@article{10.11648/j.ijdsa.20251104.11,
  author = {Charles Chege and Martin Kithinji and Peter Gachoki},
  title = {A Hybrid VAR-LSTM-GARCH Model for Multivariate Volatility Forecasting
},
  journal = {International Journal of Data Science and Analysis},
  volume = {11},
  number = {4},
  pages = {99-113},
  doi = {10.11648/j.ijdsa.20251104.11},
  url = {https://doi.org/10.11648/j.ijdsa.20251104.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20251104.11},
  abstract = {Financial markets show persistent volatility, creating barriers to achieving exact financial predictions. The forecasting of multivariate financial data requires forecasting models like the Vector Autoregressive (VAR) model for modeling linear dependencies, the Long Short-Term Memory (LSTM) model for modeling non-linear patterns, and the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model that is capable of modeling volatility clustering. Each of these models fails to handle complete data complexity on its own, as they specialize in unique properties of the data. Recent studies have been carried out that enhance forecasting accuracy by combining two models. The first case is the VAR-GARCH model, which can model linear and volatility clustering aspects but fails to model non-linear dependencies. Another case is the LSTM-GARCH model that can explain non-linear dependencies and volatility patterns, but fails to explain linear dependencies. A third instance is the VAR-LSTM model that can explain the linear and volatility aspects, but fails to model the non-linear patterns. However, there is a need to have a model that can combine the three models to explain the linear, non-linear, and volatility aspects in financial time series data collectively. This research fills this gap by combining VAR, LSTM, and GARCH into a VAR-LSTM-GARCH hybrid model, which provides improved forecasting. This study uses historical five-year daily data for VIX, US Dollar Index, and S&P 500 E-mini futures obtained from Yahoo Finance. The model-building process involves constructing a VAR (9) model selected using AIC criteria to reveal linear dependencies. The residuals from the VAR are used to train an LSTM model to capture nonlinear trends. The residuals of the LSTM are then used to fit an M-GARCH (1, 1) model, which generates volatility cluster estimates. The VAR-LSTM-GARCH hybrid model demonstrates superior performance with substantial improvements across all evaluation metrics compared to individual models, showing consistently lower prediction errors and enhanced forecasting accuracy. The progressive three-stage modeling approach demonstrates that each component contributes incrementally to forecasting performance, with the incorporation of volatility modeling through GARCH being particularly effective in enhancing predictive accuracy. The research suggests using this hybrid model for volatility prediction on multiple portfolios and emphasizes future development of real-time diagnostic processes. The new approach delivers an advanced instrument that helps financial analysts work efficiently by effectively capturing the complex interdependencies in multivariate financial time series data.
},
 year = {2025}
}

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TY  - JOUR
T1  - A Hybrid VAR-LSTM-GARCH Model for Multivariate Volatility Forecasting

AU  - Charles Chege
AU  - Martin Kithinji
AU  - Peter Gachoki
Y1  - 2025/07/14
PY  - 2025
N1  - https://doi.org/10.11648/j.ijdsa.20251104.11
DO  - 10.11648/j.ijdsa.20251104.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 99
EP  - 113
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20251104.11
AB  - Financial markets show persistent volatility, creating barriers to achieving exact financial predictions. The forecasting of multivariate financial data requires forecasting models like the Vector Autoregressive (VAR) model for modeling linear dependencies, the Long Short-Term Memory (LSTM) model for modeling non-linear patterns, and the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model that is capable of modeling volatility clustering. Each of these models fails to handle complete data complexity on its own, as they specialize in unique properties of the data. Recent studies have been carried out that enhance forecasting accuracy by combining two models. The first case is the VAR-GARCH model, which can model linear and volatility clustering aspects but fails to model non-linear dependencies. Another case is the LSTM-GARCH model that can explain non-linear dependencies and volatility patterns, but fails to explain linear dependencies. A third instance is the VAR-LSTM model that can explain the linear and volatility aspects, but fails to model the non-linear patterns. However, there is a need to have a model that can combine the three models to explain the linear, non-linear, and volatility aspects in financial time series data collectively. This research fills this gap by combining VAR, LSTM, and GARCH into a VAR-LSTM-GARCH hybrid model, which provides improved forecasting. This study uses historical five-year daily data for VIX, US Dollar Index, and S&P 500 E-mini futures obtained from Yahoo Finance. The model-building process involves constructing a VAR (9) model selected using AIC criteria to reveal linear dependencies. The residuals from the VAR are used to train an LSTM model to capture nonlinear trends. The residuals of the LSTM are then used to fit an M-GARCH (1, 1) model, which generates volatility cluster estimates. The VAR-LSTM-GARCH hybrid model demonstrates superior performance with substantial improvements across all evaluation metrics compared to individual models, showing consistently lower prediction errors and enhanced forecasting accuracy. The progressive three-stage modeling approach demonstrates that each component contributes incrementally to forecasting performance, with the incorporation of volatility modeling through GARCH being particularly effective in enhancing predictive accuracy. The research suggests using this hybrid model for volatility prediction on multiple portfolios and emphasizes future development of real-time diagnostic processes. The new approach delivers an advanced instrument that helps financial analysts work efficiently by effectively capturing the complex interdependencies in multivariate financial time series data.

VL  - 11
IS  - 4
ER  - 

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