Abstract
Volatility modeling is crucial for risk management and asset allocation; this is an influential area in financial econometrics. The central requirement of volatility modeling is to be able to forecast volatility accurately. The literature review of volatility modeling shows that the approaches of model averaging estimation are commonly used to reduce model uncertainty in order to achieve a satisfactory forecasting reliability. However, those approaches attempt to forecast more reliable volatilities by integrating all forecasting outcomes equally from several volatility models. Forecasting patterns generated by each model may be similar. This may cause redundant computation without improving forecasting reliability. The proposed multivariate volatility modeling method which is called the fuzzy-method-involving multivariate volatility model (abbreviated as FMVM) classifies the individual models into smaller scale clusters and selects the most representative model in each cluster. Hence, repetitive but unnecessary computational burden can be reduced, and forecasting patterns from representative models can be integrated. The proposed FMVM is benchmarked against existing multivariate volatility models on forecasting volatilities of Hong Kong Hang Seng Index constituent stocks. Numerical results show that it can obtain relatively lower forecasting errors with less model complexity.
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This work was supported by the PolyU grant G-YBCV.
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Appendix: A Model Classification Example of Low-Dimensional Cases
Appendix: A Model Classification Example of Low-Dimensional Cases
Assume that we have 4 assets and use one-day-ahead forecasting. The classification results are shown in Tables 4, 5, 6, 7, 8, 9, 10, 11 and 12. The first row in each table shows our benchmark. Other rows show different clustering results with the first model in each row/cluster being the representative model for this cluster; for instance, in Table 12, DCC(2, 2) and ADCC(2, 2) are grouped in cluster 6, and the DCC(2, 2) is the representative model.
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Wei, ZK., Yiu, KF.C., Wong, H. et al. A Novel Multivariate Volatility Modeling for Risk Management in Stock Markets. Int. J. Fuzzy Syst. 20, 116–127 (2018). https://doi.org/10.1007/s40815-017-0298-x
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DOI: https://doi.org/10.1007/s40815-017-0298-x