Comparative Modelling of Sharia-Compliant Stock Returns and Volatility Using GRU–GARCH and DES–GARCH: Evidence from Telkom Indonesia
TL;DR
Comparing two hybrid models for jointly modeling the return and conditional volatility of PT Telekomunikasi Indonesia Tbk, a highly liquid Sharia-compliant stock, suggests that, for daily Sharia-stock returns whose predictable component is small, a simpler smoothing-based mean model can match or exceed a deep learning model.
Abstract
The integration of deep learning and econometric models has become an active research direction in modern computational finance, particularly for capturing the nonlinear dynamics and time-varying volatility that characterize equity markets. In the Islamic capital market, reliable modeling of return and volatility matters for risk assessment and for investment decisions that stay consistent with Sharia principles. This study compares two hybrid models, GRU–GARCH and DES–GARCH, for jointly modeling the return and conditional volatility of PT Telekomunikasi Indonesia Tbk (TLKM), a highly liquid Sharia-compliant stock. A Gated Recurrent Unit (GRU) network and Double Exponential Smoothing (DES) were each used to model the conditional mean of the daily log returns, while the residuals of both were modeled with a GARCH specification to capture volatility clustering. The analysis drew on 2,463 daily observations from March 2016 to March 2026, split into 80% training and 20% testing data, with model selection based on validation performance and information criteria. Forecast accuracy was measured with the scale-independent Mean Absolute Scaled Error (MASE), complemented by the QLIKE loss for the variance forecasts, the Diebold–Mariano test for pairwise comparison, and a Kupiec backtest for Value-at-Risk. Both hybrids beat a naïve benchmark, and a GARCH(1,1) model with Student-t innovations adequately described the strong volatility persistence (about 0.98) and the heavy tails found in the return series. Contrary to the common expectation that deep learning improves accuracy, the parsimonious DES–GARCH model produced a lower MASE (0.914 against 0.983) and a lower QLIKE (2.68 against 2.83) than GRU–GARCH, and the gap in mean-forecast accuracy was statistically significant under the Diebold–Mariano test. DES–GARCH also delivered better-calibrated Value-at-Risk, passing the Kupiec test at both confidence levels while GRU–GARCH did not. These results suggest that, for daily Sharia-stock returns whose predictable component is small, a simpler smoothing-based mean model can match or exceed a deep learning model, and that a strong classical baseline should be established before more complex architectures are adopted for operational risk work.