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交叉分位相关图：分位依赖与方向预测性检验AI 解读

This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the asymptotic distribution of the cross-quantilogram and the corresponding test statistic. The limiting distributions depend on nuisance parameters. To construct consistent confidence intervals we employ a stationary bootstrap procedure; we…

含平稳与非平稳协变量的 GARCH-X 模型：拟极大似然估计的渐近理论AI 解读

This article investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE’s) of the GARCH model augmented by including an additional explanatory variable—the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as captured by its long-memory parameter dx; in particular, we allow for both stationary and nonstationary covariates. We show that the QMLE’s of the parameters entering the volatility…

含持久协变量的 ARCH/GARCH：极大似然渐近理论AI 解读

The paper considers a volatility model which introduces a persistent, integrated or near-integrated, covariate to the standard GARCH(1, 1) model. For such a model, we derive the asymptotic theory of the quasi-maximum likelihood estimator. In particular, we establish consistency and obtain limit distribution. The limit distribution is generally non-Gaussian and represented as a functional of Brownian motions. However, it becomes Gaussian if the covariate has innovation…

含持久协变量的ARCH过程的时间序列性质AI 解读

We investigate the time series properties of a volatility model, whose conditional variance is specified as in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated or nearly integrated process, with its effect on volatility given by a wide class of nonlinear volatility functions. In the paper, such a model is shown to generate many important characteristics that are commonly observed in financial time series. In particular, the…