Abstract
In real work, we often confront complete linear and nonlinear time series data. But some time series are not pure linear and nonlinear, or complicated one, we need apply two or more models to analyze and predict them. It is necessary to explore and find some novel time series hybrid methods to solve it. Human Immunodeficiency and Virus (HIV) is one of intractable and trouble diseases in the world. Thus, the author of this article wants to analyze and probe into some novel time series methods to get breaking breach in the epidemiology that find some rules in the incidence, distribution, pathogen, and control of HIV in a population. In this article, to find the best model, auto.arima function is applied to the original time series data to determine autoregressive integrated moving average, ARIMA(0,0,0); ARIMA and generalized autoregressive conditional heteroskedasticity (GARCH), that is, ARIMA-GARCH (1,1) model is used to analyze numbers of people living with HIV for the data of HIV in the world such some important parameters as mu, ar1, ar2, omega, alpha 1, or beta 1 and some specific tests, for example, Jarque-Bera Test, Shapiro-Wilk Test, Ljung-Box Test, etc. Using ARIMA (0, 0, 0) and SARIMA (0,2), seasonal ARIMA, to predict the future values and trends after 2015. Both suggest identical results.