Forecasting Airtel Stock Prices Through Decomposition and Integration: A Novel VMD-GARCH-LSTM Framework

Stock price forecasting is complex due to the nonlinear and nonstationary nature of financial time series. This study proposes a hybrid variational mode decomposition (VMD)–generalized autoregressive conditional heteroskedasticity (GARCH)–long short-term memory (LSTM) model to predict Airtel’s stock prices, integrating VMD, GARCH, and LSTM networks. VMD decomposes the stock price series into intrinsic mode functions (IMFs), enabling frequency-specific modeling. High-frequency IMFs, which exhibit volatility, are processed with GARCH to capture time-varying volatility and are then fed into LSTM to model residual nonlinear dynamics. Low-frequency IMFs, which reflect smoother trends, are directly modeled by LSTM. Final forecasts are aggregated via an additive ensemble. Initially evaluated on an 80:20 train–test split, the model underwent robustness checks with 70:30 and 90:10 splits, consistently outperforming benchmark models: transformer, GRU, LSTM, BiGRU, BiLSTM, VMD-transformer, VMD-GRU, VMD-LSTM, VMD-BiGRU, VMD-BiLSTM, VMD-GARCH-transformer, VMD-GARCH-GRU, VMD-GARCH-BiGRU, and VMD-GARCH-BiLSTM. Diebold–Mariano tests confirmed statistical superiority across MSE, MAE, and MAPE loss functions, validating the model’s enhanced accuracy. These robustness checks demonstrate the model’s stability across varied data partitions, offering investors a reliable tool for risk mitigation. By effectively addressing volatility and nonlinearity, this hybrid framework advances financial forecasting, enhances decision-making in dynamic financial stocks, and contributes to robust time-series prediction methodologies.