Related papers: On a generalised model for time-dependent variance…
The asymptotic properties of the memory structure of ARCH($\infty$) equations are investigated. This asymptotic analysis is achieved by expressing the autocovariance function of ARCH($\infty$) equations as the solution of a linear Volterra…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S\&P 500 stocks from the New York Stock Exchange. After…
This paper introduces a spatiotemporal exponential generalised autoregressive conditional heteroscedasticity (spatiotemporal E-GARCH) model, extending traditional spatiotemporal GARCH models by incorporating asymmetric volatility…
We provide finite sample properties of sparse multivariate ARCH processes, where the linear representation of ARCH models allows for an ordinary least squares estimation. Under the restricted strong convexity of the unpenalized loss…
In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time…
It is known that in some cases a Random Access Machine (RAM) benefits from having an additional input that is an arbitrary number, satisfying only the criterion of being sufficiently large. This is known as the ARAM model. We introduce a…
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…
The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What it is well…
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with…
We employ single-qubit quantum circuit learning (QCL) to model the dynamics of volatility time series. To assess its effectiveness, we generate synthetic data using the Rational GARCH model, which is specifically designed to capture…
Long-term temporal correlations in time series in a form of an event sequence have been characterized using an autocorrelation function (ACF) that often shows a power-law decaying behavior. Such scaling behavior has been mainly accounted…
We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive…
In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study…
From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…
The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold…
The autocorrelation function of volatility in financial time series is fitted well by a superposition of several exponents. Such a case admits an explicit analytical solution of the problem of constructing the best linear forecast of a…
In an asset return series there is a conditional asymmetric dependence between current return and past volatility depending on the current return's sign. To take into account the conditional asymmetry, we introduce new models for asset…
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter…
We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two…