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含外生协变量的一般因果时间序列：推断与模型选择AI 解读

In this paper, we study a general class of causal processes with exogenous covariates, including many classical processes such as the ARMA-GARCH, APARCH, ARMAX, GARCH-X and APARCH-X processes. Under some Lipschitz-type conditions, the existence of a $τ$-weakly dependent strictly stationary and ergodic solution is established. We provide conditions for the strong consistency and derive the asymptotic distribution of the quasi-maximum likelihood estimator (QMLE), both when the…

一般因果时间序列中的暂时性变点检测AI 解读

We consider an epidemic change-point detection in a large class of causal time series models, including among other processes, AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH. A test statistic based on the Gaussian quasi-maximum likelihood estimator of the parameter is proposed. It is shown that, under the null hypothesis of no change, the test statistic converges to a distribution obtained from a difference of two Brownian bridge and diverges to infinity under the…

多元时间序列变点检测的一般程序AI 解读

We consider the change-point detection in multivariate continuous and integer valued time series. We propose a Wald-type statistic based on the estimator performed by a general contrast function; which can be constructed from the likelihood, a quasi-likelihood, a least squares method, etc. Sufficient conditions are provided to ensure that the statistic convergences to a well-known distribution under the null hypothesis (of no change) and diverges to infinity under the…

一般整数值时间序列中的暂时性变点检测AI 解读

In this paper, we consider the structural change in a class of discrete valued time series, which the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter $θ^*$ which may change over time. We provide sufficient conditions for the consistency and the asymptotic normality of the Poisson quasi-maximum likelihood estimator (QMLE) of the model. We consider an epidemic change-point detection and…