A Data-Driven P-Spline Smoother and the P-Spline-Garch Models

33 Pages Posted: 27 Aug 2021

See all articles by Wolfgang K. Härdle

Wolfgang K. Härdle

Blockchain Research Center; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; National Yang Ming Chiao Tung University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Yuanhua Feng

University of Paderborn

Date Written: October 19, 2020

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 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

Suggested Citation

Härdle, Wolfgang K. and Feng, Yuanhua, A Data-Driven P-Spline Smoother and the P-Spline-Garch Models (October 19, 2020). Available at SSRN: https://ssrn.com/abstract=3714616 or http://dx.doi.org/10.2139/ssrn.3714616

Wolfgang K. Härdle

Blockchain Research Center ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Yuanhua Feng (Contact Author)

University of Paderborn ( email )

Warburger Str. 100
Paderborn, D-33098
Germany

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