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Time Series Modelling with Semiparametric Factor Dynamics

Author

Listed:
  • Szymon Borak
  • Wolfgang Härdle
  • 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.

Suggested Citation

  • Szymon Borak & Wolfgang Härdle & Enno Mammen & Byeong U. Park, 2007. "Time Series Modelling with Semiparametric Factor Dynamics," SFB 649 Discussion Papers SFB649DP2007-023, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2007-023
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    References listed on IDEAS

    as
    1. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
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    More about this item

    Keywords

    semiparametric models; factor models; implied volatility surface; vector autoregressive process; asymptotic inference.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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