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由因果 GARCH 波动驱动的非因果自回归过程AI 解读

This paper studies the introduction of causal conditional heteroskedasticity in noncausal autoregressive (AR) models. We demonstrate that, in this framework, large shocks to the innovation process driving the GARCH error term of a noncausal AR model result in heightened volatility immediately before and after a bubble crash. The non-coincidence of the σ-fields generated by past observations and past values of the GARCH process makes statistical inference nonstandard. In…

基于估计函数的弱条件位置时间序列模型断点推断AI 解读

Drawing on Godambe’s theory of estimating functions, we present a statistical approach for identifying breaks in time series dynamics under weak assumptions. We assume a parametric form for the conditional mean but make no specific assumptions about the data-generating process (DGP), nor about the other conditional moments. The cumulative sum (CUSUM) statistics and segmentation of minimal cost (SMC) statistics that we consider depend on a sequence of weights that influence…

动态系统性风险度量的统计推断AI 解读

Systemic risk measures (SRM) quantify the risk of a system induced by the possible distress of any of its components. Applications in economics and finance are numerous. We define a general dynamic framework for the risk factors, allowing us to obtain explicit expressions of the corresponding dynamic SRM. We deduce an easy-to-implement statistical approach which, based on semi-parametric assumptions, reduces to estimating univariate location-scale models and to computing…

GARCH 过程矩存在性的检验AI 解读

It is generally admitted that many financial time series have heavy tailed marginal distributions. When time series models are fitted on such data, the non-existence of appropriate moments may invalidate standard statistical tools used for inference. Moreover, the existence of moments can be crucial for risk management, for instance when risk is measured through the expected shortfall. This paper considers testing the existence of moments in the framework of GARCH processes.…

大型投资组合条件 VaR 的虚拟历史模拟AI 解读

In order to estimate the conditional risk of a portfolio’s return, two strategies can be advocated. A multivariate strategy requires estimating a dynamic model for the vector of risk factors, which is often challenging, when at all possible, for large portfolios. A univariate approach based on a dynamic model for the portfolio’s return seems more attractive. However, when the combination of the individual returns is time varying, the portfolio’s return series is typically…

函数型 GARCH 模型的准似然方法及应用AI 解读

The increasing availability of high frequency data has initiated many new research areas in statistics. Functional data analysis (FDA) is one such innovative approach towards modelling time series data. In FDA, densely observed data are transformed into curves and then each (random) curve is considered as one data object. A natural, but still relatively unexplored, context for FDA methods is related to financial data, where high-frequency trading currently takes a…

半参数多元模型驱动的投资组合 VaR 估计风险AI 解读

Joint estimation of market and estimation risks in portfolios is investigated, when the individual returns follow a semi-parametric multivariate dynamic model and the asset composition is time-varying. Under ellipticity of the conditional distribution, asymptotic theory for the estimation of the conditional Value-at-Risk (VaR) is developed. An alternative method – the Filtered Historical Simulation – which does not rely on ellipticity, is also studied. Asymptotic confidence…

利用非因果过程建模局部爆炸AI 解读

Summary The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy…

多元波动率模型的逐方程估计AI 解读

Summary The paper investigates the estimation of a wide class of multivariate volatility models. Instead of estimating an m-multivariate volatility model, a much simpler and numerically efficient method consists in estimating m univariate generalized auto-regressive conditional heteroscedasticity type models equation by equation in the first step, and a correlation matrix in the second step. Strong consistency and asymptotic normality of the equation-by-equation estimator…

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…

波动率模型中的风险参数估计AI 解读

This paper introduces the concept of risk parameter in conditional volatility models of the form ϵt=σt(θ0)ηt and develops statistical procedures to estimate this parameter. For a given risk measure r, the risk parameter is expressed as a function of the volatility coefficients θ0 and the risk, r(ηt), of the innovation process. A two-step method is proposed to successively estimate these quantities. An alternative one-step approach, relying on a reparameterization of the…

评论AI 解读

In this interesting article, the authors developed and studied a non-Gaussian quasi-maximum likelihood (NGQML) method for estimating GARCH(p, q) models. The standard Gaussian QML estimator for gene...

无需正性约束的 GARCH 模型：指数 GARCH 还是对数 GARCH？AI 解读

This paper provides a probabilistic and statistical comparison of the log-GARCH and EGARCH models, which both rely on multiplicative volatility dynamics without positivity constraints. We compare the main probabilistic properties (strict stationarity, existence of moments, tails) of the EGARCH model, which are already known, with those of an asymmetric version of the log-GARCH. The quasi-maximum likelihood estimation of the log-GARCH parameters is shown to be strongly…

时间序列边际分布的估计及其在重尾分布中的应用AI 解读

This article addresses estimating parametric marginal densities of stationary time series in the absence of precise information on the dynamics of the underlying process. We propose using an estimator obtained by maximization of the “quasi-marginal” likelihood, which is a likelihood written as if the observations were independent. We study the effect of the (neglected) dynamics on the asymptotic behavior of this estimator. The consistency and asymptotic normality of the…

非平稳非对称 GARCH 模型的统计推断AI 解读

This paper considers the statistical inference of the class of asymmetric power-transformed $\operatorname{GARCH}(1,1)$ models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two…

考虑估计误差调整的风险价值AI 解读

Standard risk measures, such as the value-at-risk (VaR), or the expected shortfall, have to be estimated, and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on n observations of the profit and loss variable induces an asymptotic bias of order 1/ n in the coverage probabilities. This paper shows how to correct for this bias by introducing a new estimator of the VaR,…

条件异方差过程幂函数的最优预测AI 解读

Summary In conditionally heteroscedastic models, the optimal prediction of powers, or logarithms, of the absolute value has a simple expression in terms of the volatility and an expectation involving the independent process. A natural procedure for estimating this prediction is to estimate the volatility in the first step, for instance by Gaussian quasi-maximum-likelihood or by least absolute deviations, and to use empirical means based on rescaled innovations to estimate…

一类多元非对称GARCH模型的准极大似然估计AI 解读

We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameters of a class of multivariate asymmetric generalized autoregressive conditionally heteroskedastic processes, allowing for cross leverage effects. The conditions required to establish the asymptotic properties of the QMLE are mild and coincide with the minimal ones in the univariate case. In particular, no moment assumption is made on the observed…

GARCH 模型的两阶段非高斯 QML 估计与高斯 QMLE 效率检验AI 解读

In generalized autoregressive conditional heteroskedastic (GARCH) models, the standard identifiability assumption that the variance of the iid process is equal to 1 can be replaced by an alternative moment assumption. We show that, for estimating the original specification based on the standard identifiability assumption, efficiency gains can be expected from using a quasi-maximum likelihood (QML) estimator based on a non Gaussian density and a reparameterization based on an…

结合非参数预测与最优线性时间序列预测AI 解读

We introduce a semiparametric procedure for more efficient prediction of a strictly stationary process admitting an ARMA representation. The procedure is based on the estimation of the ARMA representation, followed by a nonparametric regression where the ARMA residuals are used as explanatory variables. Compared to standard nonparametric regression methods, the number of explanatory variables can be reduced because our approach exploits the linear dependence of the process.…

LARCH 模型中极大似然估计的不一致性与加权最小二乘推断AI 解读

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long memory modeling when infinite orders are allowed. However, the (quasi-)maximum likelihood estimator is, in general, inconsistent. A self-weighted least-squares estimator is proposed and is shown to be asymptotically normal. A…

一般非线性 AR(1) 模型的线性性上确界检验AI 解读

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a…

GARCH 系数为零的检验：标准检验修正与相对效率比较AI 解读

This article is concerned with testing the nullity of coefficients in generalized autoregressive conditionally heteroscedastic (GARCH) models. The problem is nonstandard because the quasi-maximum likelihood estimator is subject to positivity constraints. This article establishes the asymptotic null and local alternative distributions of Wald, score, and quasi-likelihood ratio tests. Efficiency comparisons under fixed alternatives are considered. Two cases of special interest…

无需观测过程矩假设的一般 GARCH(1,1) 模型混合性质AI 解读

We consider general, and possibly nonparametric, GARCH(1,1) processes. First we give conditions for the existence and the uniqueness of stationary ergodic solutions. Then we identify additional conditions for geometric ergodicity. These conditions consist of mild restrictions on the distribution of the latent independent process. No moment assumption is made on the generalized autoregressive conditionally heteroskedastic (GARCH) process. Applications to the asymptotic…