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We propose Neural GARCH, a class of methods to model conditional heteroskedasticity in financial time series. Neural GARCH is a neural network adaptation of the GARCH 1,1 model in the univariate case, and the diagonal BEKK 1,1 model in the…
This article proposes a Model Reference Adaptive Control (MRAC) strategy to achieve fixed-time convergence of parameter estimation and tracking errors for unknown linear time-invariant systems, without relying on the persistence of…
AutoRegressive Conditional Heteroscedasticity (ARCH) models are standard for modeling time series exhibiting volatility, with a rich literature in univariate and multivariate settings. In recent years, these models have been extended to…
We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation…
In time-series analyses, particularly for finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased…
We propose a continuous-time Markov-switching generalized autoregressive conditional heteroskedasticity (COMS-GARCH) process for handling irregularly spaced time series (TS) with multiple volatilities states. We employ a Gibbs sampler in…
There is a serious and long-standing restriction in the literature on heavy-tailed phenomena in that moment conditions, which are unrealistic, are almost always assumed in modelling such phenomena. Further, the issue of stability is often…
Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of…
This paper introduces one new multivariate volatility model that can accommodate an appropriately defined network structure based on low-frequency and high-frequency data. The model reduces the number of unknown parameters and the…
This paper introduces an extension of the Markov switching GARCH model where the volatility in each state is a convex combination of two different GARCH components with time varying weights. This model has the dynamic behavior to capture…
We propose a new approach to volatility modeling by combining deep learning (LSTM) and realized volatility measures. This LSTM-enhanced realized GARCH framework incorporates and distills modeling advances from financial econometrics, high…
This work is devoted to the study of modeling geophysical and financial time series. A class of volatility models with time-varying parameters is presented to forecast the volatility of time series in a stationary environment. The modeling…
In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multi-dimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment…
The AutoRegressive Conditional Heteroskedasticity (ARCH) and its generalized version (GARCH) family of models have grown to encompass a wide range of specifications, each of them is designed to enhance the ability of the model to capture…
Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…
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…
This paper presents extensions of finite-time stability results to some prototypical adaptive control and estimation frameworks. First, we present a novel scheme of online parameter estimation that guarantees convergence of the estimation…
It is now widely accepted that volatility models have to incorporate the so-called leverage effect in order to to model the dynamics of daily financial returns.We suggest a new class of multivariate power transformed asymmetric models. It…
This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak…
In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to…