{smcl} {* 19oct2004}{...} {hline} help for {hi:gphudak} (SSC distribution 25 June 2006) {hline} {title:Estimate long memory in a timeseries via Geweke/Porter-Hudak } {p 8 17}{cmd:gphudak} {it:varname} [{cmd:if} {it:exp}] [{cmd:in} {it:range}] [{cmd:,} {cmdab:powers(}{it:numlist}{cmd:)}] {p 4 4}{cmd:gphudak} is for use with time-series data. You must {cmd:tsset} your data before using {cmd:gphudak}; see help {cmd:tsset}. {cmd:gphudak} supports the {cmd:by} prefix, which may be used to operate on each time series in a panel. Alternatively, the {cmd:if} qualifier may be used to specify a single time series in a panel. {title:Description} {p 4 4}{cmd:gphudak} computes the Geweke/Porter-Hudak (GPH, 1983) estimate of the long memory (fractional integration) parameter, {it: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 {it: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). {p_end} {p 4 4} The GPH method uses nonparametric methods--a spectral regression estimator-- to evaluate {it:d} without explicit specification of the 'short memory' (ARMA) parameters of the series. The series is usually differenced so that the resulting {it:d} estimate will fall in the [-0.5, 0.5] interval. {p_end} {p 4 4} 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 {cmd: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. {cmd:gphudak} uses the default power of 0.5. A list of powers may be given. {p_end} {p 4 4} The command displays the {it: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, {cmd:e(gph)}, formatted for display. {cmd:ereturn list} for details. {p_end} {title:Examples} {p 4 8}{stata "use http://fmwww.bc.edu/ec-p/data/Mills2d/fta.dta":. use http://fmwww.bc.edu/ec-p/data/Mills2d/fta.dta}{p_end} {p 4 8}{stata "gphudak ftap":. gphudak ftap}{p_end} {p 4 8}{stata "gphudak D.ftap, power( 0.5 0.55:0.8)":. gphudak D.ftap, power( 0.5 0.55:0.8)}{p_end} {title:Authors} {p 4 4}Christopher F. Baum, Boston College, USA{break} baum@bc.edu {p 4 4}Vince Wiggins, StataCorp LP{break} vwiggins@stata.com {title:References} {p}Baillie, R., Long Memory Processes and Fractional Integration in Econometrics, Journal of Econometrics, 73, 1996, 5-59.{p_end} {p}Geweke, J. and Porter-Hudak, S., The Estimation and Application of Long Memory Time Series Models, J. of Time Series Analysis, 1983, 221-238.{p_end} {title:Also see} {p 4 13}On-line: {help regress}, {help time}, {help tsset}, {help ac}, {help corrgram} {help modlpr} (if installed), {help roblpr} (if installed) {p_end}