论文检索

遍历及几何遍历马尔可夫链的大数定律AI 解读

For use in asymptotic analysis of nonlinear time series models, we show that with (Xt,t ≥ 0) a (geometrically) ergodic Markov chain, the general version of the strong law of large numbers applies. That is, the average converges almost surely to the expectation of φ(Xt,Xt+1,…) irrespective of the choice of initial distribution of, or value of, X0. In the existing literature, the less general form has been studied.We thank Paolo Paruolo (the co-editor) and the referee for…

摘要暂缺

非平稳 GARCH 模型的渐近推断AI 解读

Consistency and asymptotic normality are established for the highly applied quasi-maximum likelihood estimator in the GARCH(1,1) model. Contrary to existing literature we allow the parameters to be in the region where no stationary version of the process exists. This has the important implication that the likelihood-based estimator for the GARCH parameters is consistent and asymptotically normal in the entire parameter region including both stationary and explosive behavior.…

最大化似然函数的全局收敛算法AI 解读

In this paper we show global convergence, under very general assumptions, of iterative maximization procedures with cyclic fixing of groups of parameters, maximizing over the remaining parameters. Further we show that a slightly modified Newton procedure applied to the derivative of the reciprocal likelihood function in a one-dimensional exponential family, is globally convergent. We also prove that if the distribution of the sufficient statistic is infinitely divisible,…