2020/10/19 by Yuanhua Feng, Wolfgang Karl Härdle, Feng, Yuanhua +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Forecasting Techniques and Applications #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2010.09376
openalex publication_date 2020/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.