Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/25195
Authors: 
Borak, Szymon
Härdle, Wolfgang Karl
Mammen, Enno
Park, Byeong U.
Year of Publication: 
2007
Series/Report no.: 
SFB 649 discussion paper 2007,023
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.
Subjects: 
semiparametric models
factor models
implied volatility surface
vector autoregressive process
asymptotic inference
JEL: 
C14
C32
G12
Document Type: 
Working Paper

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