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超高维时变协方差模型的估计AI 解读

Estimation of time-varying covariances is a key input in risk management and asset allocation. ARCH-type multivariate models are used widely for this purpose. Estimation of such models is computationally costly and parameter estimates are meaningfully biased when applied to a moderately large number of assets. Here, we propose a novel estimation approach that suffers from neither of these issues, even when the number of assets is in the hundreds. The theory of this new…

多变量已实现准极大似然：异步交易下股票价格协变动估计AI 解读

Estimating the covariance between assets using high frequency data is challenging due to market microstructure effects and asynchronous trading. In this paper we develop a multivariate realised quasi maximum likelihood (QML) approach, carrying out inference as if the observations arise from an asynchronously observed vector scaled Brownian model observed with error. Under stochastic volatility the resulting realised QML estimator is positive definite, uses all available…

超大规模协方差矩阵的复合已实现核估计及投资组合选择应用AI 解读

We propose a composite realized kernel to estimate the ex-post covariation of asset prices. These measures can in turn be used to forecast the covariation of future asset returns. Composite realized kernels are a data-efficient method, where the covariance estimate is composed of univariate realized kernels to estimate variances and bivariate realized kernels to estimate correlations. We analyze the merits of our composite realized kernels in an ultra high-dimensional…

多元旋转 ARCH 模型AI 解读

This paper introduces a new class of multivariate volatility models which is easy to estimate using covariance targeting, even with rich dynamics. We call them rotated ARCH (RARCH) models. The basic structure is to rotate the returns and then to fit them using a BEKK-type parameterization of the time-varying covariance whose long-run covariance is the identity matrix. This yields the rotated BEKK (RBEKK) model. The extension to DCC-type parameterizations is given,…

基于高频数据的多元波动率HEAVY模型AI 解读

SUMMARY This paper introduces a new class of multivariate volatility models that utilizes high‐frequency data. We discuss the models' dynamics and highlight their differences from multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models. We also discuss their covariance targeting specification and provide closed‐form formulas for multi‐step forecasts. Estimation and inference strategies are outlined. Empirical results suggest that the HEAVY model…

多元已实现核：噪声与非同步交易下协变动的一致半正定估计AI 解读

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement error of certain types and can also handle non-synchronous trading. It is the first estimator which has these three properties which are all essential for empirical work in this area. We derive the large sample asymptotics of this estimator and assess its accuracy using a…

已实现核估计量的子采样AI 解读

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for…

利用高频波动率信息预测：HEAVY 模型AI 解读

Abstract This paper studies in some detail a class of high‐frequency‐based volatility (HEAVY) models. These models are direct models of daily asset return volatility based on realised measures constructed from high‐frequency data. Our analysis identifies that the models have momentum and mean reversion effects, and that they adjust quickly to structural breaks in the level of the volatility process. We study how to estimate the models and how they perform through the credit…

检验重要性抽样背后的假设AI 解读

Importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals. Its reliable use requires the sampler to possess a variance, for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral. However, this assumption is seldom checked. In this paper we use extreme value theory to empirically assess the appropriateness of this assumption. Our main application is the stochastic volatility…

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金融计量中双幂变差的极限定理AI 解读

In this paper we provide an asymptotic analysis of generalized bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation, and bipower variations that have been highlighted in recent years in financial econometrics. The analysis is carried out under some rather general Brownian semimartingale assumptions, which allow for standard leverage effects.Ole E. Barndorff-Nielsen's work is…

跳跃对收益与已实现方差的影响：时间变换 Lévy 过程的计量分析AI 解读

In order to assess the effect of jumps on realised variance calculations, we study some of the econometric properties of time-changed Lévy processes. We show that in general realised variance is an inconsistent estimator of the time-change, however we can derive the second order properties of realised variances and use these to estimate the parameters of such models. Our analytic results give a first indication of the degrees of inconsistency of realised variance as an…

潜在广义 ARCH 结构的似然估计AI 解读

GARCH models are commonly used as latent processes in econometrics, financial economics, and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our…

This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions, and covariances change through…

利用已实现方差估计二次变差AI 解读

Abstract This paper looks at some recent work on estimating quadratic variation using realized variance (RV)—that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high‐frequency financial return data. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent (as M → ∞) estimator of quadratic variation (QV). We express concern that without additional assumptions it…

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已实现波动率的计量分析及其在随机波动率模型估计中的应用AI 解读

Summary The availability of intraday data on the prices of speculative assets means that we can use quadratic variation-like measures of activity in financial markets, called realized volatility, to study the stochastic properties of returns. Here, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic distribution of the realized volatility error—the difference between realized volatility and the discretized integrated…

非高斯 Ornstein–Uhlenbeck 模型及其金融经济学应用AI 解读

Summary Non-Gaussian processes of Ornstein–Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical analysis. Their power is illustrated by a sustained application of OU processes within the context of finance and econometrics. We construct…

资产收益非对称随机波动率模型的估计AI 解读

A stochastic volatility model may be estimated by a quasi-maximum likelihood procedure by transforming to a linear state space form. The method is extended to handle correlation between the two disturbances in the model and applied to data on stock returns.

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