A Data-Driven P-Spline Smoother and the P-Spline-Garch Models
33 Pages Posted: 27 Aug 2021
Date Written: October 19, 2020
Penalized spline smoothing of time series and its asymptotic properties are studied. A data-driven algorithm for selecting the smoothing parameter is developed. The proposal is applied to define a semiparametric extension of the well-known Spline-GARCH, called a P-Spline-GARCH, based on the log-data transformation of the squared returns. It is shown that now the errors 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 proposal is illustrated by data examples and simulation. The proposal is further applied to value at risk and expected shortfall.
Keywords: P-spline smoother, smoothing parameter selection, P-Spline-GARCH, strong mixing, value at risk, expected shortfall
JEL Classification: C14, C51
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