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摘要暂缺

时间序列模型的变点检验与近历依赖序列的极限定理AI 解读

This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald test for change points in a general class of time series models under the no change-point hypothesis. As an application, we verify our assumptions for the long-memory fractional ARIMA model.

GARCH 模型的经验似然方法AI 解读

This paper develops an empirical likelihood approach for regular generalized autoregressive conditional heteroskedasticity (GARCH) models and GARCH models with unit roots. For regular GARCH models, it is shown that the log empirical likelihood ratio statistic asymptotically follows a χ2 distribution. For GARCH models with unit roots, two versions of the empirical likelihood methods, the least squares score and the maximum likelihood score functions, are considered. For both…

若干异方差时间序列模型中的误差分布拟合AI 解读

This paper addresses the problem of fitting a known distribution to the innovation distribution in a class of stationary and ergodic time series models. The asymptotic null distribution of the usual Kolmogorov–Smirnov test based on the residuals generally depends on the underlying model parameters and the error distribution. To overcome the dependence on the underlying model parameters, we propose that tests be based on a vector of certain weighted residual empirical…

线性移动平均模型对门限移动平均模型的检验AI 解读

This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in MA models. Under the hypothesis of no threshold, it is shown that the test statistic converges weakly to a function of the centred Gaussian process. Under local alternatives, it is shown that this test has nontrivial asymptotic power. The results are based on a new weak convergence of a linear marked empirical process, which is independently of interest. This paper also gives an…

无限方差自回归模型的自加权最小绝对偏差估计AI 解读

Summary How to undertake statistical inference for infinite variance autoregressive models has been a long-standing open problem. To solve this problem, we propose a self-weighted least absolute deviation estimator and show that this estimator is asymptotically normal if the density of errors and its derivative are uniformly bounded. Furthermore, a Wald test statistic is developed for the linear restriction on the parameters, and it is shown to have non-trivial local power.…

双重自回归模型的估计与平稳性检验AI 解读

Summary The paper considers the double-autoregressive model yt = φyt−1+ɛt with ɛt =ηt√(ω+αyt−12). Consistency and asymptotic normality of the estimated parameters are proved under the condition E ln |φ +√αηt|<0, which includes the cases with |φ|=1 or |φ|>1 as well as E(εt2)=∞. It is well known that all kinds of estimators of φ in these cases are not normal when ɛt are independent and identically distributed. Our result is novel and surprising. Two tests are proposed for…

平稳与非平稳短长记忆 ARFIMA–GARCH 模型的自适应估计与检验AI 解读

This article considers the fractionally autoregressive integrated moving average [ARFIMA(p,d,q)] models with GARCH errors. The process generated by this model is short memory, long memory, stationary, and nonstationary, respectively, when d ∈ (-1/2, 0), d ∈ (0, 1/2), d ∈ (-1/2, 1/2), and d ∈ (1/2, ∞). Using a unified approach, the local asymptotic normality of the model is established for d ∈ ∪∞j = 0(J - 1/2, J + 1/2). The adaptivity and efficiency of the estimating…

具有 GARCH(1,1) 误差的单位根过程渐近推断AI 解读

This paper investigates the so-called one-step local quasi–maximum likelihood estimator for the unit root process with GARCH(1,1) errors. When the scaled conditional errors (the ratio of the disturbance to the conditional standard deviation) follow a symmetric distribution, the asymptotic distribution of the estimated unit root is derived only under the second-order moment condition. It is shown that this distribution is a functional of a bivariate Brownian motion as in Ling…

具有 GARCH 误差的非平稳 ARMA 模型中的自适应估计AI 解读

This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfyinga generalized autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is shown that the limit experiment is neither LAN nor LAMN, but is instead LABF. For the model with symmetric density of the rescaled error, a new efficiency criterion is established for a…

向量 ARMA-GARCH 模型的渐近理论AI 解读

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) model. The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established. Consistency of the quasi-maximum-likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate autoregressive…

GARCH 与非对称幂 GARCH 模型矩存在的充要条件AI 解读

Although econometricians have been using Bollerslev's (1986, Journal of Econometrics 31, 307–327) GARCH( r , s ) model for over a decade, the higher order moment structure of the model remains unresolved. The sufficient condition for the existence of the higher order moments of the GARCH( r , s ) model was given by Ling (1999a, Journal of Applied Probability 36, 688–705). This paper shows that Ling's condition is also necessary. As an extension, the necessary and sufficient…

摘要暂缺

非平稳分数积分 ARMA 模型的渐近推断AI 解读

This paper considers nonstationary fractional autoregressive integrated moving-average ( p , d , q ) models with the fractionally differencing parameter d ∈ (− 1/2,1/2) and the autoregression function with roots on or outside the unit circle. Asymptotic inference is based on the conditional sum of squares (CSS) estimation. Under some suitable conditions, it is shown that CSS estimators exist and are consistent. The asymptotic distributions of CSS estimators are expressed as…

非平稳自回归模型中残差序贯经验过程的弱收敛AI 解读

This paper establishes the weak convergence of the sequential empirical process $\hat{K}_n$ of the estimated residuals in nonstationary autoregressive models. Under some regular conditions, it is shown that $\hat{K}_n$ converges weakly to a Kiefer process when the characteristic polynomial does not include the unit root 1; otherwise $\hat{K}_n$ converges weakly to a Kiefer process plus a functional of stochastic integrals in terms of the standard Brownian motion. The latter…

含 GARCH 误差的不稳定 ARMA 时间序列最大似然估计量的极限分布AI 解读

This paper investigates the maximum likelihood estimator (MLE) for unstable autoregressive moving-average (ARMA) time series with the noise sequence satisfying a general autoregressive heteroscedastic (GARCH) process. Under some mild conditions, it is shown that the MLE satisfying the likelihood equation exists and is consistent. The limiting distribution of the MLE is derived in a unified manner for all types of characteristic roots on or outside the unit circle and is…

带条件异方差的分数积分 ARMA 时间序列模型AI 解读

This article considers fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived.…