R: Sperio Estimate for 'd' in ARFIMA(p,d,q)

fdSperio {fracdiff} | R Documentation

## Sperio Estimate for 'd' in ARFIMA(p,d,q)

### Description

This function makes use Reisen (1994) estimator to estimate the memory parameter d in the ARFIMA(p,d,q) model. It is based on the regression equation using the smoothed periodogram function as an estimate of the spectral density.

### Usage

    fdSperio(x, bandw.exp = 0.5, beta = 0.9)

### Arguments

`x` | univariate time series data.
`bandw.exp` | numeric: exponent of the bandwidth used in the regression equation.
`beta` | numeric: exponent of the bandwidth used in the lag Parzen window.

### Details

The function also provides the asymptotic standard deviation and the standard error deviation of the fractional estimator.

The bandwidths are `bw = trunc(n ^ bandw.exp)`, where 0 < bandw.exp < 1 and n is the sample size. Default `bandw.exp= 0.5`;
and `bw2 = trunc(n ^ beta)`, where 0 < beta < 1 and n is the sample size. Default `beta = 0.9`.

### Value

a list with components

`d` | Sperio estimate
`sd.as` | asymptotic standard deviation
`sd.reg` | standard error deviation

### Author(s)

Valderio A. Reisen valderio@cce.ufes.br and Artur J. Lemonte

### References

Geweke, J. and Porter-Hudak, S. (1983) The estimation and application of long memory time series models. Journal of Time Series Analysis 4(4), 221–238.

Reisen, V. A. (1994) Estimation of the fractional difference parameter in the ARFIMA(p,d,q) model using the smoothed periodogram. Journal Time Series Analysis, 15(1), 335–350.

Reisen, V. A., B. Abraham, and E. M. M. Toscano (2001) Parametric and semiparametric estimations of stationary univariate ARFIMA model. Brazilian Journal of Probability and Statistics 14, 185–206.

### See Also

`fdGPH`, `fracdiff`

### Examples

    memory.long <- fracdiff.sim(1500, d = 0.3)
    spm <- fdSperio(memory.long$series)
    str(spm, digits=6)

[Package fracdiff version 1.4-2 Index]