{smcl}
{* 26jun2006}{...}
{hline}
help for {cmd:lomodrs}{right:(SJ6-3: sts_1; STB-60: sts18)}
{hline}

{title:Lo modified R/S test for long range dependence in time series}

{p 8 17 2}
{cmd:lomodrs}
{varname}
{ifin}
[{cmd:,} {opt maxlag(#)}]

{phang}
{cmd:lomodrs} is for use with time-series data.  {varname} may contain
time-series operators.  You must {helpb tsset} your data before using
{cmd:lomodrs}.

{phang}
{cmd:lomodrs} supports the {helpb 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.


{title:Description}

{pstd}{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 time series.

{pstd}
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 time series, such as {cmd:kpss}, {cmd:gphudak},
{cmd:modlpr}, and {cmd:roblpr}.

{pstd}
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 {cmd:maxlag()} option. If it is
set to zero, the test performed is the classical Hurst-Mandelbrot
rescaled-range statistic.

{pstd}
Critical values for the test are taken from Lo (1991, table II).

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


{title:Option}

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


{title:Examples}

{phang}{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}

{phang}{stata "lomodrs sp500ar":. lomodrs sp500ar}{p_end}

{phang}{stata "lomodrs sp500ar, max(0)":. lomodrs sp500ar, max(0)}{p_end}

{phang}{stata "lomodrs sp500ar if tin(1946,)":. lomodrs sp500ar if tin(1946,)}{p_end}


{title:Authors}

{pstd}
Christopher F. Baum, Boston College, USA{break}
baum@bc.edu

{pstd}Tairi Room, Boston College, USA{break}


{title:References}

{phang}Andrews, D. 1991. Heteroskedasticity and autocorrelation consistent
covariance matrix estimation. {it:Econometrica} 59: 817-858.

{phang}Hurst, H. 1951. Long term storage capacity of reservoirs.
{it:Transactions of the American Society of Civil Engineers} 116: 770-799.

{phang}Lo, A. W. 1991. Long-term memory in stock market prices.
{it:Econometrica} 59: 1279-1313.

{phang}Mandelbrot, B. 1972. Statistical methodology for non-periodic cycles:
From the covariance to R/S analysis. 
{it:Annals of Economic and Social Measurement} 1: 259-290.


{title:Also see}
{psee}Online: {helpb regress}, {help time}, {helpb tsset}, {helpb ac},
{helpb corrgram}; {helpb gphudak} (if installed), {helpb modlpr} (if
installed), {helpb kpss} (if installed){p_end}