A data-driven P-spline smoother and the P-Spline-GARCH models

Yuanhua Feng and Wolfgang Härdle

No 2020-016, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: 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 de ne 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 nite 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 (search for similar items in EconPapers)
JEL-codes: C14 C51 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-ore and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:irtgdp:2020016

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