Study On The Dependence Of Random Variables From ARCH

In this paper, we firstly introduce the background and development process of ARCH model, and concentrate on the problem in the dependence of random variables from ARCH. In section 1 , section 2, the background and development process, the basic property of ARCH model were introduced respectively. The section 3 is keystone. In this sector, we will discuss the dependence of random variables from ARCH in various senses, and the property based on the dependence. In this section we show that any two random variables from the time series of absolute values and squares of the ARCH sequence are positively dependent in various senses. We study the tail dependence of random variables from ARCH, we obtain the maximal inequality and the strong law of large numbers for the squares of the ARCH sequence. Several issues presented in the end of paper may be considered further, and they will be my future effort direction and I hope to obtain better conclusions.The major conclusions in this paper is below.Theorem 3.2.1 Suppose {xt} ~ ARCH(1), thenTheorem 3.3.1 Suppose {xt} ~ ARCH(1) with iid t-distribution innovations {vt}thenTheorem 3.5.1 If {xt} ~ ARCH(1), sn supposethen there exists a constant c such thatTheorem 3.6.1 Suppose α > 1/2 and if α = 1/2 then β > 3/2, suppose.