Computes Johnson's skewness adjusted t-statistic and generates bootstrapped con > fidence intervals ------------------------------------------------------------------------------- > ---------------------
Syntax ------
^skewt^ ^varlist^ ^[if]^ ^[in]^ ^,^ ^bs^ ^seed(#)^ ^reps(#)^ ^size(#)^ ^nowarn^ > ^nohead^ ^saving^ ^(bs)^ ^replace^
Description -----------
^skewtt^: This program implements the skewness adjusted bootstrapped t-statisti > c procedure as in Lyon, Barber, and Tsai (1999). The skewness adjustment is based on Johnson (197 > 8). The program requires that the user has a data file which contains the appropriate abnormal > return stored as a variable. The skewt command is issued after this data file has been opened (use > d).
The skewness adjusted t statistic is given by the following formula.
N*(s + (1/3*G*(S-squared)) +((1/(6*(N-squared)))*G ))
where G is skewness S is the standard deviation N is the square root of the number of observations
Example usage --------------
sysuse auto
skewt mpg, bs reps(1000) size(2) seed(1234) nowarn nohead saving (c:\bs) replac > e
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 procedure 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 ------------------------------------------------------------------------------
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.
Futher 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 ------------
Lyon, John D., Brad M. Barber, and Chih-Ling Tsai. 1999. Improved Methods for T > ests of Long-Run Abnormal Stock Returns. The Journal of Finance 54, no. 1:165-201.
Johnson, Norman J. 1978. Modified t Tests and Confidence Intervals for Asymmetr > ical Populations. Journal of the American Statistical Association 73, no. 363:536-544.
Author ------ Rajesh Tharyan Xfi-Centre for Finance and Investment University of Exeter 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