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6484
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Acknowledgment
We are grateful to Kit Baum for alerting us to this problem.
References
Cox, N. J. and J. B. Wernow. 2000. dm80: Changing numeric variables to string.Stata Technical Bulletin56: 8–12.
dm81Utility for time series data
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Christopher F. Baum, Boston College, baum@bc.edu
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ce Wiggins, Stata Corporation, vwiggins@stata.com
Abstract:A program entitledtsmktimis described which makes the creation of time variables more convenient.
Keywords:time series, calendar, time variables.
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117746
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Reprinted inStata Technical Bulletin Reprints, vol. 4, pp. 165–170.
Newson, R. 2000. snp15:somersd—Confidence limits for nonparametric statistics and their differences.Stata Technical Bulletin55: 47–55.
sts15Tests for stationarity of a time series
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Christopher F. Baum, Boston College, baum@bc.edu
Abs
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tract:Implements the Elliott–Rothenberg–Stock (1996)DFGLStest and the Kwiatkowski–Phillips–Schmidt–Shin (1992)
KPSStests for stationarity of a time series. TheDFGLStest is an improved version of the augmented Dickey–Fuller test.
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128194
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H. 1994. Unit roots, structural breaks and trends. InHandbook of Econometrics IV, ed. R. F. Engle and D. L. McFadden. Amsterdam:
Elsevier.
sts16Tests for long memory in a time series
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Christopher F. Baum, Boston College, baum@bc.edu
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ce Wiggins, Stata Corporation, vwiggins@stata.com
Abstract:Implements the Geweke/PorterHudak log periodogram estimator (1983), the Phillips modified log periodogram
estimator (1999b) and the Robinson log periodogram estimator (1995) for the diagnosis of long memory, or fractional
integration, in a time series.
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133068
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The stochastic processytis both stationary and invertible if all roots of\b(L)and(L)lie outside the unit circle andjdj<0.5.
The process is nonstationary ford0.5, as it possesses infinite variance; for example, see Granger and Joyeux (1980).
Assuming thatd2[0;0:5),
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Hosking (1981)
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showed that the autocorrelation function,(),ofanARFIMAprocess is
proportional tok2d1ask!1. Consequently, the autocorrelations of theARFIMAprocess decay hyperbolically to zero as
k!1in contrast to the faster, geometric decay of a stationaryARMAprocess.
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134474
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Thus, it may be predictable at long
horizons. Long memory models originated in hydrology and have been widely applied in economics and finance. An excellent
survey of long memory models is given by
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Baillie (1996)
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There are two approaches to the estimation of anARFIMA(p;d;q)model: exact maximum likelihood estimation, as
proposed by Sowell (1992), and semiparametric approaches, as described in this insert.
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An excellent
survey of long memory models is given by Baillie (1996).
There are two approaches to the estimation of anARFIMA(p;d;q)model: exact maximum likelihood estimation, as
proposed by
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Sowell (1992)
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and semiparametric approaches, as described in this insert. Sowell’s approach requires specification
of thepandqvalues, and estimation of the fullARFIMAmodel conditional on those choices. This involves all the attendant
difficulties of choosing an appropriateARMAspecification, as well as a formidable computational task for each combination of
pandqto be evaluated.
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137569
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The statistic based upon that
standard error has a standard normal distribution under the null.
modlprcomputes a modified form of theGPHestimate of the long memory parameter,d, of a time series, proposed by
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Phillips (1999a, 1999b)
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b). Phillips (1999a) points out that the prior literature on this semiparametric approach does not address
the case ofd=1, or a unit root, in (3), despite the broad interest in determining whether a series exhibits unitroot behavior or
long memory behavior, and his work showing that thebdestimate of (5) is inconsistent whend>1;withbdexhibiting asymptotic
bias toward unity.
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137597
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The statistic based upon that
standard error has a standard normal distribution under the null.
modlprcomputes a modified form of theGPHestimate of the long memory parameter,d, of a time series, proposed by
Phillips (1999a, 1999b).
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Phillips (1999a)
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points out that the prior literature on this semiparametric approach does not address
the case ofd=1, or a unit root, in (3), despite the broad interest in determining whether a series exhibits unitroot behavior or
long memory behavior, and his work showing that thebdestimate of (5) is inconsistent whend>1;withbdexhibiting asymptotic
bias toward unity.
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139656
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proves that, with appropriate assumptions on the distribution oft;the distribution of~dfollows
p
m
d~d
!N
0;
2
24
(7)
in distribution, so~dhas the same limiting distribution atd=1 as does theGPHestimator in the stationary case so~dis consistent
for values ofdaround unity. A semiparametric test statistic for a unit root against a fractional alternative is then based upon the
statistic
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(Phillips 1999a, 10)
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zd=
p
m
d~1
=24
(8)
with critical values from the standard normal distribution. This test is consistent against bothd<1andd>1fractional
alternatives.
roblprcomputes the Robinson (1995) multivariate semiparametric estimate of the long memory (fractional integration)
parameters,d(g),ofasetofGtime series,y(g),g=1;GwithG1.
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A semiparametric test statistic for a unit root against a fractional alternative is then based upon the
statistic (Phillips 1999a, 10)
zd=
p
m
d~1
=24
(8)
with critical values from the standard normal distribution. This test is consistent against bothd<1andd>1fractional
alternatives.
roblprcomputes the
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Robinson (1995)
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multivariate semiparametric estimate of the long memory (fractional integration)
parameters,d(g),ofasetofGtime series,y(g),g=1;GwithG1. When applied to a set of time series, thed(g)parameter
for each series is estimated from a single logperiodogram regression which allows the intercept and slope to differ for each
series.
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The estimator also allows for the removal of one or more initial ordinates and for the averaging of the periodogram
over adjacent frequencies. The rationale for using nondefault values of either of these options is presented in
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Robinson (1995)
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Robinson (1995) proposes an alternative logperiodogram regression estimator which he claims provides “modestly superior
asymptotic efficiency tod(0)”, (d(0)being the Geweke and PorterHudak estimator) Robinson (1995, 1052).
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140740
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The estimator also allows for the removal of one or more initial ordinates and for the averaging of the periodogram
over adjacent frequencies. The rationale for using nondefault values of either of these options is presented in Robinson (1995).
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Robinson (1995)
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proposes an alternative logperiodogram regression estimator which he claims provides “modestly superior
asymptotic efficiency tod(0)”, (d(0)being the Geweke and PorterHudak estimator) Robinson (1995, 1052).
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140952
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Robinson (1995) proposes an alternative logperiodogram regression estimator which he claims provides “modestly superior
asymptotic efficiency tod(0)”, (d(0)being the Geweke and PorterHudak estimator)
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Robinson (1995, 1052)
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. Robinson’s
formulation of the logperiodogram regression also allows for the formulation of a multivariate model, providing justification for
tests that different time series share a common differencing parameter.
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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. Modifications to this derivation when the frequencyaveraging (j) or omission of initial frequencies (l) options are
selected may be found in
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Robinson (1995)
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Examples
Data from Terence Mills’Econometric Analysis of Financial Time SeriesonUK FTAAll Share stock returns (ftaret)and
dividends (ftadiv) are analyzed.
.usehttp://fmwww.bc.edu/ecp/data/Mills2d/fta.dta
.tsset
timevariable:month,1965m1to1995m12
.gphudakftaret,power(0.50.60.7)
GPHestimateoffractionaldifferencingparameter

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