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Bespoke realized volatility: Tailored measures of risk for volatility prediction

定制已实现波动率:面向波动率预测的风险度量

Standard realized volatility (RV) measures estimate the latent volatility of an asset price using high frequency data with no reference to how or where the estimate will subsequently be used. This paper presents methods for “tailoring” the estimate of volatility to the application in which it will be used. For example, if the volatility measure will be used in a specific parametric forecasting model, it may be possible to exploit that knowledge to construct a better measure…

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A multivariate realized GARCH model

多元已实现 GARCH 模型

We propose a novel class of multivariate GARCH models that incorporate realized measures of volatility and correlations. The key innovation is an unconstrained vector parametrization of the conditional correlation matrix, which enables the use of factor models for correlations. This approach elegantly addresses the main challenge faced by multivariate GARCH models in high-dimensional settings. As an illustration, we explore block correlation matrices that naturally simplify…

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Probability distributions for realized covariance measures

已实现协方差度量的概率分布

Realized covariance measures (RCs) are an essential input for assessing the risks of different investment allocations. Thus, it is useful to model and forecast them. To this end, a realistic distributional assumption is needed. In this paper, we compare all probability distributions that have so far in the literature been applied to time-series of RCs. We derive them in a unified framework based on their stochastic representations using random lower and upper triangular…

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BUMVU estimators

一致最小方差无偏分块估计量

We provide necessary and sufficient conditions for an (Unbiased) Block estimator to have Uniformly Minimum Variance. Our theory parallels the theory of UMVU estimation, the main novel insight being the focus on the covariance among blocks. We use this theory to derive lower variance bounds for block estimators of functionals of high-frequency volatility when the block size is fixed. We further show the relevance of the new theory for the classical problem of estimation of…

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High dimensional regression coefficient test with high frequency data

高频数据下的高维回归系数检验

This paper presents the first study on high-dimensional regression coefficient tests with high-frequency financial data. These tests allow the number of regressors to be larger than the number of observations within each estimation block and can grow to infinity in asymptotics. In this paper, the sum-type test and max-type test have been proposed, where the former is suitable for the dense alternative (many small betas) and the latter is suitable for the sparse alternative…

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Robust realized integrated beta estimator with application to dynamic analysis of integrated beta

稳健的已实现积分贝塔估计及其动态分析

In this paper, we develop a robust non-parametric realized integrated beta estimator using high-frequency financial data contaminated by microstructure noise, which is robust to the stylized features, such as the time-varying beta and the price-dependent and autocorrelated microstructure noise. With this robust realized integrated beta estimator, we investigate dynamic structures of integrated betas and find a persistent autoregressive structure. To model this dynamic…

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Realized drift

已实现漂移

Drift and volatility are two mainsprings of asset price dynamics. While volatilities have been studied extensively in the literature, drifts are commonly believed to be impossible to estimate and largely ignored in the literature. This paper shows how to detect drift using realized autocovariance implemented on high-frequency data. We use a theoretical treatment in which the classical model for the efficient price, an Itō semimartingale possibly contaminated by…

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Intraday volatility patterns from short-dated options

利用短期期权估计日内波动率模式

We propose a nonparametric estimator for the deterministic periodic component of volatility from short-dated options within an in-fill asymptotic setting. The estimator uses options with zero and one day to expiration sampled at high-frequency during a trading day. At each point in time, we aggregate the options to form nonparametric estimates of conditional risk-neutral expectations of future integrated return variation for the two available option tenors. A suitable ratio…

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Robust estimation of integrated and spot volatility

积分波动率与瞬时波动率的稳健估计

We introduce a new method to estimate the integrated volatility (IV) and the spot volatility (SV) based on noisy high-frequency data. Our method employs the ReMeDI approach introduced by Li and Linton (2022) to estimate the moments of microstructure noise and thereby eliminate their influence, and the pre-averaging method to target the volatility parameter. The method is robust: it can be applied when the efficient price exhibits stochastic volatility and jumps, the…

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Estimation of common factors for microstructure noise and efficient price in a high-frequency dual factor model

高频双因子模型中微观结构噪声与有效价格共同因子的估计

We develop the Double Principal Component Analysis (DPCA) based on a dual factor structure for high-frequency intraday returns contaminated with microstructure noise. The dual factor structure allows a factor structure for microstructure noise in addition to the factor structure for efficient log-prices. We construct estimators of factors for both efficient log-prices and microstructure noise as well as their common components, and provide uniform consistency of these…

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Extremal correlation coefficient for functional data

函数型数据的极端相关系数

Abstract We propose a coefficient that measures extremal dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in two significant ways: (i) it is designed to measure dependence between curves; and (ii) it focuses only on extreme curves. The new coefficient is derived within the framework of regular variation in Banach spaces. A consistent estimator is proposed and justified by an asymptotic analysis and a simulation…

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NONPARAMETRIC ESTIMATION OF LARGE SPOT VOLATILITY MATRICES FOR HIGH-FREQUENCY FINANCIAL DATA

高频金融数据的大型瞬时波动率矩阵非参数估计

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalized shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot…

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OPTIMAL MODEL AVERAGING FOR JOINT VALUE-AT-RISK AND EXPECTED SHORTFALL REGRESSION

风险价值与期望损失联合回归的最优模型平均

Since the implementation of the Basel III Accord, expected shortfall (ES) has gained increasing attention from regulators as a complement to value-at-risk (VaR). The problem of elicitability for ES makes jointly modeling VaR and ES a popular method to study ES. In this article, we develop model averaging for joint VaR and ES regression models that selects the two weight vectors by minimizing a jackknife criterion. We show the large sample properties of the estimators under…

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A Factor-Copula Latent-Vine Time Series Model for Extreme Flood Insurance Losses

极端洪水保险损失的因子 Copula 潜在藤时间序列模型

Statistical inference on the dependence of multivariate extremes poses notable challenges, particularly in contexts characterized by large dimensions and sparse extreme observations. While copula models provide flexible parametric methods for dependence modeling, caution is warranted when using them for extremal dependence inference or tail extrapolation. In this article, a novel class of factor-vine copula models is introduced. It is designed for modeling the dependence of…

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Estimation of Out-of-Sample Sharpe Ratio for High Dimensional Portfolio Optimization

高维投资组合优化中的样本外夏普比率估计

Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the in-sample estimated covariance to evaluate the out-of-sample Sharpe, especially in the high dimensional settings. In this paper, we propose a novel method to estimate the out-of-sample Sharpe ratio using only in-sample data, based on…

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Mutually Exciting Point Processes with Latency

具有响应延迟的相互激发点过程

A novel statistical approach to estimating latency, defined as the time it takes to learn about an event and generate response to this event, is proposed. Our approach only requires a multidimensional point process describing event times, which circumvents the use of more detailed datasets which may not even be available. We consider the class of parametric Hawkes models capturing clustering effects and define latency as a known function of kernel parameters, typically the…

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Matrix-based Prediction Approach for Intraday Instantaneous Volatility Vector

日内瞬时波动率向量的矩阵预测方法

In this article, we introduce a novel method for predicting intraday instantaneous volatility based on Itô semimartingale models using high-frequency financial data. Several studies have highlighted stylized volatility time series features, such as interday auto-regressive dynamics and the intraday U-shaped pattern. To accommodate these volatility features, we propose an interday-by-intraday instantaneous volatility matrix process that can be decomposed into low-rank…

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Detecting Giver and Receiver Spillover Groups in Large Vector Autoregressions

大型 VAR 中溢出发送组与接收组的识别

I propose an algorithm that partitions the series of a large vector autoregression (VAR) into groups based on the spillover structure. The novelty of the procedure is that it is capable of simultaneously detecting both the giver and receiver group structures. I study the properties of the algorithm when the data are generated by a class of network-based VAR models and show that it consistently detects the groups within this class. The methodology is applied to study the…

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Drift Bursts in Pure Jumps: Detection and Application to Bitcoin

纯跳过程中的漂移爆发:检测及比特币应用

This article proposes a new nonparametric test for detecting short-lived locally explosive trends (drift bursts) in pure-jump processes. The new test is designed specifically to detect intraday flash crashes and gradual jumps in cryptocurrency prices recorded at a high frequency. Empirical analysis shows that drift bursts in bitcoin price occur, on average, every second day. Their economic importance is highlighted by showing that hedge funds holding cryptocurrency in their…

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Local Predictability in High Dimensions

高维环境下的局部可预测性

We propose a time series forecasting method designed to effectively handle large sets of predictive signals, many of which may be irrelevant or short-lived over time. Our method transforms predictive signals into candidate density forecasts via time-varying coefficient models, and subsequently combines them into an aggregate density forecast via time-varying subset combination. The approach is computationally efficient because it uses online prediction and updating. Through…

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Regressions under Adverse Conditions

不利情景下的回归

We introduce a new regression method that relates the mean of an outcome variable to covariates, under the “adverse condition” that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse scenarios, which receive increasing interest in economics and finance, among many others. In the terminology of the systemic risk literature, our method can be interpreted as a regression for the Marginal Expected Shortfall. We propose a two-step…

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Dynamic Conditional Correlations with Partial Information Pooling

部分信息汇集的动态条件相关模型

We propose a novel Dynamic Conditional Correlation model with Conditional Linear Information Pooling (CLIP-DCC) which endogenously determines an optimal degree of commonality in the correlation innovations. Effectively, this allows a part of the update of each individual correlation to parsimoniously depend on the information contained in all asset return pairs. In contrast to existing approaches, such as the Dynamic EquiCOrrelation (DECO) model, the CLIP-DCC model does not…

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Panel Quantile GARCH Models under Homogeneity

同质结构下的面板分位数 GARCH 模型

Empirical evidence indicates that the estimates of GARCH parameters cluster in a panel of financial assets, potentially due to assets with similar exposure to common market risks. To capture the subgroup effect on conditional quantiles of financial asset returns and improve estimation efficiency by pooling information across individuals within the same group, this article introduces the panel quantile GARCH model with homogeneous structures in the coefficient functions. A…

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Cluster GARCH

聚类 GARCH

We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-driven model for the dynamic correlation structure. We apply the Cluster GARCH…

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