The paper studies convergence of kernel autocovariance operators for stationary processes.
problem Estimating autocovariance operators of stationary processes on Polish spaces.
method Investigates convergence of empirical estimates of autocovariance operators under various conditions.
result Provides consistency results for kernel PCA and spectral analysis methods.
It is now widely accepted that, to model the dynamics of daily financial returns, volatility models have to incorporate the so-called leverage effect. We derive the asymptotic behaviour of the squared residuals autocovariances for the class of asymmetric power GARCH model when the power is unknown and is jointly estima…
Develops flexible non-parametric ACFs using B-spline kernels.
problem Flexible modelling of the autocovariance function (ACF) in time-series, spatial, and spatio-temporal analysis.
method Derives the inverse Fourier transform of B-spline spectral bases to create a general class of non-parametric ACFs.
result Provides a provably dense, flexible, and general class of non-parametric ACFs for various types of processes.
Deep learning speeds spectral density estimation for large 2D/3D grids.
problem Computational challenges in estimating spectral densities for large grids.
method Deep learning neural network for spectral density estimation.
result Deep learning estimator is a universal approximator and faster than existing methods.
This work considers the problem of modified portmanteau tests for testing the adequacy of FARIMA models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak FARIMA). We first study the joint distribution of the least squares estimator and the noise empirical autocovariances. …
Measures mode separation in high-dimensional densities via a reversible diffusion process.
problem Quantifying how sharply a distribution fragments into barrier-separated clusters in high dimensions.
method A unique reversible diffusion process with f as stationary distribution, extracting SSA and DA from its autocovariance matrix.
result Empirical autocovariance spectrum and readouts (SSA, DA) quantify mode separation using only samples and pretrained score-based models.
Generalizes memory and forecasting capacities for nonlinear recurrent networks with dependent inputs.
problem Understanding memory and forecasting capabilities in networks with dependent inputs.
method Formulated bounds for memory and forecasting capacities in terms of network size and input properties.
result Proved that memory capacity for linear recurrent networks with independent inputs is given by the rank of the controllability matrix.
We construct a new process using a fractional Brownian motion and a fractional Ornstein-Uhlenbeck process of the Second Kind as building blocks. We consider the increments of the new process in discrete time and, as a result, we obtain a more parsimonious process with similar autocovariance structure to that of a FARIM…
New k-means method clusters radar image sequences using SPD matrices.
problem Clustering radar image sequences efficiently.
method Developed k-means on SPD matrices for non-Euclidean data. result Effective clustering of radar image sequences via SPD matrices.
Develops inequalities for high-dimensional linear processes with dependent innovations.
problem Estimating high-dimensional VAR(p) systems and HAC covariance estimation.
method Concentration inequalities for l∞ norm of vector linear processes with sub-Weibull, mixingale innovations. result Obtained concentration bounds for the maximum entrywise norm of lag-h autocovariance matrices. In this paper we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving-average (SARMA) models under the assumption that the errors are uncorrelated but not necessarily independent.We relax the standard independence assumption on the error term in order to extend the range …
We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, test…
The paper examines extreme value statistics of high-dimensional sample covariances, with applications in finance and image analysis.
problem Statistical validation of normal conditions in high-dimensional time series data.
method Generalizes the maximal deviation of sample autocovariances to high dimensions and applies Gumbel-type extreme value asymptotics.
result Gumbel-type extreme value asymptotics holds true for high-dimensional sample covariances.
Two new models for volatility in Markov-switching environments capture financial time-series properties.
problem Modeling volatility in environments with regime switches and exogenous jumps.
method Generalizations of COGARCH and Barndorff-Nielsen-Shephard models using Markov-modulated generalized Ornstein-Uhlenbeck processes.
result Models inherit properties of original models and capture stylized facts of financial time-series.
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequentl…
Develops a test to distinguish between standard and rough volatility.
problem Determining whether asset volatility follows a standard semimartingale or a rough process.
method Uses sample autocovariance of high-frequency asset return data to detect negative autocorrelation at high frequencies.
result Evidence of rough volatility in SPY high-frequency data.
Estimates volatility of volatility and leverage effect using high-frequency options data.
problem Estimating volatility of volatility and leverage effect from high-frequency options data.
method Model-free estimators using characteristic function of price increments and spot volatility.
result Developed feasible inference methods for estimating volatility of volatility and leverage effect.
Novel Bayesian framework for spatio-temporal neuroimaging data.
problem Inference on multi-task sparse hierarchical regression models with complex spatio-temporal dynamics.
method Flexible hierarchical Bayesian framework with Kronecker product covariance structure, majorization-minimization optimization, and Riemannian geometry.
result Improved performance on synthetic and real M/EEG data.
The paper develops a new model for high-dimensional spatial arbitrage pricing.
problem Estimating spatial interactions in high-dimensional asset pricing.
method Integrates spatial interactions with multi-factor analysis using generalized shrinkage Yule-Walker (SYW) estimation.
result Established asymptotic properties for high-dimensional spatial arbitrage pricing models.
In order to improve the efficiency and sustainability of electricity systems, most countries worldwide are deploying advanced metering infrastructures, and in particular household smart meters, in the residential sector. This technology is able to record electricity load time series at a very high frequency rates, info…
Combines physics-based ML with hierarchical Bayesian techniques for better model performance.
problem Lack of physical knowledge in black-box machine learning models.
method Embeds physics-based models into Gaussian Process mean function and uses kernel machines to characterize discrepancies.
result Improved model performance under blind conditions through integration of physics-based knowledge.
Random neural networks with ReLU activations are non-Gaussian processes.
problem Understanding the behavior of neural networks with random initialization and rectified linear units.
method Proving these networks are non-Gaussian processes and deriving their properties.
result These networks can converge to non-Gaussian processes under certain conditions.
Filtered conformal ellipsoids for graph-native time series
problem Joint prediction sets for multivariate time series
method Filtered conformal ellipsoids
result Sharper at-target ellipsoids than static-covariance and non-filter baselines