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分数 Ornstein–Uhlenbeck 过程的谱密度AI 解读

This paper introduces a novel and easy-to-implement method for accurately approximating the spectral density of discretely sampled fractional Ornstein–Uhlenbeck (fOU) processes. The method offers a substantial reduction in approximation error, particularly within the rough region of the fractional parameter H∈(0, 0.5). This approximate spectral density has the potential to enhance the performance of estimation methods and hypothesis testing that make use of spectral…

强依赖误差下爆炸性行为的稳健检验AI 解读

A heteroskedasticity-autocorrelation robust (HAR) test statistic is proposed to test for the presence of explosive roots in financial or real asset prices when the equation errors are strongly dependent. Limit theory for the test statistic is developed and extended to heteroskedastic models. The new test has stable size properties unlike conventional test statistics that typically lead to size distortion and inconsistency in the presence of strongly dependent equation…

使用分数 Ornstein–Uhlenbeck 过程建模与预测已实现波动率AI 解读

This paper proposes to model and forecast realized volatility (RV) using the fractional Ornstein–Uhlenbeck (fO–U) process with a general Hurst parameter, H. A two-stage method is introduced for estimating parameters in the fO–U process based on discrete-sampled observations. In the first stage, H is estimated based on the ratio of two second-order differences of observations from different frequencies. In the second stage, with the estimated H, the other parameters of the…

多项式趋势下的泡沫检验AI 解读

Summary This paper develops the asymptotic theory of the least squares estimator of the autoregressive (AR) coefficient in an AR(1) regression with intercept when data is generated from a polynomial trend model in different forms. It is shown that the commonly used right-tailed unit root tests tend to favour the explosive alternative. A new procedure, which implements the right-tailed unit root tests in an AR(2) regression, is proposed. It is shown that, when the data…

连续时间模型的网格自助法AI 解读

This article proposes the new grid bootstrap to construct confidence intervals (CI) for the persistence parameter in a class of continuous-time models. It is different from the standard grid bootstrap of Hansen in dealing with the initial condition. The asymptotic validity of the CI is discussed under the in-fill scheme. The modified grid bootstrap leads to uniform inferences on the persistence parameter. Its improvement over in-fill asymptotics is achieved by expanding the…

随机系数连续时间系统：极端样本路径行为检验AI 解读

This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behavior according to specific regions of the parameter space that open up the potential for testing these forms of extreme behavior. A two-stage approach that employs realized…

分数 Vasicek 模型漂移参数估计的渐近理论AI 解读

This article develops an asymptotic theory for estimators of two parameters in the drift function in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model with long-range dependence is assumed to be driven by a fractional Brownian motion with the Hurst parameter greater than or equal to one half. It is shown that, when the Hurst parameter is known, the asymptotic theory for the persistence parameter depends…

基于MCMC输出的模型设定检验AI 解读

Two test statistics are proposed to determine model specification after a model is estimated by an MCMC method. The first test is the MCMC version of IOSA test and its asymptotic null distribution is normal. The second test is motivated from the power enhancement technique of Fan et al. (2015). It combines a component (J1) that tests a null point hypothesis in an expanded model and a power enhancement component (J0) obtained from the first test. It is shown that J0 converges…

均值结构断点估计的新分布理论AI 解读

Based on the Girsanov theorem, this paper obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model. The exact distribution is asymmetric and tri-modal, indicating that the estimator is biased. These two properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in the discrete time model, suggesting the classical long-span asymptotic theory is…

含温和爆炸性回归量的连续系统推断AI 解读

New limit theory is developed for co-moving systems with explosive processes, connecting continuous and discrete time formulations. The theory uses double asymptotics with infill (as the sampling interval tends to zero) and large time span asymptotics. The limit theory explicitly involves initial conditions, allows for drift in the system, is provided for single and multiple explosive regressors, and is feasible to implement in practice. Simulations show that double…

爆炸性连续时间模型的双重渐近理论AI 解读

This paper establishes a double asymptotic theory for explosive continuous time Lévy-driven processes and the corresponding exact discrete time models. The double asymptotic theory assumes the sample size diverges because the sampling interval (h) shrinks to zero and the time span (N) diverges. Both the simultaneous and sequential double asymptotic distributions are derived. In contrast to the long-time-span asymptotics (N→∞ with fixed h) where no invariance principle…

连续时间模型的计量分析：Phillips 工作综述与若干新结果AI 解读

Econometric analysis of continuous time models has drawn the attention of Peter Phillips for 40 years, resulting in many important publications by him. In these publications he has dealt with a wide range of continuous time models and the associated econometric problems. He has investigated problems from univariate equations to systems of equations, from asymptotic theory to finite sample issues, from parametric models to nonparametric models, from identification problems to…

连续时间模型中均值回复参数估计的偏差AI 解读

It is well known that for continuous time models with a linear drift standard estimation methods yield biased estimators for the mean reversion parameter both in finite discrete samples and in large in-fill samples. In this paper, we obtain two expressions to approximate the bias of the least squares/maximum likelihood estimator of the mean reversion parameter in the Ornstein–Uhlenbeck process with a known long run mean when discretely sampled data are available. The first…

次贷危机期间金融泡沫起止时间的测定AI 解读

A new recursive regression methodology is introduced to analyze the bubble characteristics of various financial time series during the subprime crisis. The methods modify a technique proposed in Phillips, Wu, and Yu (2011) and provide a technology for identifying bubble behavior with consistent dating of their origination and collapse. The tests serve as an early warning diagnostic of bubble activity and a new procedure is introduced for testing bubble migration across…

多元与一元扩散过程估计中的偏差AI 解读

Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic…

时间序列估计中的经验特征函数AI 解读

Because the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. The method is applied to estimate the stable…

短期利率连续时间模型的高斯估计方法AI 解读

This paper proposes a Gaussian estimator for nonlinear continuous time models of the short-term interest rate. The approach is based on a stopping time argument that produces a normalizing transformation facilitating the use of a Gaussian likelihood. A Monte Carlo study shows that the finite-sample performance of the proposed procedure offers an improvement over the discrete approximation method proposed by Nowman (1997). An em-pirical application to US and British interest…