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用多元分数布朗运动建模与预测已实现波动率AI 解读

A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility (RV). We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel method to estimate model parameters, establishing its consistency and asymptotic normality. Additionally, we develop a time-reversibility test, which is typically not rejected by RV data. When the data generating process is a…

基于广义 Fisher 变换的多元随机波动率模型AI 解读

Modeling multivariate stochastic volatility (MSV) can pose significant challenges, particularly when both variances and covariances are time-varying. In this study, we tackle these complexities by introducing novel MSV models based on the generalized Fisher transformation (GFT) proposed by Archakov and Hansen (2021). Our model exhibits remarkable flexibility, ensuring the positive-definiteness of the variance–covariance matrix, and disentangling the driving forces of…

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…

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…

潜变量模型与错设模型的偏差信息准则AI 解读

Deviance information criterion (DIC) has been widely used for Bayesian model comparison, especially after Markov chain Monte Carlo (MCMC) is used to estimate candidate models. This paper first studies the problem of using DIC to compare latent variable models when DIC is calculated from the conditional likelihood. In particular, it is shown that the conditional likelihood approach undermines theoretical underpinnings of DIC. A new version of DIC, namely DICL, is proposed to…

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…

一种半参数随机波动率模型AI 解读

In this paper the correlation structure in the classical leverage stochastic volatility (SV) model is generalized based on a linear spline. In the new model the correlation between the return and volatility innovations is time varying and depends nonparametrically on the type of news arrived to the market. Theoretical properties of the proposed model are examined. The model estimation and comparison are conducted by Bayesian methods. The performance of the estimates are…

潜变量模型中的贝叶斯假设检验AI 解读

Hypothesis testing using Bayes factors (BFs) is known not to be well defined under the improper prior. In the context of latent variable models, an additional problem with BFs is that they are difficult to compute. In this paper, a new Bayesian method, based on the decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that…

基于两阶段已实现波动率的离散观测扩散过程估计AI 解读

This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in [Jacod, J., 1994. Limit of random measures associated with the increments of a Brownian semiartingal. Working paper, Laboratoire de Probabilities, Universite Pierre et Marie Curie, Paris] and [Barndorff-Nielsen, O., Shephard, N., 2002.…

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用于比较随机波动率模型的偏差信息准则AI 解读

stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components, and heavy-tailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this article is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It…