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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…
Modifications of the Cont-Bouchaud percolation model for price fluctuations give an asymmetry for time-reversal, an asymmetry between high and low prices, volatility clustering, effective multifractality, correlations between volatility and…
Multivariate dynamic time series models are widely encountered in practical studies, e.g., modelling policy transmission mechanism and measuring connectedness between economic agents. To better capture the dynamics, this paper proposes a…
Our article considers a regression model with observed factors. The observed factors have a flexible stochastic volatility structure that has separate dynamics for the volatilities and the correlation matrix. The correlation matrix of the…
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried…
In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…
The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. In this Letter, we propose to verify the inversion formula using high-frequency…
The $GARCH$ algorithm is the most renowned generalisation of Engle's original proposal for modelising {\it returns}, the $ARCH$ process. Both cases are characterised by presenting a time dependent and correlated variance or {\it…
Low-frequency historical data, high-frequency historical data and option data are three major sources, which can be used to forecast the underlying security's volatility. In this paper, we propose two econometric models, which integrate…
It is commonly believed that the correlations between stock returns increase in high volatility periods. We investigate how much of these correlations can be explained within a simple non-Gaussian one-factor description with time…
We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions…
This study utilised the dynamics of five time-varying models to estimate six essential features of financial return volatility that are relevant for robust risk management. These features include pronounced persistence, mean reversion,…
Various spatiotemporal and network GARCH models have recently been proposed to capture volatility interactions, such as the transmission of market risk across financial networks. These approaches rely heavily on the specification of the…
The study of long-horizon returns has received a great deal of attention in recent years (see, for example, Boudoukh, Richardson, and Whitelaw (2008), Neuberger (2012) and Lee (2013), Fama and French (2018)). While most of the discussions…
It is now widely accepted that, to model the dynamics of daily financial returns, volatility models have to incorporate the so-called leverage effect. We derive the asymptotic behaviour of the squared residuals autocovariances for the class…
We extend the theory from Fan and Li (2001) on penalized likelihood-based estimation and model-selection to statistical and econometric models which allow for non-negativity constraints on some or all of the parameters, as well as…
Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and…
We study the volatility time series of 1137 most traded stocks in the US stock markets for the two-year period 2001-02 and analyze their return intervals $\tau$, which are time intervals between volatilities above a given threshold $q$. We…