A fast fractional difference algorithm. (English) Zbl 1311.65009
Summary: We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (number of arithmetic operations) is of order \(T^{2}\), where \(T\) is the length of the time series. Our algorithm allows calculation speed of order \(T\log T\). For moderate and large sample sizes, the difference in computation time is substantial.
MSC:
| 65C60 | Computational problems in statistics (MSC2010) |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
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