Year: 2025
Type: article
Abstract: Penalized spline smoothing of time series with a truncated polynomial basis are studied. Some existing asymptotic results obtained under i.i.d. errors are adjusted to the current context. An approximation of the optimal smoothing parameter is obtained and justified theoretically. An iterative plug-in algorithm for selecting the smoothing parameter is developed based on this result. Practical relevance of this algorithm is confirmed by a simulation. Subsequently, a penalized extension of the Spline-GARCH, called a P-Spline-GARCH, is defined based on the log-transformation of the squared returns. It is shown that now the error process is exponentially strong mixing with finite moments of all orders. Asymptotic normality of the P-Spline smoother in this context is proved. Practical relevance of the P-Spline-GARCH is confirmed by a simulation and illustrated by data examples with application to value at risk and expected shortfall.
Authors: Yuanhua Feng, Wolfgang Karl Härdle
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: hybrid
OpenAlex ID: W4287637535