-------------------------------------------------------------------------------
help for roblpr    (SSC distribution 25 Jun 2006)
-------------------------------------------------------------------------------

Estimate long memory in a set of timeseries via Log-Periodogram Regression

        roblpr varname [if exp] [in range] [, powers(numlist) l(#) j(#)
                 constraints(numlist)]

    roblpr is for use with time-series data.  You must tsset your data before
    using roblpr; see help tsset.  roblpr 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.


Description

    roblpr computes the Robinson (1995) multivariate semiparametric estimate of
    the long memory (fractional integration) parameters, d(g), of a set of
    timeseries, y(g), g=1,G. G may be one. 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, with d a real number. When applied to a set of timeseries,
    the d(g) parameter for each series is estimated from a single
    log-periodogram regression which allows the intercept and slope to differ
    for each series. The standard errors for the estimated parameters are
    derived from a pooled estimate of the variance in the multivariate case, so
    that their interval estimates differ from those of their univariate
    counterparts.

    A choice must be made of the number of harmonic ordinates to be included in
    the spectral regression. One of the innovations of Robinson's estimator is
    that it is not restricted to using a small fraction of the ordinates of the
    empirical periodogram of the series. The estimator also allows for the
    removal of one or more initial ordinates, and for the averaging of the
    periodogram over adjacent frequencies.

    Results of the estimation are returned after the command; type return list
    to see the returned results. If more than one series is specified in
    varlist, an F-test of the equality of the d(g) coefficients is performed,
    and those values are returned as well.


Options

powers(numlist) specifies the number of ordinates (nord) entering the 
    log-periodogram regression. Each value in numlist is taken as the value p
    in nord = N^p.  The default value of p, following Robinson, is 0.9. More
    than one p may be specified in numlist only if there is a single
    variable in the varlist.

l(#) specifies the number of initial ordinates to be excluded from the 
    log-periodogram regression. Some researchers have found that such
    exclusion improves the properties of tests based on log-periodogram
    regressions. The default value of l is zero.

j(#) specifies that the log-periodogram is to be computed from sums of 
    adjacent periodogram ordinates. The default value of j is 1, so that no
    averaging is performed. With j=2, the number of ordinates is halved; with
    j=3, divided by three; and so on.

powers(constraints) specifies the constraint numbers of the linear constraints
    to be applied during estimation; see help constraint.  The default is to
    perform unconstrained estimation.

    This option allows the imposition of linear constraints prior to
    estimation of the pooled coefficient vector. For instance, if the
    varlist contains prices, dividends, and returns, and your prior (or
    previous findings) states that prices' and dividends' order of integration
    is indistinguishable, one might impose that constraint to improve the
    power of the F-test provided by roblpr.  One would specify the
    constraints prior to the roblpr command, and then provide the list of
    constraints in the constraints option to roblpr.
    
    Technical note on constraints.  When constraints are imposed it is
    difficult to identify the number of numerator degrees of freedom in the 
    test for equality of d coefficients reported at the bottom of roblpr's 
    output. Since constraints can be of any general form and it is possible
    specify constraints that are not unique, roblpr determines the
    degrees of freedom from the rank of the matrix used to compute the Wald
    statistic. Determining that matrix rank from a numerical standpoint can be
    problematic, in which case roblpr may overstate the number
    of constraints being tested and thereby incorrectly compute the numerator 
    degrees of freedom for the test.  This rarely has a meaningful impact on
    the statistical test, but you may wish to test only the unconstrained
    coefficients if the computed degrees of freedom are wrong.

    For example, after the final example below, we could perform the test by
    typing test ftap == ftaret.  In this case, the degrees of freedom were
    correct, so we needn't have gone to the trouble.


Examples

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

    . roblpr ftap

    . roblpr ftap ftadiv

    . roblpr ftap ftadiv ftaret, j(2)

    . roblpr ftap, power(0.7 0.75:0.9)

    . roblpr ftap, j(2)

    . roblpr D.ftap, j(2) l(1)

    . constraint define 1 ftap = ftadiv
    . roblpr ftap ftadiv ftaret, c(1)


Authors

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

    Vince Wiggins, StataCorp LP
    vwiggins@stata.com

References
Robinson, P.M. Log-Periodogram Regression of Time Series with Long Range
Dependence. Annals of Statistics 23:3, 1995, 1048-1072.
      

Also see

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