Hybrid ARIMA-Spatial Autocorrelation (Moran Index and LISA) for Covid-19 Vaccination in All Indonesian Provinces

Abstract

Numerous issues arise from stochastic processes with temporal and spatial index parameters. From 2020, Covid-19 has occurred worldwide. Combining time series with geographical analysis is crucial. ARIMA and spatial autocorrelation analysis using Moran’s Index and LISA are prominent models for the two analyses. ARIMA predicts future values. The ARIMA model is applied to all recorded locations since it involves a stochastic process with a time and location parameter index. Then the prediction results at each location were examined using spatial autocorrelation, starting with the Moran index to see global relationships, then LISA (to look at the relationship between locations locally, to see which locations have a significant effect). The Queen Contiguity weight matrix calculates spatial autocorrelation (assuming that locations that are directly adjacent to each other have a spatial effect). Spatial autocorrelation will divide each place into four quadrants: High-High (HH), High-Low (HL), Low-High (LH), and Low-Low (LL). This approach was applied to 2021 Indonesian vaccination rates in all 34 provinces (354 days). Hence, the ARIMA model was applied to the 34 provinces, and each location received three forecasting. Moran’s Index revealed spatial autocorrelation in the 354th and 355th time forecasts. LISA shows that Aceh (LL), West Sumatra (LH), South Sumatra (HH), Lampung (LH), and North Maluku (LL) influence other provinces (LH).