Related papers: Analytic Moments for GARCH Processes

Here, we have analysed a GARCH(1,1) model with the aim to fit higher order moments for different companies' stock prices. When we assume a gaussian conditional distribution, we fail to capture any empirical data when fitting the first three…

This paper studies the joint inference on conditional volatility parameters and the innovation moments by means of bootstrap to test for the existence of moments for GARCH(p,q) processes. We propose a residual bootstrap to mimic the joint…

For the multivariate COGARCH process, we obtain explicit expressions for the second-order structure of the "squared returns" process observed on an equidistant grid. Based on this, we present a generalized method of moments estimator for…

This paper derives the analytic form of the $h$-step ahead prediction density of a GARCH(1,1) process under Gaussian innovations, with a possibly asymmetric news impact curve. The contributions of the paper consists both in the derivation…

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…

One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time…

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 construct fractionally integrated continuous-time GARCH models, which capture the observed long range dependence of squared volatility in high-frequency data. Since the usual Molchan-Golosov and Mandelbrot-van-Ness fractional kernels…

Ranking data are frequently obtained nowadays but there are still scarce methods for treating these data when temporally observed. The present paper contributes to this topic by proposing and developing novel models for handling time series…

This paper introduces a novel quantile approach to harness the high-frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized GARCH model and employ…

This note is concerned with accurate and computationally efficient approximations of moments of Gaussian random variables passed through sigmoid or softmax mappings. These approximations are semi-analytical (i.e. they involve the numerical…

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…

Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the…

COGARCH models are continuous time version of the well known GARCH models of financial returns. They are solution of a stochastic differential equation driven by a L\'evy process. The first aim of this paper is to show how the method of…

This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient…

Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time…

This paper develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of Kolmogorov-Smirnov…

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…

For many financial applications, it is important to have reliable and tractable models for the behavior of assets and indexes, for example in risk evaluation. A successful approach is based on ARCH processes, which strike the right balance…

This paper is concerned with some properties of the generalized GARCH models, obtained by extending GARCH models with exogenous variables, the so-called GARCH extended (GARCHX) models. For these, we establish sufficient conditions for some…