A generalized nonlinear model for long memory conditional heteroscedasticity

作者：Grublyte Ieva^*; Skarnulis Andrius

来源：Statistics, 2017, 51(1): 123-140.

DOI：10.1080/02331888.2016.1259813

• Asymmetric ARCH model
• LARCH model
• leverage
• long memory

We study the existence and properties of stationary solution of ARCH-type equation r(t) = xi(t)sigma(t), where.t are standardized i.i.d. random variables and the conditional variance satisfies an AR(1) equation sigma(2)(t) = Q(2)(a + Sigma(infinity)(j=1) b(j)r(t-j)) + gamma sigma(2)(t-1) with a Lipschitz function Q(x) and real parameters alpha, gamma, b(j). The paper extends the model and the results in Doukhan, Grublyt. e, and Surgailis [A nonlinear model for long memory conditional heteroscedasticity. Lithuanian Math J. 2016;56:164-188] from the case gamma = 0 to the case 0 < gamma < 1. We also obtain a new condition for the existence of higher moments of rt which does not include the Rosenthal constant. In the particular case when Q is the square root of a quadratic polynomial, we prove that rt can exhibit a leverage effect and long memory. Wealso present simulated trajectories and histograms of marginal density of st for different values of gamma.

• 出版日期2017