PERMODELAN KETERKAITAN DINAMIS ANTARA TEMPERATURE RATA - RATA DAN KELEMBAPAN RATA - RATA HARIAN MENGGUNAKAN VARMA - GARCH

Abstract

Humidity and temperature are two meteorological variables that are physically and dynamically interconnected, making them suitable to be analyzed as multivariate time series that exhibit interactions across periods. This study aims to model the dynamic linkage and joint volatility between daily average temperature (TAVG) and daily average relative humidity (RHAVG) in Bengkulu City using a combination of the Vector Autoregressive Moving Average (VARMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) frameworks. The analytical procedure includes initial exploration, stationarity testing, identification of the mean model order based on information criteria, Granger causality testing, VARMA residual diagnostics, volatility modeling using univariate eGARCH(1,1) for each residual series, and final diagnostic evaluation along with forecasting accuracy assessment. Model selection results indicate that VARMA(6,0) is the most appropriate order for capturing the mean dynamics of both variables. Granger causality tests reveal a bidirectional relationship between TAVG and RHAVG, implying that the historical information of each variable contributes to forecasting the other. Residual diagnostics for the mean model show reduced autocorrelation but the presence of conditional heteroskedasticity and departures from normality, thus necessitating variance modeling. The eGARCH(1,1) model with a Student-t distribution yields significant parameters and successfully eliminates ARCH effects and autocorrelation in both standardized and squared residuals. A 30-step-ahead forecast based on the VARMA(6,0)–eGARCH(1,1) combination produces MAPE values of approximately 4.46% for TAVG and 5.12% for RHAVG, indicating excellent predictive accuracy. These findings demonstrate that the VARMA–GARCH approach effectively captures the mean dynamics and volatility of meteorological conditions, reinforcing its potential for early-warning systems and climate-informed local planning.

Keywords: Multivariate time series, VARMA, GARCH, Temperature, Humidity.