Generalized space time autoregressive integrated autoregressive conditional heteroscedastic (GSTARI-ARCH) modeling with least squares and MLE parameter estimation

Space time or spatial time series data is time series data that is not only related to events at previous times, but also has a relationship to location. Generalized space time autoregressive integrated-autoregressive conditional heteroscedastic is a model used to analyze spatial time series data where this model considers the differentiation process. According to the law of probability, the process does not change over time, so if the data is not stationary, it can make the estimation results less precise, so a differentiation (integrated) process is needed. In reality, it is often found that the variance changes over time or is heteroscedastic. Autoregressive conditional heteroscedastic analyzes the error variance problem differently for each time series observation. In this condition, the variance error not only functions from the independent variable, but also depends on how big the previous error was. The aim of this research is to model Covid-19 cases with the GSTARI-ARCH model which is compared with the GSTARI model by estimating model parameters using two methods. Parameter estimation using the least squares method produces the linear form β^(i)=(Xi’Xi)−1Xi’Xi. The error in the autoregressive conditional heteroscedastic model is estimated using the maximum likelihood method assuming constant correlation, so that Σ = Dt RDt is obtained. The modeling results show that the MAPE value of GSTARI-ARCH is smaller than GSTARI, so the GSTARI-ARCH model is the best model.