help for gphudak (SSC distribution 12 March 2023)

Estimate long memory in a timeseries via Geweke/Porter-Hudak

gphudak
varname
[if exp]
[in range]
[, powers(numlist)]

gphudak is for use with time-series data.
You must tsset your data before using gphudak; see help tsset.
gphudak supports the by prefix, which may be used to operate on each
time series in a panel. Alternatively, the if qualifier may be used to specify
a single time series in a panel. The varname can contain a time-series operator.

Description

gphudak
computes the Geweke/Porter-Hudak (GPH, 1983) estimate of the long
memory (fractional integration) parameter, d, of a timeseries. If a series
exhibits long memory, it is neither stationary (I[0]) nor is it a unit
root (I[1]) process; it is an I[{it:d] process, with d a real number. A series
exhibiting long memory, or persistence, has an autocorrelation function
that damps hyperbolically, more slowly than the geometric damping exhibited
by 'short memory' (ARMA) processes. Thus, it may be predictable at long
horizons. An excellent survey of long memory models--which originated in
hydrology, and have been widely applied in economics and finance--is given
by Baillie (1996).

The GPH method uses nonparametric methods--a spectral regression estimator--
to evaluate d without explicit specification of the 'short memory' (ARMA)
parameters of the series. The series is usually differenced so that the
resulting d estimate will fall in the [-0.5, 0.5] interval.

A choice must be made of the number of harmonic ordinates to be included
in the spectral regression. The regression slope estimate is an estimate of
the slope of the series' power spectrum in the vicinity of the zero
frequency; if too few ordinates are included, the slope is calculated from
a small sample. If too many are included, medium and high-frequency components
of the spectrum will contaminate the estimate. A choice of root(T), or
power = 0.5 is often employed. To evaluate the robustness of the GPH estimate,
a range of power values (from 0.4 - 0.75) is commonly calculated as well.
gphudak uses the default power of 0.5. A list of powers may be given.

The command displays the d estimate, number of ordinates, conventional
standard error and P-value, as well as the asymptotic standard error.
These values are returned in a matrix, e(gph), formatted for display.
return list for details. Contents of the last row of this matrix are also returned as scalars.

Examples

. use http://fmwww.bc.edu/ec-p/data/Mills2d/fta.dta

. gphudak ftap

. gphudak D.ftap, power( 0.5 0.55:0.8)

Authors

Christopher F. Baum, Boston College, USA

baum@bc.edu

Vince Wiggins, StataCorp LP

vwiggins@stata.com

References

Baillie, R., Long Memory Processes and Fractional Integration in
Econometrics, Journal of Econometrics, 73, 1996, 5-59.

Geweke, J. and Porter-Hudak, S., The Estimation and Application
of Long Memory Time Series Models, J. of Time Series Analysis,
1983, 221-238.

Also see

On-line: regress, time, tsset, ac,
corrgram modlpr (if installed), roblpr (if installed)