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help for ^hallt^
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Computes Hall's skewness adjusted t-statistic and generates bootstrapped confidence intervals
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Syntax
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^hallt^ ^varlist^ ^[if]^ ^[in]^ ^,^ ^bs^ ^reps(#)^ ^size(#)^ ^nowarn^ ^nohead^ ^saving^ ^(bs)^ ^replace^
Description
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^hallt^: This program implements a skewness adjusted bootstrapped t-statistic procedure.This is implemented in Eventus
software for event studies as the skewness adjusted transformed normal test (Cowan 2008).The skewness adjustment is based
on (Hall 1992) who proposed an alternative adjustment to account for skewness even 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 (used).
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
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sysuse auto
hallt mpg, bs reps(100) size(2) nowarn nohead saving (c:\bs) replace
Output from the program
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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 the following table is displayed
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| Observed Bootstrap Normal-based
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
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_bs_1 | 38.72841 7.316759 5.29 0.000 24.38782 53.06899
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Other confidence intervals can be displayed by giving the command below after the skewt command
Options for the bootstrap
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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.
Further details
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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
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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
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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
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STB: STB-26 sg40 - for the johnson ado
Manual: [5s] ttest
On-line: help for @ttest@, @skewt@.