ARIMA-GARCH Based EWMA Control Chart for Rupiah-US Dollar Exchange Rate

Abstract. The Exponentially Weighted Moving Average (EWMA) control chart is more responsive to small shifts because it assigns greater weight to recent observations. This property is relevant for monitoring the Indonesian Rupiah-U.S. Dollar (IDR/USD) exchange rate, which is highly sensitive to global dynamics and exhibits substantial fluctuations. However, exchange-rate time series often exhibit serial correlation and conditional heteroskedasticity, which can reduce the accuracy of conventional control charts. To address this issue, an Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional Heteroskedasticity (ARIMA-GARCH) model provides a more reliable statistical basis by capturing both temporal dependence and volatility dynamics. This study aims to develop an EWMA control chart based on ARIMA-GARCH residuals for monitoring the IDR/USD exchange rate and to evaluate its performance using the in-control average run length (IC-ARL) and out-of-control average run length (OC-ARL). The best ARIMA-GARCH specification was selected using the Akaike information criterion and parameter significance tests. Residuals from the selected model, which were free from serial correlation and remaining heteroskedasticity, were used to construct EWMA charts with smoothing parameters  = 0.05, 0.1, and 0.3 and control limits  = 3. The ARIMA (3,1,2)-GARCH (1,1) model was identified as the best specification. Based on its residuals, the EWMA chart with  = 0.1 detected 20 out-of-control points associated with periods of global instability while maintaining a low false-alarm rate. Overall, the proposed ARIMA-GARCH-based EWMA chart improves monitoring sensitivity and stability compared with a conventional EWMA chart, and  = 0.1 provides the most balanced performance.