[R-SIG-Finance] Skewness function for intraday data return distribution

[Patrick Burns]

The skewness of c * X should be equal to
the skewness of X.  If I'm reading the
formulas correctly, that is true of the
second one but not the first.

It would be interesting to hear if you find
different results intraday than I did with
daily data over a year:

http://www.portfolioprobe.com/2011/10/03/predictability-of-kurtosis-and-skewness-in-sp-constituents/

On 31/10/2011 05:18, Roupell, Darko wrote:
> Hi All,
>
> I have written a skew function to calculate stock skewness using intraday 5 min data. However, going through literature I have come across two very similar formulas, though they produce different skewness coefficient and wonder if anyone else has used similar formulas and know which one is the correct one.
>
> mq_skewness = function(data){
> data = dataformatc(data);
>    #returns midquote log returns as xts object
>    mq_ret = mq_return(data);
>    #returns midquote log returns as xts object
>    mq_ret_sqr = mq_ret^2;
>    #returns realized daily volatility as xts object
>    RVar=sum(  mq_ret_sqr)
>    n = length(mq_ret);
>
>    #first formula to measure skewness
>    mq_skewness = sqrt(n) * (sum(mq_ret^3))/sum(mq_ret_sqr)^(2/3)
>
>   # second formula to measure skewness
>    mq_skewness = sqrt(n) * sum((mq_ret/sqrt(RVar))^3)
>
>    return(mq_skewness);
> }
>
>    #first formula to measure skewness
>    mq_skewness = sqrt(n) * (sum(mq_ret^3))/sum(mq_ret_sqr)^(2/3)
> [1] 0.0003991095
>    # second formula to measure skewness
>    mq_skewness = sqrt(n) * sum((mq_ret/sqrt(RVar))^3)
> [1] 0.09759751
> # this is output from base package function but this may not be appropriate to use for intraday data
> skewness(mq_ret)
> [1] 0.3035787
> __________________________________________________
> Darko Roupell
>
>
>
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-- 
Patrick Burns
patrick at burns-stat.com
http://www.burns-stat.com
http://www.portfolioprobe.com/blog
twitter: @portfolioprobe