Estimate long memory in a timeseries via Modified Log-Periodogram Regression
modlpr varname [if exp] [in range] [, powers(numlist) [ notrend ]
modlpr is for use with time-series data. You must tsset your data before using modlpr; see help tsset. modlpr 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.
modlpr computes a modified form of the Geweke/Porter-Hudak (GPH, 1983) estimate of the long memory (fractional integration) parameter, d, of a timeseries, proposed by Phillips (1999a, 1999b). If a series exhibits long memory, it is neither stationary (I) nor is it a unit root (I) process; it is an I(d) process, with d a real number. However, distinguishing unit-root behavior from fractional integration may be problematic, given that the GPH estimator is inconsistent against d>1 alternatives.
This weakness of the GPH estimator (see gphudak^) is solved by Phillips' Modified Log Periodogram Regression estimator, in which the dependent variable is modified to reflect the distribution of d under the null hypothesis that d=1. The estimator gives rise to a test statistic for d=1 which is a standard normal variate under the null. Phillips suggests (p.11) that deterministic trends should be removed from the series before application of the estimator. By default, a linear trend is extracted from the series. This may be suppressed with the notrend option.
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 estimates, a range of power values (from 0.4 - 0.75) is commonly calculated as well. modlpr uses the default power of 0.5. A numlist of powers may be given.
The command displays the d estimate, number of ordinates, conventional standard error and P-value, as well as the test statistic (zd) for the test of d=1, and its p-value. These values are returned in a matrix, e(modlpr), formatted for display. ereturn list for details. If modlpr is used in a panel context and the returned results are to be saved, the if qualifier should be used rather than the by prefix to loop over panels.
. use http://fmwww.bc.edu/ec-p/data/Mills2d/fta.dta, clear
. modlpr ftap
. modlpr ftap, power( 0.5 0.55:0.8)
. webuse grunfeld, clear
. modlpr invest if company==6
. by company: modlpr invest
Christopher F. Baum, Boston College, USA firstname.lastname@example.org
Vince Wiggins, StataCorp LP email@example.com
References Geweke, J. and Porter-Hudak, S., The Estimation and Application of Long Memory Time Series Models, J. of Time Series Analysis, 1983, 221-238.
Phillips, Peter C.B., Discrete Fourier Transforms of Fractional Processes, 1999a. Unpublished working paper No. 1243, Cowles Foundation for Research in Economics, Yale University. http://cowles.econ.yale.edu/P/cd/d12a/d1243.pdf Phillips, Peter C.B., Unit Root Log Periodogram Regression, 1999b. Unpublished working paper No. 1244, Cowles Foundation for Research in Economics, Yale University. http://cowles.econ.yale.edu/P/cd/d12a/d1244.pdf Also see
On-line: regress, time, tsset, ac, corrgram gphudak (if installed), roblpr (if installed)