GPH Procedure

@GPH estimates the fractional difference power for series using the frequency domain regression techniques of Geweke and Porter-Hudak(1983). This runs a linear regression on transformed data over a small set of low frequencies. A related procedure with an updated calculation is @AGFRACTD. Another alternative for estimating the fractional difference power is @RGSE.

@GPH( options ) series start end

Parameters

series	series to analyze
start, end	range of series to use. By default, the defined range of series.

Options

POWER=Power of T for low frequencies used in running the regression [.5]

[PRINT]/NOPRINT

TITLE="title for output" ["Geweke-Porter-Hudak Regression: Series ...]

Variables Defined

%%D	estimated value of d (REAL)
%%DSE	estimated standard error of d (REAL)
%NOBS	number of ordinates in the regression (INTEGER)

Example

* Hamilton, Times Series Analysis

* Fractional integration (page 448).

* Use of the Geweke-Porter-Hudak frequency domain estimation technique.

* The "power" in the output indicates which power of the number of

* observations which is used to figure out the number of frequencies

* near 0 which are used in the estimating regression.

cal(q) 1947

open data gnptbill.txt

data(format=prn,org=obs) 1947:1 1989:1

@gph tbill

set lgnp = 100.0*log(gnp)

@gph lgnp

Sample Output

With 169 data points and the default POWER value of .5, this runs the GPH regression on 13 data points. There are two standard error calculations, one based upon the asymptotics, one the standard OLS standard error.

Geweke-Porter-Hudak Regression, Series TBILL

Data From 1947:01 to 1989:01

Power 0.50000

Regression Ordinates 13

Estimated d 0.95116

Asymp Standard Error 0.24272

OLS Standard Error 0.23806