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依赖随机映射的迭代与非线性动态中的外生性AI 解读

We discuss the existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated into the dynamic. To this end, we consider the convergence of the backward iterations of dependent random maps. In particular, we give a new result when the classical condition of contraction on average is replaced with a contraction in conditional expectation. Under some conditions, we also discuss the dependence properties of these…

局部平稳性与时变 Markov 链AI 解读

A primary motivation of this contribution is to define new locally stationary Markov models for categorical or integer-valued data. For this initial purpose, we propose a new general approach for dealing with time-inhomogeneity that extends the local stationarity notion developed in the time series literature. We also introduce a probabilistic framework which is very flexible and allows us to consider a much larger class of Markov chain models on arbitrary state spaces,…

时变 ARCH 模型中的参数稳定性与半参数推断AI 解读

Summary We develop a complete methodology for detecting time varying or non-time-varying parameters in auto-regressive conditional heteroscedasticity (ARCH) processes. For this, we estimate and test various semiparametric versions of time varying ARCH models which include two well-known non-stationary ARCH-type models introduced in the econometrics literature. Using kernel estimation, we show that non-time-varying parameters can be estimated at the usual parametric rate of…

退化 ARCH 模型参数推断的一族对比准则AI 解读

In this paper, we introduce a family of contrasts for parametric inference in ARCH models the volatility of which exhibits some degeneracy. We focus specifically on ARCH processes with a linear volatility (called LARCH processes), for which the Gaussian quasi-likelihood estimator may be inconsistent. Our approach generalizes that of Beran and Schützner (2009) and gives an interesting alternative to the WLSE used by Francq and Zakoïan (2010) for an autoregressive process with…