Dual Sides Sign Preserving Power Transformation

It is well known that "non normality is normal".In the field of practical application,it is rarely encountered that the data involved strictly obey the normal distribution.Therefore,looking for the transformation of data normality into a classic problem in the field of statistical research has been concerned by both theoretical circles and practical users,and many research results have emerged.All kinds of transformation methods have achieved certain success in some specific data sets,but as shown in the article,these methods are not satisfactory for extremely unbalanced data sets(the thickness of left and right tail is quite different).Therefore,we will propose a dual sign preserving power transformation method,which provides transformation parameters independently for positive and negative data.In the aspect of determining transformation parameters,this paper proposes an estimation method of transformation parameters based on minimizing Jarque-Bera statistics.The experimental results show that the method based on the minimization of Jarque-Bera statistics can accurately and effectively estimate the optimal transformation parameters.Thirdly,this paper uses simulated data and California electricity price yield data to test the normality after dual sign preserving power transformation,dual power transformation,Box-Cox transformation and Yeo-Johnson transformation,and makes its Q-Q diagram.The experimental results show that: the kurtosis and jbstat value of the electricity price yield data after Box-Cox transformation and Yeo-Johnson transformation are still very high,so the transformed data still does not obey the normal distribution;However,the Q-Q chart and the normality test statistics of the electricity price yield data after the dual sign preserving power transformation show that the data obey the normal distribution,and the dual power transformation does not improve the normality of the data.Finally,the ARIMA model is established by using the untransformed data,as well as the return data processed by dual sign preserving power transformation,dual power transformation,Box-Cox transformation and Yeo-Johnson transformation.The experimental results show that: the best fitting effect is ANN model,the fitting effect of Yeo Johnson transform ARIMA model and dual sign preserving power transform ARIMA model is similar,the effect is second only to ANN model,and the BIC value of bilateral sign preserving power transform ARIMA model is the smallest.The best prediction effect is the dual sign preserving power transformation ARIMA model,which is better than the ANN model.Therefore,the dual sign preserving power transform proposed in this paper can effectively enhance the normality of extremely skewed and negative data,and the effect is better than Box-Cox transform and Yeo-Johnson transform.Applying the data processed by this method to ARIMA model can effectively increase the fitting ability and prediction accuracy of the model.