On the recurrent neural network model with robust expectile-based loss function in economic data forecasting

Recurrent Neural Networks (RNNs), particularly their Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) variants, are standard methods for modeling sequential data. However, their robustness is often limited when faced with non-stationary and heterogeneous time series data. This limitation is largely due to their reliance on symmetric loss functions such as mean squared error, which implicitly assume homogeneous data patterns. To address this, we propose a new framework, Expectile-based Recurrent Neural Network (E-RNN), which integrates expectile regression into the RNN architecture. We implement and compare two E-RNN variants, namely E-LSTM and E-GRU, to obtain the best forecast. . By leveraging the asymmetric least squares loss function, the E-RNN model is able to model various parts of the conditional data distribution, not just its central tendency. This allows forecasting across scenarios, ranging from pessimistic to optimistic, by adjusting the asymmetric parameter (<i>τ</i>), a value within the range (0, 1) where <i>τ</i>〈 0.5 yields pessimistic and <i>τ</i>〉 0.5 yields optimistic forecasts.. We demonstrate this methodology by forecasting Indonesia's quarterly economic growth data from 2001 to 2025. Empirical results show that the E-RNN model consistently exhibits superior performance, evidenced by lower Expectile-based Generalized Approximate Cross Validation (EGACV) scores for model selection and higher forecast accuracy. This superiority becomes particularly significant on more volatile quarter-to-quarter (qtq) data, highlighting the effectiveness of this framework in adapting to complex data dynamics and improving forecast reliability under uncertain conditions. • Integrates expectile properties into RNN architectures to create models that are adaptive to changes in data distribution and are not tied to the homogeneity assumption. • Introduces a robust model selection criterion: Expectile-based Generalized Approximate Cross Validation (EGACV). This criterion effectively balances model fit with complexity within an expectile framework.. • Generates a set of forecasts for various outcome scenarios (e.g., pessimistic, optimistic) by adjusting a single asymmetric parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>)</mml:mo></mml:mrow> </mml:math> , moving beyond single-point estimation.