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help for ^lomodrs^                                                (STB-60: sts18)
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Lo Modified R/S test for long range dependence in timeseries
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    ^lomodrs^ varname  [^if^ exp] [^in^ range] [^,^ ^m^axlag^(^#^)^ ]


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

varname may contain time-series operators; see help @varlist@.


Description
-----------

^lomodrs^ performs Lo's (1991) modified rescaled range (R/S, "range over 
standard deviation") test for long range dependence of a time series. 
The classical R/S test, devised by Hurst (1951) and Mandelbrot (1972),
is shown to be excessively sensitive to "short-range dependence" (e.g.,
ARMA components). Lo's modified version of the statistic takes account
of short-range dependence by performing a Newey-West correction (using 
a Bartlett window) to derive a consistent estimate of the long-range 
variance of the timeseries.

Inference from the modified R/S test for long range dependence is
complementary to that derived from that of other tests for long memory, or
fractional integration in a timeseries, such as ^kpss^, ^gphudak^, ^modlpr^
and ^roblpr^.

The maximum lag order for the test is by default calculated from the sample
size and the first-order autocorrelation coefficient of the ^varname^ 
using the data-dependent rule of Andrews (1991), assuming that the dgp is
AR(1). The maximum lag order may be specified with the ^maxlag^ option.
If it is set to zero, the test performed is the classical Hurst-Mandelbrot 
rescaled-range statistic. 

Critical values for the test are taken from Lo, 1991, Table II.

The test statistic and number of observations are placed in the return array.


Options
-------

^maxlag(^#^)^ specifies the maximum lag order to be used in calculating the 
    test. If omitted, the maximum lag order is calculated as described above.


Examples
--------

	. ^use http://fmwww.bc.edu/ec-p/data/Mills2d/sp500a.dta^

	. ^lomodrs sp500ar^
	
	. ^lomodrs sp500ar, max(0)^
	
	. ^lomodrs sp500ar if tin(1946,)^


References
----------

Andrews, D. Heteroskedasticity and Autocorrelation Consistent Covariance
Matrix Estimation. Econometrica, 59, 1991, 817-858.

Hurst, H. Long Term Storage Capacity of Reservoirs. Transactions of the
American Society of Civil Engineers, 116, 1951, 770-799.

Lo, Andrew W. Long-Term Memory in Stock Market Prices. Econometrica,
59, 1991, 1279-1313.

Mandelbrot, B. Statistical Methodology for Non-Periodic Cycles: From the
Covariance to R/S Analysis. Annals of Economic and Social Measurement,
1, 1972, 259-290.

Authors
------

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

Tairi Room, Boston College, USA
room@@bc.edu


Also see
--------

On-line:  help for @time@, @tsset@, @kpss@ (if installed), 
          @gphudak@ (if installed), @modlpr@ (if installed), @roblpr@ (if installed)