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On the forecasting of multivariate financial time series using hybridization of DCC-GARCH model and multivariate ANNs

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Abstract

Volatility plays a crucial role in financial markets and accurate prediction of the stock price indices is of high interest. In multivariate time series, Dynamic Conditional Correlation (DCC)-Generalized Autoregressive Conditional Heteroscedastic (GARCH) is used to model and forecast the volatility (risk) and co-movement between stock prices data. We propose multivariate artificial neural networks (MANNs) hybridized with the DCC-GARCH model to forecast the volatility of stock prices and to examine the time-varying correlation. The daily share price data of five stock markets: S&P 500 (USA), FTSE-100 (UK), KSE-100 (Pakistan), Malaysia (KLSE) and BSESN (India) covering the period from 1st, January 2013 to 17th, March 2020 are considered for empirical analysis. Moreover, the hybrid models of MANNs and DCC-GARCH are developed in two ways: (i) MANNs is provided as an input to DCC-GARCH (1,1) producing a hybrid model of DCC-GARCH(1,1)-MANNs and (ii) DCC-GARCH(1,1) model is set as an input to MANNs resulting hybrid model of MANNs-DCC-GARCH(1,1). Furthermore, the performances of the proposed models are compared with single models via the root mean square (RMSE), mean absolute error (MAE) and relative mean absolute error (RMAE). The empirical results show that DCC-GARCH (1,1)-MANNs, a parametric model, outperforms both in-sample and out-sample forecasts and helps to examine the time-varying correlation and also provides volatility forecast as well, whereas the hybrid model MANNs-DCC-GARCH (1,1) provides forecast only. Therefore, the hybrid model of DCC-GARCH (1,1)-MANNs is found suitable as compared to MANNs-DCC-GARCH(1,1) to model and forecast the stock price indices under consideration.

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Authors and Affiliations

  1. Department of Statistics, University of Karachi, Karachi, Pakistan

    Samreen Fatima & Mudassir Uddin

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  1. Samreen Fatima
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  2. Mudassir Uddin
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Correspondence to Samreen Fatima.

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Appendix 1

Appendix 1

1.1 ADF test of stationarity

Null and alternative hypothesis:

H0

Series contains a unit root.

H1

Series is stationary (Table

Table 6 Output of ADF test for the log returns series of the BSESN, KSE-100, USA, FTSE-100 & KLSE
Full size table

6).

1.2 ARCH–LM test of heteroscedasticity

Null and alternative hypothesis:

H0

No ARCH effect is present (Heteroscedasticity is not present).

H1

ARCH effect is present (Heteroscedasticity is present) (Table

Table 7 Output of ARCH–LM test of the log returns series for the selected stock prices
Full size table

7).

1.3 AIC and BIC (Table 8)

Table 8 AIC and BIC
Full size table

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Fatima, S., Uddin, M. On the forecasting of multivariate financial time series using hybridization of DCC-GARCH model and multivariate ANNs. Neural Comput & Applic 34, 21911–21925 (2022). https://doi.org/10.1007/s00521-022-07631-5

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