论文标题
通过神经网络学习Charme模型
Learning CHARME models with neural networks
论文作者
论文摘要
在本文中，我们考虑了一种称为Charme的模型（专家的有条件异质性自回归混合物），这是一类非线性非参数AR-ARCH时间序列的广义混合物。在某些Lipschitz型条件下，在自回归和波动率功能方面，我们证明该模型是固定的，ergodic的，并且$τ$ - 依赖性。这些条件比处理该模型的文献中介绍的条件要弱得多。此外，该结果构成了基本（非）参数估计的渐近理论的理论基础，我们为此模型提供了这一理论。作为一种应用，从神经网络的通用近似特性（NN）中，我们为模型的基于NN的自回归功能开发了一种学习理论，在弱条件下保证了NN权重和偏见的强估计估计量的强一致性和渐近正态性。
In this paper, we consider a model called CHARME (Conditional Heteroscedastic Autoregressive Mixture of Experts), a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. Under certain Lipschitz-type conditions on the autoregressive and volatility functions, we prove that this model is stationary, ergodic and $τ$-weakly dependent. These conditions are much weaker than those presented in the literature that treats this model. Moreover, this result forms the theoretical basis for deriving an asymptotic theory of the underlying (non)parametric estimation, which we present for this model. As an application, from the universal approximation property of neural networks (NN), we develop a learning theory for the NN-based autoregressive functions of the model, where the strong consistency and asymptotic normality of the considered estimator of the NN weights and biases are guaranteed under weak conditions.
