{smcl}
{* 26jun2006}{...}
{hline}
help for {hi:lomodrs}                 (SSC distribution 26 Jun 2006)
{hline}


{title:Lo Modified R/S test for long range dependence in timeseries}

{p 8 17}{cmd:lomodrs}
{it:varname}
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}] 
[{cmd:,} {cmdab:maxlag(}{it:#}{cmd:)}]

{p 4 4}{cmd:lomodrs} is for use with time-series data. 
You must {cmd:tsset} your data before using {cmd:lomodrs}; see help {cmd:tsset}. 
{cmd:lomodrs} supports the {cmd:by} prefix, which may be used to operate on each 
time series in a panel. Alternatively, the {cmd:if} qualifier may be used to specify 
a single time series in a panel.

{p 4 4}
{it:varname} may contain time-series operators; {cmd:help varlist}.{p_end}

{title:Description}

{p 4 4}{cmd: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.{p_end}

{p 4 4}
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 {cmd:kpss}, {cmd:gphudak}, 
{cmd:modlpr} and {cmd:roblpr}. {p_end}

{p 4 4}
The maximum lag order for the test is by default calculated from the sample
size and the first-order autocorrelation coefficient of the {it: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 {it:maxlag} option.
If it is set to zero, the test performed is the classical Hurst-Mandelbrot 
rescaled-range statistic. 
{p_end}

{p 4 4}
Critical values for the test are taken from Lo, 1991, Table II.
{p_end}

{p 4 4}
The test statistic and number of observations are placed in the return array.
{p_end}

{title:Options}

{p 4 4}
{cmdab:maxlag(}{it:#}{cmd:)} specifies the maximum lag order to be used in calculating the 
test. If omitted, the maximum lag order is calculated as described above.
{p_end}

{title:Examples}


{p 4 8}{stata "use http://fmwww.bc.edu/ec-p/data/Mills2d/sp500a.dta":. use http://fmwww.bc.edu/ec-p/data/Mills2d/sp500a.dta}{p_end}

{p 4 8}{stata "lomodrs sp500ar":. lomodrs sp500ar}{p_end}
	
{p 4 8}{stata "lomodrs sp500ar, max(0)":. lomodrs sp500ar, max(0)}{p_end}
	
{p 4 8}{stata "lomodrs sp500ar if tin(1946,)":. lomodrs sp500ar if tin(1946,)}{p_end}

{title:Authors}

{p 4 4}Christopher F. Baum, Boston College, USA{break} 
       baum@bc.edu
       
{p 4 4}Tairi Room, Boston College, USA{break} 

{title:References}

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

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

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

{p}
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.{p_end}


{title:Also see}

{p 4 13}On-line: {help regress}, {help time}, {help tsset}, {help ac}, 
{help corrgram}; {help gphudak} (if installed), {help modlpr} (if installed),
{help kpss} (if installed)
{p_end}
