Time series modelling with semiparametric factor dynamics

Szymon Borak, Wolfgang Härdle, Enno Mammen and Byeong U. Park

No 2007-023, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: High-dimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the low-dimensional time series analysis. Such highdimensional problems occur frequently in many different fields of science. In this paper we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modelling approach poses an important question: Is it justified, from inferential point of view, to base statistical inference on the estimated times series factors? We show that the difference of the inference based on the estimated time series and 'true' unobserved time series is asymptotically negligible. Our results justify fitting vector autoregressive processes to the estimated factors, which allows one to study the dynamics of the whole high-dimensional system with a low-dimensional representation. We illustrate the theory with a simulation study. Also, we apply the method to a study of the dynamic behavior of implied volatilities and discuss other possible applications in finance and economics.

Keywords: semiparametric models; factor models; implied volatility surface; vector autoregressive process; asymptotic inference (search for similar items in EconPapers)
JEL-codes: C14 C32 G12 (search for similar items in EconPapers)
Date: 2007
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Journal Article: Time Series Modelling With Semiparametric Factor Dynamics (2009)
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