Soft Computing

, Volume 22, Issue 16, pp 5279–5297 | Cite as

Value-at-risk forecasts by dynamic spatial panel GJR-GARCH model for international stock indices portfolio

  • Wei-Guo Zhang
  • Guo-Li MoEmail author
  • Fang Liu
  • Yong-Jun Liu


To provide accurate value-at-risk (VaR) forecasts for the returns of international stock indices portfolio, this paper proposes a dynamic spatial panel with generalized autoregressive conditional heteroscedastic model (DSP-GJR-GARCH). The proposed model considers the spatiotemporal dependence as well as asymmetric volatility of returns, with the theories of spatial econometrics. We construct an economic spatial weight matrix and set part of the initial estimated values as unknown parameters to get more acute of parameter estimations. After that, we compare the proposed model with three closely related models including GARCH, spatiotemporal-AR, dynamic spatial panel GARCH models, with respect to the performances of daily volatility and VaR forecasting. The empirically comparative data involve six composite indices of major countries, namely USA (DJI), German (DAX), France (FCHI), U.K. (ISEQ), Japan (N225) and China (SSE). The comparative computational results show that, since the proposed model considers spatial dependence and time series correlation simultaneously, it could get more accurate prediction of VaR than the three ones. Moreover, the findings reveal that the predictive accuracy of a spatial regressive model can be improved by considering asymmetric volatility in the disturbances. Thus, we can conclude that DSP-GJR-GARCH model performs better than the other three compared models.


Value at risk Stock index Spatial panel model GARCH 



The paper is supported by the National Natural Science Foundation of China (Nos. 71720107002, 71571054 and 71501076), Guangdong Natural Science Foundation (No. 2017A030312001) and Guangzhou financial service innovation and risk management research base, as well as 2017 Guangxi high school innovation team and outstanding scholars plan (T3110097911).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Business AdministrationSouth China University of TechnologyGuangzhouChina
  2. 2.School of Mathematics and Information ScienceGuangxi UniversityNanningChina

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