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稳定型 Cox–Ingersoll–Ross 模型的波动率与跳跃活跃度估计AI 解读

We consider the parametric estimation of the volatility and jump activity in a stable Cox-Ingersoll-Ross ($α$-stable CIR) model driven by a standard Brownian Motion and a non-symmetric stable Lévy process with jump activity $α\in (1,2)$. The main difficulties to obtain rate efficiency in estimating these quantities arise from the superposition of the diffusion component with jumps of infinite variation. Extending the approach proposed in Mies (2020), we address the joint…

用于高维协方差矩阵的层级 DCC-HEAVY 模型AI 解读

We introduce a HD DCC-HEAVY class of hierarchical-type factor models for high-dimensional covariance matrices, employing the realized measures built from higher-frequency data. The modelling approach features straightforward estimation and forecasting schemes, independent of the cross-sectional dimension of the assets under consideration, and accounts for sophisticated asymmetric dynamics in the covariances. Empirical analyses suggest that the HD DCC-HEAVY models have a…

粗糙波动率的非参数检验AI 解读

We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test utilizes the fact that volatility is rough if and only if volatility increments are negatively autocorrelated at high frequencies. It is based on the sample autocovariance of increments of spot volatility estimates computed from high-frequency…

通过高维贝叶斯协整构建低波动股票组合AI 解读

We employ a Bayesian modelling technique for high dimensional cointegration estimation to construct low volatility portfolios from a large number of stocks. The proposed Bayesian framework effectively identifies sparse and important cointegration relationships amongst large baskets of stocks across various asset spaces, resulting in portfolios with reduced volatility. Such cointegration relationships persist well over the out-of-sample testing time, providing practical…

通过相关系数多重检验正则化股票收益协方差矩阵AI 解读

This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock returns. The approach involves simultaneous testing of all pairwise correlations, followed by setting non-statistically significant elements to zero. This adaptive thresholding is achieved through sign-based Monte Carlo resampling within…

通过最优传输自动校正异常值AI 解读

In this paper, we propose a novel conceptual framework to detect outliers using optimal transport with a concave cost function. Conventional outlier detection approaches typically use a two-stage procedure: first, outliers are detected and removed, and then estimation is performed on the cleaned data. However, this approach does not inform outlier removal with the estimation task, leaving room for improvement. To address this limitation, we propose an automatic outlier…

检验因子增强回归中的稀疏特异成分AI 解读

We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative augmenting model with sparse idiosyncratic components. The asymptotic properties of the test are established under time series dependence and polynomial tails. We outline a data-driven rule to select the tuning parameter and prove its theoretical validity. In simulation experiments, our procedure exhibits high power against sparse alternatives and low power…

高维金融时间序列因子模型中的块对角特异协方差估计AI 解读

Estimation of high-dimensional covariance matrices in latent factor models is an important topic in many fields and especially in finance. Since the number of financial assets grows while the estimation window length remains of limited size, the often used sample estimator yields noisy estimates which are not even positive definite. Under the assumption of latent factor models, the covariance matrix is decomposed into a common low-rank component and a full-rank idiosyncratic…

大型偏斜 t Copula 模型与日内股票收益的非对称依赖AI 解读

Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do…

干扰参数不确定性对实用数据科学模型统计推断的影响AI 解读

For multiple reasons -- such as avoiding overtraining from one data set or because of having received numerical estimates for some parameters in a model from an alternative source -- it is sometimes useful to divide a model's parameters into one group of primary parameters and one group of nuisance parameters. However, uncertainty in the values of nuisance parameters is an inevitable factor that impacts the model's reliability. This paper examines the issue of uncertainty…

粗糙度指数及其无模型估计AI 解读

Motivated by pathwise stochastic calculus, we say that a continuous real-valued function $x$ admits the roughness exponent $R$ if the $p^{\text{th}}$ variation of $x$ converges to zero if $p>1/R$ and to infinity if $p<1/R$. For the sample paths of many stochastic processes, such as fractional Brownian motion, the roughness exponent exists and equals the standard Hurst parameter. In our main result, we provide a mild condition on the Faber--Schauder coefficients of $x$ under…

粗糙波动率的统计推断：中心极限定理AI 解读

In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter $H < 0.5$. In this paper, we derive a consistent and asymptotically mixed normal estimator of $H$ based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting…

数字时代电子金融市场的概率模型与统计方法AI 解读

The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional…

Cluster GARCH：具有聚类依赖结构的多元波动模型AI 解读

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 the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH…

结合稳健协方差与条件风险价值约束的投资组合优化AI 解读

The measure of portfolio risk is an important input of the Markowitz framework. In this study, we explored various methods to obtain a robust covariance estimators that are less susceptible to financial data noise. We evaluated the performance of large-cap portfolio using various forms of Ledoit Shrinkage Covariance and Robust Gerber Covariance matrix during the period of 2012 to 2022. Out-of-sample performance indicates that robust covariance estimators can outperform the…

预测回归中平稳或持续随机系数的检验AI 解读

This study considers tests for coefficient randomness in predictive regressions. Our focus is on how tests for coefficient randomness are influenced by the persistence of random coefficient. We show that when the random coefficient is stationary, or I(0), Nyblom's (1989) LM test loses its optimality (in terms of power), which is established against the alternative of integrated, or I(1), random coefficient. We demonstrate this by constructing a test that is more powerful…

用GARCH与机器学习建模和预测能源市场波动率AI 解读

This paper presents a comparative analysis of univariate and multivariate GARCH-family models and machine learning algorithms in modeling and forecasting the volatility of major energy commodities: crude oil, gasoline, heating oil, and natural gas. It uses a comprehensive dataset incorporating financial, macroeconomic, and environmental variables to assess predictive performance and discusses volatility persistence and transmission across these commodities. Aspects of…

具有高维资产特征的动态潜在因子模型AI 解读

We develop novel estimation procedures with supporting econometric theory for a dynamic latent-factor model with high-dimensional asset characteristics, that is, the number of characteristics is on the order of the sample size. Utilizing the Double Selection Lasso estimator, our procedure employs regularization to eliminate characteristics with low signal-to-noise ratios yet maintains asymptotically valid inference for asset pricing tests. The crypto asset class is…

Lasso 筛选后的提升回归与股票收益线性预测AI 解读

We consider a two-stage estimation method for linear regression. First, it uses the lasso in Tibshirani (1996) to screen variables and, second, re-estimates the coefficients using the least-squares boosting method in Friedman (2001) on every set of selected variables. Based on the large-scale simulation experiment in Hastie et al. (2020), lassoed boosting performs as well as the relaxed lasso in Meinshausen (2007) and, under certain scenarios, can yield a sparser model.…

多元 Hawkes 过程的稀疏性检验AI 解读

Multivariate Hawkes processes (MHP) are a class of point processes in which events at different coordinates interact through mutual excitation. The weighted adjacency matrix of the MHP encodes the strength of the relations, and shares its support with the causal graph of interactions of the process. We consider the problem of testing for causal relationships across the dimensions of a marked MHP. The null hypothesis is that a joint group of adjacency coefficients are null,…

聚类多时间序列波动率的非参数检验AI 解读

Contagion arising from clustering of multiple time series like those in the stock market indicators can further complicate the nature of volatility, rendering a parametric test (relying on asymptotic distribution) to suffer from issues on size and power. We propose a test on volatility based on the bootstrap method for multiple time series, intended to account for possible presence of contagion effect. While the test is fairly robust to distributional assumptions, it depends…

英伟达次日股价预测：LSTM、MLP、ARIMA 与 ARIMA-GARCH 比较AI 解读

Forecasting stock prices remains a considerable challenge in financial markets, bearing significant implications for investors, traders, and financial institutions. Amid the ongoing AI revolution, NVIDIA has emerged as a key player driving innovation across various sectors. Given its prominence, we chose NVIDIA as the subject of our study.

含积分分数成分过程的跳跃检验与 Hurst 指数的跳跃稳健推断AI 解读

We develop and investigate a test for jumps based on high-frequency observations of a fractional process with an additive jump component. The Hurst exponent of the fractional process is unknown. The asymptotic theory under infill asymptotics builds upon extreme value theory for weakly dependent, stationary time series and extends techniques for the semimartingale case from the literature. It is shown that the statistic on which the test is based on weakly converges to a…

具有群组结构的高维稳健因子分析AI 解读

In this paper, we focus on exploiting the group structure for large-dimensional factor models, which captures the homogeneous effects of common factors on individuals within the same group. In view of the fact that datasets in macroeconomics and finance are typically heavy-tailed, we propose to identify the unknown group structure using the agglomerative hierarchical clustering algorithm and an information criterion with the robust two-step (RTS) estimates as initial values.…