Despite the invention of vaccines and various medications, influenza-like illness still brings a burden to both physical and economic situations in the world. Many research have been done in pursuit of the ability to predict influenza epidemics as accurately as possible, with hopes to help health insurance providers and public health facilities. The main idea of this thesis is to give a probabilistic model to capture the future influenza activity in different regions of the United States. We use autoregressive moving average (ARMA) model with generalized autoregressive conditional heteroskedasticity (GARCH) model, together with pair-copula constructions to depict the dependencies between regions, describing jointly the residuals of the ARMA-GARCH models. The model has been able to predict influenza-like illness activity by utilizing historical data provided by the Centers for Disease Control (CDC) over the desired future time horizon.