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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Nurhayati Nurhayati
Universitas Pertahanan
Mathematics

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ARIMA–GGJR–GARCH Modeling of Asymmetric Conditional Volatility in Wind Speed Time Series Nurhayati Nurhayati; Andi Fitriawati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41180

Abstract

Volatility modeling plays a crucial role in time-series forecasting, particularly for wind speed, where variability and asymmetric responses to shocks are commonly observed. Accurate wind speed forecasting can help mitigate potential risks associated with extreme or uncontrolled wind events. While the Autoregressive Integrated Moving Average (ARIMA) model is widely used to model the conditional mean of time series, it does not capture time-varying volatility or asymmetric effects. To address this limitation, we combine ARIMA with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and asymmetric extensions, including the Glosten–Jagannathan–Runkle GARCH (GJR-GARCH) and its generalized form (GGJR-GARCH). This framework allows simultaneous modeling of the conditional mean and conditional variance, accommodating heteroscedasticity and leverage effects in wind speed data. The empirical results indicate that negative shocks exert a stronger impact on conditional volatility than positive shocks, confirming the presence of asymmetry. Based on forecasting performance evaluation, the ARIMA(2,0,1)–GGJR-GARCH(1,1) specification provides the most accurate predictions among the competing models.
Co-Authors Andi Fitriawati