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A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for…

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…

A Bayesian method of moments/instrumental variable (BMOM/IV) approach is developed and applied in the analysis of the important mean and multiple regression models. Given a single set of data, it is shown how to obtain posterior and…

Betas are possibly the most frequently applied tool to analyze how securities relate to the market. While in very widespread use, betas only express dynamics derived from second moment statistics. Financial returns data often deviate from…

This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model…

Integer-valued time series exist widely in economics, finance, biology, computer science, medicine, insurance, and many other fields. In recent years, many types of models have been proposed to model integer-valued time series data, in…

Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market…

We propose a new class of financial volatility models, called the REcurrent Conditional Heteroskedastic (RECH) models, to improve both in-sample analysis and out-ofsample forecasting of the traditional conditional heteroskedastic models. In…

In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…

We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…

Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…

Here, we use Machine Learning (ML) algorithms to update and improve the efficiencies of fitting GARCH model parameters to empirical data. We employ an Artificial Neural Network (ANN) to predict the parameters of these models. We present a…

Over the last few decades, various methods have been proposed for estimating prediction intervals in regression settings, including Bayesian methods, ensemble methods, direct interval estimation methods and conformal prediction methods. An…

We introduce a general approach for modeling the dynamic of multivariate time series when the data are of mixed type (binary/count/continuous). Our method is quite flexible and conditionally on past values, each coordinate at time $t$ can…

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…

In this paper, we propose the realized Hyperbolic GARCH model for the joint-dynamics of lowfrequency returns and realized measures that generalizes the realized GARCH model of Hansen et al.(2012) as well as the FLoGARCH model introduced by…

This paper proposes Fourier-based and wavelet-based techniques for analyzing periodic financial time series. Conventional models such as the periodic autoregressive conditional heteroscedastic (PGARCH) and periodic autoregressive…

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a…

Varying coefficient models are widely used to characterize dynamic associations between longitudinal outcomes and covariates. Existing work on varying coefficient models, however, all assumes that observation times are independent of the…