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超越均值：无限均值自回归条件持续时间的极限理论与检验AI 解读

Abstract Integrated autoregressive conditional duration (ACD) models serve as counterparts to integrated generalized autoregressive conditional heteroskedastic models used for financial returns. However, despite their resemblance, asymptotic theory for ACD is still incomplete. Central challenges arise from the facts that (i) integrated ACD processes imply durations with infinite expectation and (ii) conventional asymptotic approaches break down due to the randomness in the…

ACD 模型的尾部行为及其对似然估计的影响AI 解读

We establish new results for estimation and inference in financial durations models, where events are observed over a given time span, such as a trading day, or a week. For the classical autoregressive conditional duration (ACD) models by Engle and Russell (1998), we show that the large sample behavior of likelihood estimators is highly sensitive to the tail behavior of the financial durations. In particular, even under stationarity, asymptotic normality breaks down for tail…

利用自助法极值相关图估计极端序列依赖AI 解读

Davis and Mikosch (2009a) introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram. A major difficulty was the construction of credible confidence bands for the extremogram. In this paper, we employ the stationary bootstrap to overcome this problem. The use of the stationary bootstrap for the extremogram and the…

条件异方差时间序列的准极大似然估计：随机递推方程方法AI 解读

This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt=σtZt, where the unobservable volatility σt is a parametric function of (Xt−1, …, Xt−p, σt−1, …, σt−q) for some p, q≥0, and (Zt) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equations which satisfy a contraction (random Lipschitz coefficient) property. These assumptions are…

GARCH(1,1) 过程样本自相关与极值的极限理论AI 解读

The asymptotic theory for the sample autocorrelations and extremes of a GARCH (1, 1) process is provided. Special attention is given to the case when the sum of the ARCH and GARCH parameters is close to 1, that is, when one is close to an infinite variance marginal distribution. This situation has been observed for various financial log-return series and led to the introduction of the IGARCH model. In such a situation, the sample autocorrelations are unreliable estimators of…

重尾过程的样本自相关及其在 ARCH 模型中的应用AI 解读

We study the sample ACVF and ACF of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying. This includes linear and bilinear processes with regularly varying noise and ARCH processes, their squares and absolute values. We show that the distributional limits of the sample ACF can be random, provided that the variance of the marginal distribution is infinite and the process is nonlinear. This is in…

无限方差创新下 ARMA 模型的参数估计AI 解读

We consider a standard ARMA process of the form $\phi(B)X_t = \theta(B)Z_t$, where the innovations $Z_t$ belong to the domain of attraction of a stable law, so that neither the $Z_t$ nor the $X_t$ have a finite variance. Our aim is to estimate the coefficients of $\phi$ and $\theta$. Since maximum likelihood estimation is not a viable possibility (due to the unknown form of the marginal density of the innovation sequence), we adopt the so-called Whittle estimator, based on…