Empirical Economics

, Volume 50, Issue 3, pp 1091–1109 | Cite as

Spatial dependence in stock returns: local normalization and VaR forecasts

  • Thilo A. Schmitt
  • Rudi Schäfer
  • Dominik Wied
  • Thomas Guhr


We analyze a recently proposed spatial autoregressive model for stock returns and compare it to a one-factor model and the sample covariance matrix. The influence of refinements to these covariance estimation methods is studied. We employ power mapping and the shrinkage estimator as noise reduction techniques for the correlations. Further, we address the empirically observed time-varying trends and volatilities of stock returns. Local normalization strips the time series of changing trends and fluctuating volatilities. As an alternative method, we consider a GARCH fit. In the context of portfolio optimization, we find that the spatial model and the shrinkage estimator have the best match between the estimated and realized risk measures.


GARCH One-factor model Power mapping Spatial autoregressive model 



This work was supported by Deutsche Forschungsgemeinschaft [SFB 823, project A1].


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Thilo A. Schmitt
    • 1
  • Rudi Schäfer
    • 1
  • Dominik Wied
    • 2
  • Thomas Guhr
    • 1
  1. 1.Fakultät für PhysikUniversität Duisburg-EssenDuisburgGermany
  2. 2.Fakultät StatistikDortmundGermany

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