Do the time series statistical properties influence the goodness of fit of GRNN models? Study on financial series

Recent researches on Generalized Regression Neural Networks show that this technique could be a promising option for modeling nonlinear time series, in general, and for financial series, in particular. Different types of artificial neural networks have been extensively studied, but the relationship between the statistical properties of the input data series and the models' accuracy was not emphasized. Therefore, our aim is to provide such an analysis. We study the Bucharest Exchange Trading series registered during the period from October 2000 to September 2014. Firstly, we test the series randomness, the existence of an increasing or nonlinear trend, its stationarity around a deterministic trend, and the breakpoints existence. Then, using the series decomposition, we define the detrended series and the deseasonalized series. Secondly, we build Generalized Regression Neural Network models for the original series, the subseries detected after the segmentation, the detrended, and deseasonalized ones. Comparing the modeling results, we conclude that some “regularity” properties (as normality and homoskedasticity) do not influence the models' quality (as expected).