| By: |
Szymon Borak;
Wolfgang HÃÂärdle;
Enno Mammen;
Byeong U. Park |
| 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. |
| JEL: |
C14 C32 G12 |
| Date: |
2007–04 |
| URL: |
http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2007-023&r=ict |