extend the "ARIMA(p, d, q)" notation for models, by simply allowing the order of differencing, d, to take fractional values. Fractional differencing and the ARFIMA model were introduced in the early 1980s by Clive Granger, Roselyne Joyeux, and Jonathan Hosking.[1][2][3]

  1. ^ Granger, C. W. J.; Joyeux, Roselyne (1980). "An Introduction to Long-Memory Time Series Models and Fractional Differencing". Journal of Time Series Analysis. 1 (1): 15–29. doi:10.1111/j.1467-9892.1980.tb00297.x. ISSN 0143-9782.
  2. ^ Hosking, J. R. M. (1981). "Fractional Differencing". Biometrika. 68 (1): 165–176. doi:10.2307/2335817. ISSN 0006-3444.
  3. ^ Robinson, Peter M., ed. (2011). Time series with long memory. Advanced texts in econometrics (Repr ed.). Oxford: Oxford Univ. Press. ISBN 978-0-19-925730-0.