Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 104, Issue 485, Pages 284-298Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/jasa.2009.0105
Keywords
Asymptotic inference; Factor models; Implied volatility surface; Semiparametric models; Vector autoregressive process
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Funding
- Deutsche Forschungsgemeinschaft
- Sonderforschungsbereich 649 Okonomisches Risiko.
- Korean Government (MOEHRD) [KRF-2005-070-C00021]
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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 high-dimensional problems occur frequently in many different fields of science. In this article we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modeling approach poses an important question: Is it justified, from an 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 to the analysis of functional magnetic resonance imaging (fMRI) data.
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