Narrow Results

In this paper, we construct a nonlinear wavelet estimator of conditional density function for a left truncation model. We provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. It is assumed that the lifetime observations form a stationary α-mixing sequence. Unlike for kernel estimator, the MISE expression of the nonlinear wavelet estimator is not affected by the presence of discontinuities in the curves.

This paper adopts a new approach to estimating the conditional probability distribution of asset returns. It is evident that the exact conditional mean or variance is inherently unobservable for time series. In practice, the popular way is to derive from different models such as GARCH by assuming distributions such as normal, student t, or skewed t. Thus the accuracy of forecast strongly depends on the assumption of distribution. The new method avoids the need to assume any distribution by using a neural network (NN) to estimate the potentially nonlinear relationship between VaR (Value at Risk) and returns. Our results show that the forecast from neural network outperforms traditional GARCH models.