Study forecasts volatility and risk in electricity markets using matrix-HAR models.
problem Forecasting volatility and risk in electricity markets.
method Constructed a parsimonious matrix-HAR type model to estimate realized covariation and risk premia in electricity markets.
result Inclusion of longer time horizons and renewable generation information improves forecasts.
Paper proposes a deep learning method for better covariance matrix forecasting.
problem Suboptimal predictive performance in traditional matrix volatility forecasting.
method Riemannian-geometry-aware deep learning framework for symmetric positive definite matrices.
result Our method outperforms traditional approaches in predictive accuracy.
The covariant derivative of the Kähler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically.
VOLARE provides standardized realized volatility measures from financial data.
problem Lack of standardized realized volatility measures from ultra-high-frequency data.
method Asset-specific pipeline for cleaning and sampling data, providing a wide range of realized estimators.
result Comprehensive set of realized estimators for equities, exchange rates, and futures.
A streaming algorithm estimates quadratic covariation from financial data efficiently.
problem Estimating quadratic covariation from ultra-high-frequency financial data with limited memory.
method Formulated multi-scale, realized kernel, pre-averaging, and modulated realized covariance estimators with fixed bandwidth.
result Fixed bandwidth estimators require higher bandwidth for positive semidefiniteness.
Improved covariance matrix forecasting for S&P 500 using factor models and shrinkage.
problem Forecasting large covariance matrices of returns in finance.
method Decompose covariance matrix into firm-level factors and sectoral restrictions. Estimate using VHAR models with LASSO.
result Significantly improved forecasting precision compared to benchmarks.
In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compu…
This paper compares HMC and RNN expressivity using SRT.
problem Comparing expressivity of HMC and RNN models.
method Embed HMC and RNN in a GUM, use SRT to compare structured covariance series.
result Conditions for realizing covariance series by GUM, HMC, or RNN.
Study improves Hayashi-Yoshida estimator for high-dimensional stock covolatility.
problem Inconsistent performance of Hayashi-Yoshida estimator in high dimensions.
method Analyzed the limiting spectral distribution of the Hayashi-Yoshida estimator.
result Established the connection between the estimator's spectrum and the true covariance matrix in high dimensions.
The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for th…
Optimizes treatment allocation using covariates for better outcomes.
problem Improving treatment allocation in multi-armed bandit problems.
method Maximizes a functional of the conditional potential outcome distribution.
result Developed expected regret lower bounds and near minimax optimal policy.
Average Oracle outperforms DCC+NLS in portfolio optimization.
problem Optimizing portfolio performance in volatile markets.
method Comparing the Average Oracle to various DCC+NLS variants.
result The Average Oracle consistently yields higher Sharpe ratios.
We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We show that in the high dimensional case when the dimension p and the observati…
New method tests independence with single nonstationary time series.
problem Testing independence in nonstationary nonlinear time series.
method Time-varying nonlinear regression, local long-run covariance estimation, strong Gaussian approximation.
result First framework for conditional independence testing with a single realization of a nonstationary nonlinear process.
Study analyzes bond price covariation robustly under no-arbitrage conditions.
problem Identifying the number of statistically relevant factors in the bond market.
method Nonparametric analysis of realized covariations in a general no-arbitrage setting.
result A high number of factors is needed to describe term structure evolution and term structure of volatility varies over time.
Method cleans covariance matrices for better statistical inference.
problem Reducing estimation noise in covariance matrices for better statistical inference.
method Robust yet flexible hierarchical ansatz with bootstrap procedure.
result Lower realized risk in global minimum variance portfolios.
The article detects market regimes from covariance matrices using VLSTAR and clustering models.
problem Market regime switching is hard to detect due to time-varying correlation coefficients.
method The article applies VLSTAR and unsupervised hierarchical clustering on monthly realized covariance matrices.
result VLSTAR outperforms clustering in detecting market regimes.
Study on friction forces for nonholonomic systems using affine connections.
problem Realizing nonholonomic constraints with strong friction forces.
method Affine connection approach, covariant derivatives, recursive procedure.
result Approximations of slip velocities and dynamics up to second order.
Develops robust methods for infinite-dimensional stochastic processes.
problem Measuring covariations in stochastic evolution equations in infinite dimensions.
method Asymptotic theory for jump robust measurement of covariations.
result Identifies scaling limits for realized covariations.
We construct the generalized version of covariant Z_3-graded differential calculus introduced by one of us (R.K.), and then extended to the case of arbitrary Z_N grading. Here our main purpose is to establish the recurrence formulae for the N-th power of covariant q-differential D_q = d_q + A and to analyze more closel…
We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available market returns is often of similar order to the number of assets, so that t…
CASP improves portfolio optimization by considering asset covariance.
problem Infeasibility in cardinality-constrained portfolio optimization.
method CASP uses volatility-normalized selection and covariance-aware projection.
result CASP-Basic delivers lower portfolio variance than standard Euclidean repair.
Study examines how imputation accuracy affects prediction accuracy in regression problems with missing covariates.
problem Missing covariates in regression or classification problems.
method Simulation and empirical analysis using UCI datasets and statistical inference.
result Imputation accuracy impacts prediction accuracy, especially with Machine Learning methods.
We describe a set of conformally covariant boundary operators associated to the sixth-order GJMS operator on a conformally invariant class of manifolds which includes compactifications of Poincaré--Einstein manifolds. This yields a conformally covariant energy functional for the sixth-order GJMS operator on such manifo…
Enhances UPSA to reduce noise in financial data.
problem Noise in financial data affects UPSA's performance.
method Time-averaging optimal penalty weights and using Average Oracle correlation eigenvalues.
result Combining time-averaging and Average Oracle correlation eigenvalues improves UPSA's performance.
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping
MuyGPs efficiently estimates GP hyperparameters using local cross-validation.
problem Efficiently estimating GP hyperparameters for large datasets.
method Uses nearest neighbors structure and leave-one-out cross-validation.
result Outperforms state-of-the-art competitors in time and prediction accuracy.
Paper estimates Hurst parameter from implied volatilities.
problem Estimating Hurst parameter from implied volatilities.
method Uses covariance between asset return and realized volatility, and applies limit theorems for stochastic volatility models.
result Direct relation between covariance and slope of at-the-money implied volatility established.
Study high-dimensional covariance matrix estimators for complex portfolios, improving financial metrics.
problem Estimating covariance matrices in high-dimensional portfolios with nested and one-factor structures.
method Combining random matrix theory, free probability, deterministic equivalents, and two-step covariance estimators.
result Two-step estimators improve financial metrics in complex and one-factor covariance models.
We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of derivatives in order to gain exposure to an index and/or market factors that may be not di…
We define a new kind of algebroid which fulfills a Leibniz rule, a Jacobi identity twisted by a 3-form H with values in the kernel of the anchor map, and the twist is closed under a naturally occurring exterior covariant derivative. We give examples and define three kinds of cohomology two via realization as Q-struct…
We show that the equivalence problem for three-dimensional Lorentzian manifolds requires at most the fifth covariant derivative of the curvature tensor. We prove that this bound is sharp by exhibiting a class of 3D Lorentzian manifolds which realize this bound. The analysis is based on a three-dimensional analogue of t…
This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate Itô semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and jumps. Second-order expansion reveals explicit biases and a pathway to bias correc…
We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows for dynamically changing rewards that better describe applications where side inf…
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regi…
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support of the inverse covariance matrix corresponds to the edges of the graphical model…
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in the sheaf cohomology of the geometric quantization line bundle. The correspondin…
Develops a neural network for global minimum variance portfolio optimization.
problem Minimizing portfolio variance for large equity covariance matrices.
method Rotation-invariant neural network that learns lag-transformed returns and covariance regularization.
result End-to-end trained model outperforms competitors in realized volatility and Sharpe ratios.
Study on estimating Gaussian mean with missing data in high dimensions.
problem Estimating Gaussian mean in high dimensions with missing data due to realizable contamination.
method Statistical Query model, Low-Degree Polynomials, PTF tests, and algorithms.
result Established information-computation gap and developed efficient algorithms.
We propose an efficient method for estimating covariate effects in doubly-stochastic spatial models.
problem Computational demands and restrictive assumptions in existing doubly-stochastic spatial models.
method Penalized regression method for estimating covariate effects in doubly-stochastic point processes.
result Consistency and asymptotic normality of the covariate effect estimates achieved despite model misspecification.
Extracts representative scenarios from large data panels.
problem Creating representative scenarios from large data panels.
method Two novel algorithms: one identifies new scenarios, the other selects known important data points.
result Efficient algorithms for consistent scenario-based modeling and multi-dimensional numerical integration.
In this paper, we establish a general inequality for locally strongly convex centroaffine hypersurfaces in Rn+1 involving the norm of the covariant derivatives of both the difference tensor K and the Tchebychev vector field T. Our result is optimal in that, applying our recent classification for local…
Estimates for covariant derivatives and Riesz transforms on differential forms.
problem Bounding covariant derivatives and Riesz transforms on differential forms.
method Use Bismut derivative formula to prove heat kernel bounds and Riesz transform boundedness.
result Formulate and prove conjecture on boundedness of covariant local Riesz-transforms in L^p.
Frengression models causal data flexibly and faithfully.
problem Challenges in robust benchmarking and evaluation of causal inference with real-world data.
method Introduces frengression, a deep generative model for joint distribution of covariates, treatments, and outcomes.
result Frengression provides accurate estimation and flexible simulation of multivariate, time-varying data.
In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the algebra of Clifford bivectors is isomorphic to the Lie algebra of Sl(2,C). In that way the pullback of the …
Bayesian framework improves robustness in nonlinear regression models.
problem Measurement error, model misspecification, and distributional misspecification in regression analyses.
method Joint Dirichlet process prior on latent covariate-response distribution, updating with posterior pseudo-samples.
result Improved stability and consistency in estimators under increasing measurement error.
Modeling joint log-volatility dynamics with multivariate fractional Ornstein-Uhlenbeck process.
problem Empirical evidence of joint behavior in realized volatility time series.
method Multivariate fractional Ornstein-Uhlenbeck process with different Hurst exponents and non-trivial interdependencies.
result Model accurately captures asymmetries and spillover effects in realized-volatility time series.
We formalize causal separation in portfolio theory, deriving a closed-form projected Markowitz solution.
problem Portfolio optimization under causal separation conditions.
method Derive a closed-form solution for portfolio optimization using causal separation conditions.
result A closed-form projected Markowitz solution is derived under causal separation conditions.