Related papers: ECF identification of GARCH systems driven by L\'e…
In this paper, we introduce a new single model maneuvering target tracking approach using stochastic differential equation (SDE) based on GARCH volatility. The traditional input estimation (IE) techniques assume constant acceleration level…
One of the most important features of financial time series data is volatility. There are often structural changes in volatility over time, and an accurate estimation of the volatility of financial time series requires careful…
Effective forces -- derived from experimental or {\it in silico} molecular dynamics time traces -- are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. Thus, designing…
Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…
The electrocardiogram (ECG) is a cost-effective, highly accessible and widely employed diagnostic tool. With the advent of Foundation Models (FMs), the field of AI-assisted ECG interpretation has begun to evolve, as they enable model reuse…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…
Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have…
The extremal coefficient function (ECF) of a max-stable process $X$ on some index set $T$ assigns to each finite subset $A\subset T$ the effective number of independent random variables among the collection $\{X_t\}_{t\in A}$. We introduce…
A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting framework employing multiple realized measures is developed. The proposed framework extends the realized exponential GARCH model to be semi-parametrically…
This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute…
Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…
We develop an adaptive feedback control technique that combines an extremum-seeking-based command generator (ECG) with indirect adaptive control. In particular, ECG is used to generate commands that asymptotically optimize a cost function…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
Range-measured return contains more information than the traditional scalar-valued return. In this paper, we propose to model the [low, high] price range as a random interval and suggest an interval-valued GARCH (Int-GARCH) model for the…
Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…
Quantile regression (QR) relies on the estimation of conditional quantiles and explores the relationships between independent and dependent variables. At high probability levels, classical QR methods face extrapolation difficulties due to…
This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…
GARCH models are useful tools in the investigation of phenomena, where volatility changes are prominent features, like most financial data. The parameter estimation via quasi maximum likelihood (QMLE) and its properties are by now well…
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and…
We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with…