Computes Hall's skewness adjusted t-statistic and generates bootstrapped confid > ence intervals ------------------------------------------------------------------------------- > ---------------
Syntax ------
^hallt^ ^varlist^ ^[if]^ ^[in]^ ^,^ ^bs^ ^reps(#)^ ^size(#)^ ^nowarn^ ^nohead^ > ^saving^ ^(bs)^ ^replace^
Description -----------
^hallt^: This program implements a skewness adjusted bootstrapped t-statistic p > rocedure.This is implemented in Eventus software for event studies as the skewness adjusted transformed normal test (Co > wan 2008).The skewness adjustment is based on (Hall 1992) who proposed an alternative adjustment to account for skewness e > ven when there is large skewness and sample size is small.The program requires that the user has a data file which contains > the appropriate abnormal returns stored as a variable.The hallt command is issued after this data file has been opened (us > ed).
The Skewness adjusted transformed t-statistic is given by the following formula > .
N * (s + (1/3*G*(S-squared)) +((1/(6*N-squared))*G ) + ((1/27)*(G-squared)* (S- > cubed)))
wher G is skewness S is the standard deviation N is the square root of the number of observations
Example usage -------------
sysuse auto
hallt mpg, bs reps(100) size(2) nowarn nohead saving (c:\bs) replace
Output from the program ------------------------- The program displays the parameters (N, S, G and the sample Mean) calculated fr > om the sample that feed into the formula to compute the skewness adjusted t statistic
The program displays the following parameters for the example usage above.
N coefficient = 8.602325267042627 S-coefficient = 2.09027474443816 G-coefficient = 1.653433511704859 Sample mean = 6165.256756756757
after the bootstrap the following table is displayed
------------------------------------------------------------------------------ | Observed Bootstrap Normal-based | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- _bs_1 | 38.72841 7.316759 5.29 0.000 24.38782 53.06899 ------------------------------------------------------------------------------
Other confidence intervals can be displayed by giving the command below after t > he skewt command
Options for the bootstrap -------------------------
reps (#): This determines the number of replications
size(#) : This determines what proportion of the sample is used for the bootstr > ap. #=1 implies all the data is used. #=2 implies half of the data is used.
saving () : This is used to save the bootstrapped values. For example, saving ( > C:\bs) will save the results in c:\ . The file name will be the name of the varibale selected for th > e test, prefixed with bs_.
replace: the option replace replaces the file in which the bootstrapped values > are stored.
Further details ---------------
Further details and cutoffs for other significance levels can be calcuated from > the saved file. To do that, First open the file containing the saved bootstrap resu > lts, for example,
use "c:\bs_mpg.dta",clear
then issue the following commands
* To inspect the bootstrapped distribution
estat bootstrap, all tabstat _bs*,s(mean median p5 p25 p75 p95 p99 max min) histogram _bs_1,normal
* To retreive the percentile condifence intervals
_pctile _bs_1, p(.5, 2.5, 5, 95, 97.5, 99.5) return li
References ----------
Hall, Peter. 1992. On the Removal of Skewness by Transformation. Journal of the > Royal Statistical Society. Series B (Methodological) 54, no. 1:221-228.
Cowan, Arnold R. Eventus 8.0 User’s Guide, Standard Edition 2.1.(Cowan Research > LC, Ames, Iowa, 2007.), p31, p87.
Author ------ Rajesh Tharyan University of Exeter Centre for Finance and Investment www.ex.ac.uk\xfi r.tharyan@ex.ac.uk
Scott Merryman scott.merryman@gmail.com
Also see --------
STB: STB-26 sg40 - for the johnson ado Manual: [5s] ttest