Second-Moment/Order Approximations by Kernel Smoothers with Application to Volatility Estimation

León Beleña (), Ernesto Curbelo, Luca Martino and Valero Laparra
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León Beleña: Department of Signal Processing, Universidad Rey Juan Carlos, 28942 Fuenlabrada, Spain
Ernesto Curbelo: Department of Statistics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
Luca Martino: Department of Signal Processing, Universidad Rey Juan Carlos, 28942 Fuenlabrada, Spain
Valero Laparra: Image Processing Lab, Universitat de Valencia, 46980 Paterna, Spain

Mathematics, 2024, vol. 12, issue 9, 1-15

Abstract: Volatility estimation and quantile regression are relevant active research areas in statistics, machine learning and econometrics. In this work, we propose two procedures to estimate the local variances in generic regression problems by using kernel smoothers. The proposed schemes can be applied in multidimensional scenarios (not just for time series analysis) and easily in a multi-output framework as well. Moreover, they enable the possibility of providing uncertainty estimation using a generic kernel smoother technique. Several numerical experiments show the benefits of the proposed methods, even compared with the benchmark techniques. One of these experiments involves a real dataset analysis.

Keywords: quantile regression; kernel smoothers; times series; heteroscedasticity; nearest neighbors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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