RGSE Procedure

@RGSE estimates the "d" parameter for fractional integration using Robinson's Gaussian Semiparametric Estimator from Robinson(1992). Typically, you will difference the series first and apply this to the differenced series. If fractional differencing is appropriate, a full difference overshoots, so the estimate will generally be negative. That is, if you apply this to \((1 - L)y\) and get an estimate of \(d = - .2\), the conclusion is that \({(1 - L)^{.8}}y\) is stationary where the \(.8 = 1 - .2\).

It estimates "d" by examining the spectral density at low frequencies, where "low" is determined by the power of the number of observations set using the POWER option. Alternative procedures for estimating d are @GPH (Geweke–Porter-Hudak) and @AGFRACTD (Andrews-Guggenberger).

@RGSE( options ) series start end

Parameters

series	series to analyze
start, end	estimation range, by default, the range of series

Options

POWER=power of number of observations to use as frequencies [.8]

[PRINT]/NOPRINT

TITLE="title of report" ["Robinson GSE, Series xxx"]

Variables Defined

%%D	estimated value of d (REAL)
%%DSE	estimated standard error of d (REAL)

Example

* Replication file for Lebo and Box-Steffensmeier(2008), "Dynamic

* Conditional Correlations in Political Science", American Journal of

* Political Science, vol 53, no 2, 688-704.

* Table 1 (Tse CC tests)

calendar(m) 1978

open data pres7804.xls

data(format=xls,org=obs) 1978:1 2004:7

* Get the fractionally differenced, stationary, versions of the

* variables before testing

difference ics / icsd

@rgse icsd

diff(d=-.11) icsd / icsdf

difference Npros5 / Npros5d

@rgse Npros5d

diff(d=-.25) Npros5d / Npros5df

Sample Output

The estimate is roughly -.11, suggesting that for the original series (this was done on the differences), fractional differencing of .89 is in order. -.11 is barely significantly different from 0 at conventional levels given the .05 standard error.

Robinson GSE, Series ICSD

Observations 318

Frequencies 100

d-hat -0.1087

std error 0.0500