Local polynomial and neural network estimators for the analysis of financial data

We analyze the problem of estimating nonparametrically the volatility function of a financial time series. For such estimator, we consider two different nonparametric tools: the Local polynomial estimator and the Neural Network estimator. The two nonparametric methods are compared by means of a simulation study. In the framework analyzed, it is evident that the Local Polynomial procedure outperforms the Neural Network procedure for the estimation of the unknown function, provided that the bandwidth parameter of the kernel estimator is chosen correctly.