论文标题
从次要方向上偏go的自动锻炼，并具有自回归有条件异方差性
Subgeometrically ergodic autoregressions with autoregressive conditional heteroskedasticity
论文作者
论文摘要
在本文中，我们考虑了单变量非线性自动化的子几何（特别是多项式）的细节，具有自动回归有条件的异性恋性（ARCH）。 1980年代，在马尔可夫链文献中引入了子几何形状的概念，这意味着过渡概率度量以比几何速度慢的速率收敛到固定措施。该速率也与$β$混合系数的收敛速率密切相关。虽然现有的有关次要层面上的自动锻炼的文献假定同性恋误差术语，但本文为有条件的异性恋拱形型错误提供了扩展，从而大大扩大了潜在应用的范围。具体而言，我们考虑适当定义的具有非线性拱形误差的高阶非线性自动化，并表明它们是在适当的条件下以多项式速率的地球上的偏角。使用能量部门波动率指数数据的经验示例说明了使用次要层面上的Ergodic AR-Arch模型的使用。
In this paper, we consider subgeometric (specifically, polynomial) ergodicity of univariate nonlinear autoregressions with autoregressive conditional heteroskedasticity (ARCH). The notion of subgeometric ergodicity was introduced in the Markov chain literature in 1980s and it means that the transition probability measures converge to the stationary measure at a rate slower than geometric; this rate is also closely related to the convergence rate of $β$-mixing coefficients. While the existing literature on subgeometrically ergodic autoregressions assumes a homoskedastic error term, this paper provides an extension to the case of conditionally heteroskedastic ARCH-type errors, considerably widening the scope of potential applications. Specifically, we consider suitably defined higher-order nonlinear autoregressions with possibly nonlinear ARCH errors and show that they are, under appropriate conditions, subgeometrically ergodic at a polynomial rate. An empirical example using energy sector volatility index data illustrates the use of subgeometrically ergodic AR-ARCH models.
