FDWhittle {fractal} | R Documentation |
Using an estimate of the spectral density function for an input time series, Whittle's method fits the parameters of a specified SDF model to the data by optimizing an appropriate functional. In this case, the SDF for a fractionally differenced (FD) process model is used and an estimate of (delta), the FD parameter, is returned.
FDWhittle(x, method="continuous", dc=FALSE, freq.max=0.5, delta.min=-1,delta.max=2.5, sdf.method="direct", ...)
x |
a vector containing a uniformly-sampled real-valued time series. |
... |
optional SDF estimation arguments passed directly to the SDF function.
See help documentation for the SDF function for more information. |
dc |
a logical value. If FALSE , the DC component of the SDF (corresponding to the sample
mean of the series) is not used in optimizing the Whittle functional.
Default: FALSE . |
delta.max |
the maximum value for the FD parameter to use in the
constrained optimization problem. Default: 2.5 . |
delta.min |
the minimum value for the FD parameter to use in the
constrained optimization problem. Default: -1 . |
freq.max |
the largerst normalized frequency of the SDFs use in the analysis.
Default: 0.25 . |
method |
a character string indicating the method to be used in estimating the Hurst coefficient (H).
Choices are:
Default: "continuous" . |
sdf.method |
a character string denoting the method to use in estimating the SDF.
Choices are "direct" , "lag window" , "wosa" (Welch's Overlapped Segment Averaging),
"multitaper" . See help documentation for the SDF function for more information. Default: "direct" . |
estimate of the FD parameter of the time series.
M. S. Taqqu and V. Teverovsky, On Estimating the Intensity of Long- Range Dependence in Finite and Infinite Variance Time Series (1998), in A practical Guide to Heavy Tails: Statistical Techniques and Applications, pp. 177–217, Birkhauser, Boston.
set.seed(100) walk <- cumsum(rnorm(1024)) FDWhittle(walk, method="discrete", sdf.method="multitaper") FDWhittle(walk, method="continuous", sdf.method="multitaper")