ggbr_semipara function

Extract semiparametric estimates of the Gegenbauer factors.

Extract semiparametric estimates of the Gegenbauer factors.

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")

Arguments

  • x: (num) This should be a numeric vector representing the process to estimate.

  • periods: (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.

  • k: (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.

  • alpha: (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.

  • 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).

Returns

An object of class "garma_semipara".

Examples

data(AirPassengers)
ap <- as.numeric(diff(AirPassengers, 12))
sp <- ggbr_semipara(ap)
print(sp)

References

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.

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