Correlation Coefficient

No unique method has been so far specified for determining the number of neurons in hidden layers of Multi-Layer Perceptron (MLP) neural networks used for prediction. The present research is intended to optimize the number of neurons using two meta-heuristic procedures namely genetic and hill climbing algorithms. The data used in the present research for prediction are consumption data of water subscribers in Fasa City of Fars Province (Iran) between the years 2010 to 2013. Ultimately, using the respective data set, the data of the subsequent year 2014 can be predicted. In the present research it was observed that the mean square errors of per data (MSEPD) for the abovementioned algorithms are less than 0.2, indicating a high performance in the neural networks’ prediction. Correlation coefficients using genetic and hill climbing algorithms were respectively equal to 0.891 and 0.759. Thus, GA was able to leave a better effect on optimization of neural network.

One of the main demands of investors (depositors and shareholders) of banks is transparency. However, in addition to the requirements for meeting this demand, measuring how to meet it has become challenging. So far, researchers have proposed different qualitative criteria for transparency. In this study, while introducing the correlation coefficient between book and market value at risk (VaRs) as a criterion of transparency, we seek to examine the stability of this criterion in different economic conditions. For this purpose, first, by using the e-garch model, the value at risk was estimated based on the balance sheet (book) information and also the market information of the banks' shares, then by calculating the correlation coefficients between book and market VaR’s under normal conditions, we predict book and market VaR’s using vector auto-regressive (VAR) models, along with defining three stress scenarios (Mild - Severe - hyper stress). We examined the significance of the difference between the calculated correlation coefficients in the three stress test modes. We thus tested the stability of the correlation coefficient of the defined scenarios. The findings showed that except for the correlation caused by the unemployment rate factor in mild and hyper-stress scenarios, in other cases, no evidence of H0 rejection was found, indicating the stability of the correlation coefficient between book and market VaRs as a measure of transparency.