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Time Series Modelling With Semiparametric Factor Dynamics

Byeong U. Park, Enno Mammen, Wolfgang Härdle and Szymon Borak
Journal of the American Statistical Association
Vol. 104, No. 485 (March 2009), pp. 284-298
Stable URL: http://www.jstor.org/stable/40591918
Page Count: 15
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Time Series Modelling With Semiparametric Factor Dynamics
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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 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 lowdimensional 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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