Estimation of multivariate GARCH models is usually carried out by quasi maximum likelihood (QMLE), for which recently consistency and asymptotic normality have been proven under quite general conditions. However, there are to date no results on the efficiency loss of QMLE if the true innovation distribution is not multinormal. We investigate this issue by suggesting a nonparametric estimation o...

Yingfu Xie. Maximum Likelihood Estimation and Forecasting for GARCH, Markov Switching, and Locally Stationary Wavelet Processes. Doctoral Thesis. ISSN 1652-6880, ISBN 978-91-85913-06-0. Financial time series are frequently met both in daily life and the scientific world. It is clearly of importance to study the financial time series, to understand the mechanism giving rise to the data, and/or p...

This paper aims to investigate a Bayesian sampling approach to parameter estimation in the semiparametric GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This mixture density has the form of a kernel density estimator of the errors with its bandwidth being the ...

We address the IGARCH puzzle, by which we understand the fact that a GARCH(1,1) model fitted to virtually any financial dataset exhibit the property thatˆα + ˆ β is close to one. We do this by proving that if data is generated by a stochastic volatility model but fitted to a GARCH(1,1) model one would get thatˆα + ˆ β tends to one in probability as the sampling frequency is increased. We also d...

This paper introduces a unified model, which can accommodate both a continuoustime Itô process used to model high-frequency stock prices and a GARCH process employed to model low-frequency stock prices, by embedding a discrete-time GARCH volatility in its continuous-time instantaneous volatility. This model is called a unified GARCH-Itô model. We adopt realized volatility estimators based on hi...

Since ARCH and GARCH models are presented, more and more authors are interested in the study of volatilities in financial markets with GARCH models. Method for estimating the coefficients of GARCH models is mainly the maximum likelihood estimation. Now we consider another method—MCMC method to substitute for maximum likelihood estimation method. Then we compare three GARCH models based on it. M...

This paper is mainly talking about several volatility models and its ability to predict and capture the distinctive characteristics of conditional variance about the empirical financial data. In my paper, I choose basic GARCH model and two important models of the GARCH family which are E-GARCH model and GJR-GARCH model to estimate. At the same time, in order to acquire the forecasting performan...

We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework we allow for different distributions of the historical and the pricing return dynamics enhancing the model flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing...

One of the most used methods to forecast price volatility is the generalized autoregressive conditional heteroskedasticity (GARCH) model. Nonetheless, the errors in prediction using this approach are often quite high. Hence, continued research is conducted to improve forecasting models employing a variety of techniques. In this paper, we extend the field of expert systems, forecasting, and mode...

We introduce a new semiparametric model, GARCH with Functional EX ogeneous Liquidity (GARCH-FunXL), to capture the impact of liquidity, as implied by a stock exchange’s complete electronic limit order book (LOB), on asset price volatility. LOB-implied liquidity can be viewed as a functional rather than scalar or vectorial stochastic process. We adopt recent ideas from the functional data analys...