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序贯数据的不变因果预测AI 解读

We investigate the problem of inferring the causal predictors of a response Y from a set of d explanatory variables (X1, …, Xd). Classical ordinary least-square regression includes all predictors that reduce the variance of Y. Using only the causal predictors instead leads to models that have the advantage of remaining invariant under interventions; loosely speaking they lead to invariance across different “environments” or “heterogeneity patterns.” More precisely, the…

平稳类别时间序列的可变长度马尔可夫链筛自助法AI 解读

A bootstrap for stationary categorical time series based on the method of sieves is studied here. The data-generating process is approximated by the so-called variable-length Markov chain (VLMC), a flexible class of Markov models that allows for parsimonious structure. Then the resampling is given by simulating from the fitted model. It is shown that for a whole class of stationary categorical time series that is more general than VLMC, the VLMC sieve has faster rate of…

超越混合条件的弱依赖与非参数回归渐近理论AI 解读

We consider a new concept of weak dependence, introduced by Doukhan and Louhichi [Stochastic Process. Appl. 84 (1999) 313–342], which is more general than the classical frameworks of mixing or associated sequences. The new notion is broad enough to include many interesting examples such as very general Bernoulli shifts, Markovian models or time series bootstrap processes with discrete innovations. Under such a weak dependence assumption, we investigate nonparametric…

树结构广义自回归条件异方差模型AI 解读

Summary We propose a new generalized autoregressive conditional heteroscedastic (GARCH) model with tree-structured multiple thresholds for the estimation of volatility in financial time series. The approach relies on the idea of a binary tree where every terminal node parameterizes a (local) GARCH model for a partition cell of the predictor space. The fitting of such trees is constructed within the likelihood framework for non-Gaussian observations: it is very different from…

可变长度马尔可夫链AI 解读

We study estimation in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of high order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary high-order Markov chains. From an algorithmic view, the VLMC model class has attracted interest in information theory and machine learning, but statistical properties have not yet been explored.…

非平稳时间序列平滑的筛自助法AI 解读

We propose a sieve bootstrap procedure for time series with a deterministic trend. The sieve for constructing the bootstrap is based on nonparametric trend estimation and autoregressive approximation for some noise process. The bootstrap scheme itself does i.i.d. resampling of estimated innovations from fitted autoregressive models. We show the validity and indicate second-order correctness of such sieve bootstrap approximations for the limiting distribution of nonparametric…