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High Dimensional Nonstationary Time Series Modelling with Generalized Dynamic Semiparametric Factor Model

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  • Song Song
  • Wolfgang K. Härdle
  • Ya'acov Ritov

Abstract

(High dimensional) time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science. In this article, we separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant functions via functional factor analysis. We propose a two-step estimation procedure. At the first step, we detect the deterministic trends of the time series by incorporating time basis selected by the group Lasso-type technique and choose the space basis based on smoothed functional principal component analysis. We show properties of this estimator under various situations extending current variable selection studies. At the second step, we obtain the detrended low dimensional stochastic process, but it also poses an important question: is it justified, from an inferential point of view, to base further statistical inference on the estimated stochastic time series? We show that the difference of the inference based on the estimated time series and "true" unobserved time series is asymptotically negligible, which finally allows one to study the dynamics of the whole high-dimensional system with a low dimensional representation together with the deterministic trend. We apply the method to our motivating empirical problems: studies of the dynamic behavior of temperatures (further used for pricing weather derivatives), implied volatilities and risk patterns and correlated brain activities (neuro-economics related) using fMRI data, where a panel version model is also presented.

Suggested Citation

  • Song Song & Wolfgang K. Härdle & Ya'acov Ritov, 2010. "High Dimensional Nonstationary Time Series Modelling with Generalized Dynamic Semiparametric Factor Model," SFB 649 Discussion Papers SFB649DP2010-039, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2010-039
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2010-039.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Nicole Wiebach & Lutz Hildebrandt, 2010. "Context Effects as Customer Reaction on Delisting of Brands," SFB 649 Discussion Papers SFB649DP2010-056, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    4. Enno Mammen & Christoph Rothe & Melanie Schienle, 2010. "Nonparametric Regression with Nonparametrically Generated Covariates," SFB 649 Discussion Papers SFB649DP2010-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    6. Ralf Sabiwalsky, 2010. "Executive Compensation Regulation and the Dynamics of the Pay-Performance Sensitivity," SFB 649 Discussion Papers SFB649DP2010-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
    8. Franziska Schulze, 2010. "Spatial Dependencies in German Matching Functions," SFB 649 Discussion Papers SFB649DP2010-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Vladimir Panov, 2010. "Estimation of the signal subspace without estimation of the inverse covariance matrix," SFB 649 Discussion Papers SFB649DP2010-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Maria Grith & Volker Krätschmer, 2010. "Parametric estimation of risk neutral density functions," SFB 649 Discussion Papers SFB649DP2010-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Semiparametric model; Factor model; Group Lasso; Seasonality; Spectral Analysis; Periodic; Asymptotic inference; Weather; fMRI; Implied Volatility Surface;

    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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