For a Gegenbauer process, use semi-parametric methods to estimate the Gegenbauer frequency and fractional differencing.
ggbr_semipara(x, periods = NULL, k = 1, alpha = 0.8, method = "gsp")An object of class "garma_semipara".
(num) This should be a numeric vector representing the process to estimate.
(num) This parameter can be used to specify a fixed period or set of periods for the Gegenbauer periodicity. For instance if you have monthly data, then it might be sensible (after an examination of the periodogram) to set `periods = 12`. The default value is NULL. Either `periods` or `k` parameters must be specified but not both - `periods` implies fixed period(s) are to be used and `k` implies that the periods should be estimated.
(int) This parameter indicates that the algorithm should estimate the `k` frequencies semi-parametrically, before estimating the degree of fractional differencing at each period.
An alternative is the `periods` parameter which can be used to specify exactly which periods should be used by the model.
(num) Default = 0.8 - This is the bandwidth for the semiparametric estimate, and should be between 0 and 1. Robinson (1994) indicated optimality for a (scaled) version of `alpha` = 0.8, at least for the "lpr" `method`.
(char) One of "gsp" or "lpr" - lpr is the log-periodogram-regression technique, "gsp" is the Gaussian semi-parametric technique. "gsp" is the default. Refer Arteche & Robinson (1998).
J Arteche and P Robinson. Semiparametric inference in seasonal and cyclical long memory processes. Journal of Time Series Analysis, 21(1):1–25, 2000. DOI: https://doi.org/10.1111/1467-9892.00170
P Robinson. Rates of convergence and optimal spectral bandwidth for long range dependence. Probability Theory and Related Fields, 99:443–473, 1994. DOI: https://doi.org/10.1007/BF01199901.
data(AirPassengers)
ap <- as.numeric(diff(AirPassengers, 12))
sp <- ggbr_semipara(ap)
print(sp)
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