The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent "respectively safe" investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd -- 6'th cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was examined for daily shares' returns of companies traded on the Warsaw Stock Exchange.  It was shown that the algorithm gives the investment portfolios that are on average better than portfolios achieved by other methods, as well as than the proposed benchmark . Remark that the algorithm of is based on cumulant tensors up to the 6'th order  , what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.
The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd -- 6'th cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent . Remark that the algorithm of is based on cumulant tensors up to the 6'th order calculated for a multidimensional random variable , what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.
D
"respectively safe"
R
examined for daily shares' returns of companies traded
tested during the recent crash
A
To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA.
R
the algorithm gives the investment portfolios that are
introduced algorithm is
R
than portfolios achieved by other methods, as well as than the proposed benchmark
that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent
A
calculated for a multidimensional random variable