|
on Econometric Time Series |
| By: | Yuanhua Feng (Paderborn University); Jan Beran (University of Konstanz); Sebastian Letmathe (Paderborn University); Sucharita Ghosh (Swiss Federal Research Institute WSL) |
| Abstract: | Volatility modelling is applied in a wide variety of disciplines, namely finance, en- vironment and societal disciplines, where modelling conditional variability is of in- terest e.g. for incremental data. We introduce a new long memory volatility model, called FI-Log-GARCH. Conditions for stationarity and existence of fourth moments are obtained. It is shown that any power of the squared returns shares the same memory parameter. Asymptotic normality of sample means is proved. The practical performance of the proposal is illustrated by an application to one-day rolling forecasts of the VaR (value at risk) and ES (expected shortfall). Comparisons with FIGARCH, FIEGARCH and FIAPARCH models are made using a criterion based on different traffic light test. The results of this paper indicate that the FI-Log- GARCH often outperforms the other models, and thus provides a useful alternative to existing long memory volatility models. |
| Keywords: | FI-Log-GARCH, stationary solutions, finite fourth moments, covariance structure, rolling forecasting VaR and ES, traffic light test of ES |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:137&r=all |
| By: | Liu, Xiaobin (Zhejiang University); Shi, Shuping (Macquarie University); Yu, Jun (School of Economics, Singapore Management University) |
| Abstract: | This paper contributes to an ongoing debate on volatility dynamics. We introduce a discrete-time fractional stochastic volatility (FSV) model based on the fractional Gaussian noise. The new model has the same limit as the fractional integrated stochastic volatility (FISV) model under the in-fill asymptotic scheme. We study the theoretical properties of both models and introduce a memory signature plot for a model-free initial assessment. A simulated maximum likelihood (SML) method, which maximizes the time-domain log-likelihoods obtained by the importance sampling technique, is employed to estimate the model parameters. Simulation studies suggest that the SML method can accurately estimate both models. Our empirical analysis of several financial assets reveals that volatilities are both persistent and rough. It is persistent in the sense that the estimated autoregressive coefficients of the log volatilities are very close to unity, which explains the observed long-range dependent feature of volatilities. It is rough as the estimated Hurst (fractional) parameters of the FSV (FISV) model are significantly less than half (zero), which is consistent with the findings of the recent literature on ‘rough volatility’. |
| Keywords: | Fractional Brownian motion; stochastic volatility; memory signature plot; long memory; asymptotic; variance-covariance matrix; rough volatility |
| JEL: | C15 C22 C32 |
| Date: | 2020–11–03 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2020_023&r=all |
| By: | Ding, Y. |
| Abstract: | We prove that Real-time GARCH (RT-GARCH) models converge to the same type of stochastic differential equations as the standard GARCH models as the length of sampling interval goes to zero. The additional parameter of RT-GARCH can be interpreted as current information risk premium. We show RT-GARCH has the same limiting stationary distribution and shares the same asymptotic properties for volatility filtering and forecast as standard GARCH. Simulation results confirm the current information parameter decreases with the length of sampling interval and hence, GARCH and RT-GARCH models behave increasingly similar for high frequency data. Moreover, empirical results show the current information risk premium has increased significantly after the 2008 financial crisis for S&P 500 index returns. |
| Keywords: | GARCH, RT-GARCH, SV, diffusion limit, high frequency data |
| JEL: | C22 C32 C58 |
| Date: | 2020–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:20112&r=all |
| By: | L. Bauwens; E. Otranto |
| Abstract: | Time series of realized covariance matrices can be modelled in the conditional autoregressive Wishart model family via dynamic correlations or via dynamic covariances. Extended parameterizations of these models are proposed, which imply a specific and time-varying impact parameter of the lagged realized covariance (or correlation) on the next conditional covariance (or correlation) of each asset pair. The proposed extensions guarantee the positive definiteness of the conditional covariance or correlation matrix with simple parametric restrictions, while keeping the number of parameters fixed or linear with respect to the number of assets. An empirical study on twenty-nine assets reveals that the extended models have superior forecasting performances than their simpler versions. |
| Keywords: | realized covariances;dynamic covariances and correlations;Hadamard exponential matri |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:cns:cnscwp:202007&r=all |