Improved parameter estimation of Time Dependent Kernel Density by using Artificial Neural Networks

Abstract

Time Dependent Kernel Density Estimation (TDKDE) used in modelling time-varying phenomenon requires two input parameters known as bandwidth and discount to perform. A Maximum Likelihood Estimation (MLE) procedure is commonly used to estimate these parameters in a set of data but this method has a weakness; it may not produce stable kernel estimates. In this article, a novel estimation procedure is developed using Artificial Neural Networks which eliminates this inherent issue. Moreover, evaluating the performance of the kernel estimation in terms of the uniformity of Probability Integral Transform (PIT) shows a significant improvement using the proposed method. A real-life application of TDKDE parameter estimation on NASDQ stock returns validates the flawless performance of the new technique. Keywords: Time Dependent Kernel Density Estimation, Artificial Neural Networks, Probability Integral Transform, Finance, Machine learning, 2010 MSC: 62G07, 62M45, 91G50