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Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure…
Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…
Uncertainty quantification is crucial in time series prediction, and quantile regression offers a valuable mechanism for uncertainty quantification which is useful for extreme value forecasting. Although deep learning models have been…
The paper compares the small-sample properties of two non-parametric quantile regression estimators. The first is based on constrained B-spline smoothing (COBS) and the other is based on a variation and slight extension of a running…
Quantitative susceptibility mapping (QSM) has been increasingly applied in longitudinal studies of neurodegenerative diseases and aging to assess temporal alterations in brain iron and myelin. The accuracy of such investigations depends on…
Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…
Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…
This paper presents a methodological approach to financial time series analysis by combining causal discovery and uncertainty-aware forecasting. As a case study, we focus on four key U.S. macroeconomic indicators -- GDP, economic growth,…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
Forecasting faithful trajectories of multivariate time series from practical scopes is essential for reasonable decision-making. Recent methods majorly tailor generative conditional diffusion models to estimate the target temporal…
In this study, we apply 1D quantum convolution to address the task of time series forecasting. By encoding multiple points into the quantum circuit to predict subsequent data, each point becomes a feature, transforming the problem into a…
Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is…
The Cauchy-Schwarz (CS) divergence was developed by Pr\'{i}ncipe et al. in 2000. In this paper, we extend the classic CS divergence to quantify the closeness between two conditional distributions and show that the developed conditional CS…
The quantile varying coefficient (VC) model can flexibly capture dynamical patterns of regression coefficients. In addition, due to the quantile check loss function, it is robust against outliers and heavy-tailed distributions of the…
This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the…
During the COVID-19 pandemic, a massive number of attempts on the predictions of the number of cases and the other future trends of this pandemic have been made. However, they fail to predict, in a reliable way, the medium and long term…
This paper addresses the challenge of integrating sequentially arriving data within the quantile regression framework, where the number of features is allowed to grow with the number of observations, the horizon is unknown, and memory is…
Many economic variables feature changes in their conditional mean and volatility, and Time Varying Vector Autoregressive Models are often used to handle such complexity in the data. Unfortunately, when the number of series grows, they…
We obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes. Analogous to a well known lower bound on the randomness parameter, the lower bounds on skewness…
Time series prediction underpins a broad range of downstream tasks across many scientific domains. Recent advances and increasing adoption of black-box machine learning models for time series prediction highlight the critical need for…