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重尾时间序列的变点检验：缩尾 CUSUM 方法AI 解读

It is well-known that the detection of change-points in heavy-tailed time series is an open problem since the traditional tests may not have a power. This article introduces a winsorized cumulative sum (CUSUM) approach to solve this problem. We begin by investigating the winsorized CUSUM process and then use it to construct the Kolmogorov-Smirnov (KS) test and the Self-normalized (SN) test. Under the null hypothesis, it is shown that each weakly converges to the maximum of a…

整数值平滑转换 GARCH 模型：设定与检验AI 解读

This paper introduces a new class of nonlinear models known as the Z-valued smooth transition GARCH model, designed to accommodate Z-valued time series that display asymmetric, nonlinear and highly persistent volatility. The paper outlines the maximum likelihood estimation procedure and establishes its consistency and asymptotic normality of the estimated parameters. Three types of tests are studied, including sup-type linearity test, score-based goodness-of-fit test, and…

非零中位数 GARCH 型噪声下重尾 AR 模型的两步估计AI 解读

This paper develops a novel two-step estimating procedure for heavy-tailed AR models with nonzero median GARCH-type noises, allowing for time-varying volatility. We first establish the self-weighted quantile regression estimator (SQE) across all quantile levels τ∈(0,1) for the AR parameters θ0. We show that the SQE, less a bias, converges weakly to a Gaussian process at a rate of n−1/2. The bias is zero if and only if τ equals τ0, the probability that the noise is less than…

预测回归向门限预测回归变化的结构检验AI 解读

This article investigates two test statistics for testing structural changes and thresholds in predictive regression models. The generalized likelihood ratio (GLR) test is proposed for the stationary predictor and the generalized F test is suggested for the persistent predictor. Under the null hypothesis of no structural change and threshold, it is shown that the GLR test statistic converges to a function of a centered Gaussian process, and the generalized F test statistic…

重尾 G-GARCH(1,1) 噪声下自回归模型的 LAD 推断AI 解读

This paper explores the least absolute deviation (LAD) estimator of the autoregressive model with heavy-tailed G-GARCH(1, 1) noise. When the tail index α∈(1,2], it is shown that the LAD estimator asymptotically converges to a linear function of a series of α-stable random vectors with a rate of convergence n1−1/α. The result is significantly different from that of the corresponding least square estimator which is not consistent, and partially solves the problem on the…

高维时间序列数据的序列相关与 ARCH 效应检验AI 解读

This article proposes several tests for detecting serial correlation and ARCH effect in high-dimensional data. The dimension of data p=p(n) may go to infinity when the sample size n→∞

厚尾向量误差修正模型的推断AI 解读

This paper first studies the full rank least squares estimator (FLSE) of the heavy-tailed vector error correction (VEC) models. It is shown that the rate of convergence of the FLSE related to the long-run parameters is n (sample size) and its limiting distribution is a stochastic integral in terms of two stable random processes when the tail index α∈(0,2). Furthermore, we show that the rate of convergence of the FLSE related to the short-term parameters is n1∕αL̃(n) and its…

ZD-GARCH 模型：研究异方差的新方法AI 解读

This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH model, the ZD-GARCH(1, 1) model is always non-stationary regardless of the sign of the Lyapunov exponent γ0, but interestingly it is stable with its sample path oscillating randomly between zero and infinity over time when γ0=0. Furthermore, this paper studies the generalized quasi-maximum likelihood…

重尾多阈值双重自回归模型的统计推断AI 解读

This article develops a systematic inference procedure for heavy-tailed and multiple-threshold double autoregressive (MTDAR) models. We first study its quasi-maximum exponential likelihood estimator (QMELE). It is shown that the estimated thresholds are n-consistent, each of which converges weakly to the smallest minimizer of a two-sided compound Poisson process. The remaining parameters are n$\sqrt{n}$-consistent and asymptotically normal. Based on this theory, a…

重尾门槛自回归模型的自加权 LAD 推断AI 解读

The least squares estimator of the threshold autoregressive (TAR) model may not be consistent when its tail is less than or equal to 2. Neither theory nor methodology can be applied to model fitting in this case. This paper is to develop a systematic procedure of statistical inference for the heavy-tailed TAR model. We first investigate the self-weighted least absolute deviation estimation for the model. It is shown that the estimated slope parameters are n-consistent and…

线性与非线性时间序列模型的变点估计AI 解读

This paper develops an asymptotic theory for estimated change-points in linear and nonlinear time series models. Based on a measurable objective function, it is shown that the estimated change-point converges weakly to the location of the maxima of a double-sided random walk and other estimated parameters are asymptotically normal. When the magnitude d of changed parameters is small, it is shown that the limiting distribution can be approximated by the known distribution as…

门限双重自回归模型的检验与估计AI 解读

This article first proposes a score-based test for a double autoregressive model against a threshold double autoregressive (AR) model. It is an asymptotically distribution-free test and is easy to implement in practice. The article further studies the quasi-maximum likelihood estimation of a threshold double autoregressive model. It is shown that the estimated threshold is n-consistent and converges weakly to a functional of a two-sided compound Poisson process and the…

多门槛双重自回归模型的渐近推断AI 解读

This paper investigates a class of multiple-threshold models, called Multiple Threshold Double AR (MTDAR) models. A sufficient condition is obtained for the existence and uniqueness of a strictly stationary and ergodic solution to the first-order MTDAR model. We study the Quasi-Maximum Likelihood Estimator (QMLE) of the MTDAR model. The estimated thresholds are shown to be n-consistent, asymptotically independent, and to converge weakly to the smallest minimizer of a…

时间序列与金融计量经济学前沿：概览AI 解读

Two of the fastest growing frontiers in econometrics and quantitative finance are time series and financial econometrics. Significant theoretical contributions to financial econometrics have been made by experts in statistics, econometrics, mathematics, and time series analysis. The purpose of this special issue of the journal on “Frontiers in Time Series and Financial Econometrics” is to highlight several areas of research by leading academics in which novel methods have…

含厚尾 G-GARCH 噪声的自回归模型渐近推断AI 解读

It is well known that the least squares estimator (LSE) of an AR( p ) model with i.i.d. (independent and identically distributed) noises is n 1/ α L ( n )-consistent when the tail index α of the noise is within (0,2) and is n 1/2 -consistent when α ≥ 2, where L ( n ) is a slowly varying function. When the noises are not i.i.d., however, the case is far from clear. This paper studies the LSE of AR( p ) models with heavy-tailed G-GARCH(1,1) noises. When the tail index α of…

未知重尾异方差噪声下 ARMA 模型的最小绝对偏差推断AI 解读

This article develops a systematic procedure of statistical inference for the auto-regressive moving average (ARMA) model with unspecified and heavy-tailed heteroscedastic noises. We first investigate the least absolute deviation estimator (LADE) and the self-weighted LADE for the model. Both estimators are shown to be strongly consistent and asymptotically normal when the noise has a finite variance and infinite variance, respectively. The rates of convergence of the LADE…

评论AI 解读

Congratulation to authors because of their interesting estimation approach. In this discussion, we compare the finite performance of the non-Gaussian quasi maximum likelihood estimator (NGQMLE) wit...

评论AI 解读

Congratulations to the authors for their very interesting work.The authors define a cumulative generalized kurtosis matrix to summarize the volatility dependence of multivariate time series in (2) ...

门限移动平均模型最小二乘估计的渐近理论AI 解读

This paper studies the asymptotic theory of least squares estimation in a threshold moving average model. Under some mild conditions, it is shown that the estimator of the threshold is n -consistent and its limiting distribution is related to a two-sided compound Poisson process, whereas the estimators of other coefficients are strongly consistent and asymptotically normal. This paper also provides a resampling method to tabulate the limiting distribution of the estimated…

有限或无限方差 ARMA 模型的全局加权最小绝对偏差估计AI 解读

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA( p , q ) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of the global SLAD estimators. In this paper the asymptotic theory of the global LAD estimator for finite and infinite variance ARMA( p , q ) models is established in the literature…

多区制门槛自回归模型的最小二乘估计AI 解读

This paper studies the least squares estimator (LSE) of the multiple-regime threshold autoregressive (TAR) model and establishes its asymptotic theory. It is shown that the LSE is strongly consistent. When the autoregressive function is discontinuous over each threshold, the estimated thresholds are n-consistent and asymptotically independent, each of which converges weakly to the smallest minimizer of a one-dimensional two-sided compound Poisson process. The remaining…

ARMA–GARCH/IGARCH 模型的全局自加权与局部准最大指数似然估计AI 解读

This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA–GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given…

区分随机游走与均值变化备择AI 解读

We study test procedures that detect structural breaks in underlying data sequences. In particular, we wish to discriminate between different reasons for these changes, such as (1) shifting means, (2) random walk behavior, and (3) constant means but innovations switching from stationary to difference stationary behavior. Almost all procedures presently available in the literature are simultaneously sensitive to all three types of alternatives. The test statistics under…

长记忆与短记忆时间序列的残差经验过程AI 解读

This paper studies the residual empirical process of long- and short-memory time series regression models and establishes its uniform expansion under a general framework. The results are applied to the stochastic regression models and unstable autoregressive models. For the long-memory noise, it is shown that the limit distribution of the Kolmogorov–Smirnov test statistic studied in Ho and Hsing [Ann. Statist. 24 (1996) 992–1024] does not hold when the stochastic regression…