Further Development of the Double Conditional Smoothing for Nonparametric Surfaces Under a Lattice Spatial Model

• Activity Number: 290 - Big Data in Time Series and Spatial Data Analysis: Theory and Applications
• Type: Topic Contributed
• Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Royal Statistical Society
• Author(s): Yuanhua Feng* and Bastian Schäfer
• Companies: and Paderborn University
• Keywords: Spatial model; high-frequency financial data; double conditional smoothing; functional smoothing; bandwith selection

Abstract

Nonparametric estimation of high-frequency financial data under a lattice spatial model has high demand on computation, due to the huge size of the data and the bivariate nature of the estimators. The double conditional smoothing offers a way to reduce complexity of estimation. In this paper, we first extend the double conditional smoothing by using boundary kernels and propose a much quicker functional smoothing scheme. Then we obtain the asymptotic formulas for the bias and variance, as well as the optimal bandwidths of this estimator under independent errors. An iterative plug-in algorithm for selecting the optimal bandwidths by double conditional smoothing is developed. Both, the Nadaraya-Watson estimator and local linear approaches are considered. The performance of the proposals is compared to the traditional bivariate kernel smoothing through a simulation study and further confirmed by application to financial data.