What question did this study set out to answer?

To generalize standard autoregressive integrated moving-average (ARIMA) time series models by allowing the degree of differencing to take non-integer, fractional values.

January 1, 1981Biometrika

Fractional differencing

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Authors

JHJ. R. M. HoskingAmazon (United States)

Discussion

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Implication

Theoretical analysis demonstrates flexible long-term persistence in time series processes, indicating enhanced modeling of simultaneous short- and long-run dynamics.

Key Points

To generalize standard autoregressive integrated moving-average (ARIMA) time series models by allowing the degree of differencing to take non-integer, fractional values.
Defined a fractional differencing operator using an infinite binomial series expansion expressed in powers of the backward-shift operator.
Formulated mathematical models to characterize processes displaying both long-term persistence and antipersistence.
Demonstrated that fractionally differenced processes maintain dependencies between distant observations that decay substantially slower over time than standard time series models.
Established that the proposed family of models offers greater flexibility in simultaneously capturing short-term and long-term behaviors for applications in fields like economics and hydrology.

Cite This Study

J. R. M. Hosking (1981) studied this question.

synapsesocial.com/papers/6a04be62149eb95b702d32d1 https://doi.org/10.1093/biomet/68.1.165

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January 1, 1981Biometrika

Fractional differencing

View Full Paper

Ask AI

Bookmark

Authors

JHJ. R. M. HoskingAmazon (United States)

Discussion

Member takes

Implication

Theoretical analysis demonstrates flexible long-term persistence in time series processes, indicating enhanced modeling of simultaneous short- and long-run dynamics.

Key Points

To generalize standard autoregressive integrated moving-average (ARIMA) time series models by allowing the degree of differencing to take non-integer, fractional values.
Defined a fractional differencing operator using an infinite binomial series expansion expressed in powers of the backward-shift operator.
Formulated mathematical models to characterize processes displaying both long-term persistence and antipersistence.
Demonstrated that fractionally differenced processes maintain dependencies between distant observations that decay substantially slower over time than standard time series models.
Established that the proposed family of models offers greater flexibility in simultaneously capturing short-term and long-term behaviors for applications in fields like economics and hydrology.

Cite This Study

J. R. M. Hosking (1981) studied this question.

synapsesocial.com/papers/6a04be62149eb95b702d32d1 https://doi.org/10.1093/biomet/68.1.165

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