Strong Law of Large Numbers of Absolute Value Sequences from Varying-Coefficient ARCH Models

In this paper we introduce a varying-coefficient ARCH model in which the model coefficient is a function of time variable t. It is consistent with the fact that the coefficients are different in different time intervals in modeling, so this kind of model is more reasonable. We believe that the varying-coefficient ARCH model has several potential advantages for practical uses, it is more flexible. Here we discuss the strong law of large numbers of absolute value sequences from varying-coefficient ARCH models.