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On the Correlation Structure of Microstructure Noise: A Financial Economic Approach

微观结构噪声的相关结构:金融经济学视角

We introduce the financial economics of market microstructure to the financial econometrics of asset return volatility estimation. In particular, we derive the cross-correlation function between latent returns and market microstructure noise in several leading microstructure environments. We propose and illustrate several corresponding theory-inspired volatility estimators, which we apply to stock and oil prices. Our analysis and results are useful for assessing the validity…

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A test for the rank of the volatility process: The random perturbation approach

波动率过程秩的检验:随机扰动方法

In this paper, we present a test for the maximal rank of the matrix-valued volatility process in the continuous Itô semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Itô semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank…

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Efficient learning via simulation: A marginalized resample-move approach

通过模拟高效学习参数:边际化重抽样—移动方法

In state–space models, parameter learning is practically difficult and is still an open issue. This paper proposes an efficient simulation-based parameter learning method. First, the approach breaks up the interdependence of the hidden states and the static parameters by marginalizing out the states using a particle filter. Second, it applies a Bayesian resample-move approach to this marginalized system. The methodology is generic and needs little design effort. Different…

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Density approximations for multivariate affine jump-diffusion processes

多元仿射跳跃扩散过程的密度近似

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in…

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Predictability of currency carry trades and asset pricing implications

货币套息交易的可预测性及其资产定价含义

This paper studies the time series predictability of currency carry trades, constructed by selecting currencies to be bought or sold against the US dollar, based on forward discounts. Changes in a commodity index, currency volatility and, to a lesser extent, a measure of liquidity predict in-sample the payoffs of dynamically re-balanced carry trades, as evidenced by individual and joint p-values in monthly predictive regressions at horizons up to six months. Predictability…

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Pricing the term structure with linear regressions

用线性回归为利率期限结构定价

We show how to price the time series and cross section of the term structure of interest rates using a three-step linear regression approach. Our method allows computationally fast estimation of term structure models with a large number of pricing factors. We present specification tests favoring a model using five principal components of yields as factors. We demonstrate that this model outperforms the Cochrane and Piazzesi (2008) four-factor specification in out-of-sample…

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Modeling the Conditional Distribution of Daily Stock Index Returns: An Alternative Bayesian Semiparametric Model

股指日收益条件分布建模:一种替代性的贝叶斯半参数模型

This article introduces a new family of Bayesian semiparametric models for the conditional distribution of daily stock index returns. The proposed models capture key stylized facts of such returns, namely, heavy tails, asymmetry, volatility clustering, and the “leverage effect.” A Bayesian nonparametric prior is used to generate random density functions that are unimodal and asymmetric. Volatility is modeled parametrically. The new model is applied to the daily returns of…

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Long-Horizon Return Regressions With Historical Volatility and Other Long-Memory Variables

使用历史波动率及其他长记忆变量的长期收益回归

The predictability of long-term asset returns increases with the time horizon as estimated in regressions of aggregated-forward returns on aggregated-backward predictive variables. This previously established evidence is consistent with the presence of common slow-moving components that are extracted upon aggregation from returns and predictive variables. Long memory is an appropriate econometric framework for modeling this phenomenon. We apply this framework to explain the…

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Large Covariance Estimation by Thresholding Principal Orthogonal Complements

主正交补阈值化方法与高维协方差估计

Summary The paper deals with the estimation of a high dimensional covariance with a conditional sparsity structure and fast diverging eigenvalues. By assuming a sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the principal orthogonal complement thresholding method ‘POET’ to explore such an approximate factor structure with sparsity.…

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Bayesian semiparametric multivariate GARCH modeling

贝叶斯半参数多元GARCH建模

This paper proposes a Bayesian nonparametric modeling approach for the return distribution in multivariate GARCH models. In contrast to the parametric literature the return distribution can display general forms of asymmetry and thick tails. An infinite mixture of multivariate normals is given a flexible Dirichlet process prior. The GARCH functional form enters into each of the components of this mixture. We discuss conjugate methods that allow for scale mixtures and…

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Why Gaussian macro-finance term structure models are (nearly) unconstrained factor-VARs

为何高斯宏观金融期限结构模型几乎是不受约束的因子VAR

This paper explores the implications of filtering and no-arbitrage for the maximum likelihood estimates of the entire conditional distribution of the risk factors and bond yields in Gaussian macro-finance term structure model (MTSM) when all yields are priced imperfectly. For typical yield curves and macro-variables studied in this literature, the estimated joint distribution within a canonical MTSM is nearly identical to the estimate from an economic-model-free factor…

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Inference in nonstationary asymmetric GARCH models

非平稳非对称 GARCH 模型的统计推断

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…

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Volatility occupation times

波动率占用时间

We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a…

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Optimal sparse volatility matrix estimation for high-dimensional Itô processes with measurement errors

含测量误差的高维 Itô 过程稀疏波动率矩阵最优估计

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high-dimensional Itô process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility matrices. By combining the multi-scale and threshold approaches we construct a…

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Modelling volatility by variance decomposition

基于方差分解的波动率建模

In this paper, we propose two parametric alternatives to the standard GJR-GARCH model of Glosten et al. (1993), based on additive and multiplicative decompositions of the variance. They allow the variance of the model to have a smooth time-varying structure. The suggested parameterizations describe structural change in the conditional and unconditional variances where the transition between regimes over time is smooth. The main focus is on the multiplicative decomposition of…

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NONPARAMETRIC INFERENCE FOR CONDITIONAL QUANTILES OF TIME SERIES

时间序列条件分位数的非参数推断

This paper considers model-free hypothesis testing and confidence interval construction for conditional quantiles of time series. A new method, which is based on inversion of the smoothed empirical likelihood of the conditional distribution function around the local polynomial estimator, is proposed. The associated inferential procedures do not require variance estimation, and the confidence intervals are automatically shaped by data. We also construct the bias-corrected…

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ESTIMATION OF AND INFERENCE ABOUT THE EXPECTED SHORTFALL FOR TIME SERIES WITH INFINITE VARIANCE

无限方差时间序列的预期损失估计与推断

We study estimation and inference of the expected shortfall for time series with infinite variance. Both the smoothed and nonsmoothed estimators are investigated. The rate of convergence is determined by the tail thickness parameter, and the limiting distribution is in the stable class with parameters depending on the tail thickness parameter of the time series and on the dependence structure, which makes inference complicated. A subsampling procedure is proposed to carry…

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ESTIMATION-ADJUSTED VAR

考虑估计误差调整的风险价值

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,…

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FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA

利用高频金融数据估计大型波动率矩阵的快速收敛率

Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency data. Many existing estimators of a volatility matrix of small dimensions become inconsistent when the size of the matrix is close to or larger than the sample size. This paper introduces a new type of large volatility matrix estimator based on nonsynchronized high-frequency data, allowing for the presence of microstructure noise. When both the…

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MULTIVARIATE VOLATILITY MODELING OF ELECTRICITY FUTURES

电力期货的多元波动率建模

SUMMARY We model the dynamic volatility and correlation structure of electricity futures of the European Energy Exchange index. We use a new multiplicative dynamic conditional correlation (mDCC) model to separate long‐run from short‐run components. We allow for smooth changes in the unconditional volatilities and correlations through a multiplicative component that we estimate nonparametrically. For the short‐run dynamics, we use a GJR‐GARCH model for the conditional…

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Identification-Robust Estimation and Testing of the Zero-Beta CAPM

零贝塔 CAPM 的识别稳健估计与检验

We propose exact simulation-based procedures for: (i) testing mean-variance efficiency when the zero-beta rate is unknown; (ii) building confidence intervals for the zero-beta rate. On observing that this parameter may be weakly identified, we propose likelihood-ratio-type tests as well as Fieller-type procedures based on a Hotelling-HAC statistic, which are robust to weak identification and allow for non-Gaussian distributions including parametric GARCH structures. The…

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The leverage effect puzzle: Disentangling sources of bias at high frequency

杠杆效应之谜:分解高频估计中的偏误来源

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation…

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Realized Volatility Forecasting in the Presence of Time-Varying Noise

时变噪声下的已实现波动率预测

Observed high-frequency financial prices can be considered as having two components, a true price and a market microstructure noise perturbation. It is an empirical regularity, coherent with classical market microstructure theories of price determination, that the second moment of market microstructure noise is time-varying. We study the optimal, from a finite-sample forecast mean squared error (MSE) standpoint, frequency selection for realized variance in linear variance…

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Dynamic Conditional Correlation: On Properties and Estimation

动态条件相关:性质与估计

This article addresses some of the issues that arise with the Dynamic Conditional Correlation (DCC) model. It is proven that the DCC large system estimator can be inconsistent, and that the traditional interpretation of the DCC correlation parameters can result in misleading conclusions. Here, we suggest a more tractable DCC model, called the cDCC model. The cDCC model allows for a large system estimator that is heuristically proven to be consistent. Sufficient stationarity…

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