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Estimate long memory in a timeseries via Modified Log-Periodogram Regression

modlprvarname[ifexp] [inrange] [,powers(numlist)[notrend]

modlpris for use with time-series data. You musttssetyour data before usingmodlpr; see helptsset.modlprsupports thebyprefix, which may be used to operate on each time series in a panel. Alternatively, theifqualifier may be used to specify a single time series in a panel.

Description

modlprcomputes 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[0]) nor is it a unit root (I[1]) process; it is an I(d) process, withda real number. However, distinguishing unit-root behavior from fractional integration may be problematic, given that the GPH estimator is inconsistent againstd>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 ofdunder the null hypothesis thatd=1. The estimator gives rise to a test statistic ford=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 thenotrendoption.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.modlpruses the default power of 0.5. Anumlistof 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 ofd=1, and its p-value. These values are returned in a matrix, e(modlpr), formatted for display.ereturn listfor details. Ifmodlpris used in a panel context and the returned results are to be saved, theifqualifier should be used rather than thebyprefix to loop over panels.

Examples. 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

AuthorsChristopher F. Baum, Boston College, USA baum@bc.edu

Vince Wiggins, StataCorp LP vwiggins@stata.com

Geweke, J. and Porter-Hudak, S., The Estimation and Application of Long Memory Time Series Models, J. of Time Series Analysis, 1983, 221-238.ReferencesPhillips, 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 seeOn-line: regress, time, tsset, ac, corrgram gphudak (if installed), roblpr (if installed)