.- help for ^skewt^ .- Computes Johnson's skewness adjusted t-statistic and generates bootstrapped confidence 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-statistic procedure as in Lyon, Barber, and Tsai (1999). The skewness adjustment is based on Johnson (1978). 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 (used). 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) replace Output from the program ----------------------- The program displays the parameters (N, S, G and the sample Mean) calculated from 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 bootstrap. #=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 the 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 results, 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 Tests 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 Asymmetrical 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 On-line: help for @ttest@, @hallt@.