Unveiling Asymptotic Behavior in Precipitation Time Series: A GARCH-Based Second Order Semi-Parametric Autocorrelation Framework for Drought Monitoring in the Semi-Arid Region of India

This study evaluated ten drought indices focusing on their ability to monitor drought events in Marathwada, a semi-arid region of India. High-resolution gridded monthly total precipitation data for 75 years (1950–2024) from the European Centre for Medium-Range Weather Forecasts (ECMWF) were used to evaluate the drought indices. These indices were computed across six timescales: 1, 3, 4, 6, 9, and 12 months. A Generalized Autoregressive Conditional Heteroscedastic (GARCH) model was employed to detect temporal volatility in precipitation, followed by a second-order geospatial autocorrelation eigenfunction eigendecomposition using Global Moran’s Index statistics to geolocate both aggregated and non-aggregated precipitation locations. The performance of drought indices was assessed using non-parametric Spearman’s correlation to identify the strength, direction, and similarity of regional-specific drought events. The temporal lag interdependence between meteorological and agricultural droughts was assessed using a non-parametric Spearman’s cross correlation function (SCCF). The findings revealed that the GARCH model with a skewed Student’s t distribution effectively captured conditional temporal volatility and asymptotic behavior in the precipitation series. The model’s sensitivity enabled the incorporation of temporal fluctuations related to droughts and extreme meteorological events. The Bhalme and Mooley Drought Index (BMDI-6) and Z-Score Index (ZSI-6) were the most applicable indices for drought monitoring. Spearman’s cross-correlation analysis revealed that meteorological droughts influenced agricultural droughts with a time lag of up to 4 months.