ARCH and GARCH models have been used recently in model-based signal processing applications, such as speech and sonar signal processing. In these applications, additive noise is often inevitable. Conventional methods for parameter estimation of ARCH and GARCH processes assume that the data are clean. The parameter estimation performance degrades greatly when the measurements are noisy. In this ...

ARCH and GARCH models are widely used to model financial market volatilities in risk management applications. Considering a GARCH model with heavy-tailed innovations, we characterize the limiting distribution of an estimator of the conditional Value-at-Risk (VaR), which corresponds to the extremal quantile of the conditional distribution of the GARCH process. We propose two methods, the normal ...

In this paper, we develop and evaluate speech enhancement algorithms, which are based on supergaussian generalized autoregressive conditional heteroscedasticity (GARCH) models in the short-time Fourier transform (STFT) domain. We consider three different statistical models, two fidelity criteria, and two approaches for the estimation of the variances of the STFT coefficients. The statistical mo...

GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model, which has been introduced a few years ago by Klüppelberg, Lindner and Maller, and Nelson’s diffusion limit are the only functional continuous-time limits of GARCH in distribution. In contrast to Nelson’s diffusion limit, COGARCH reprodu...

I n this paper, we specify that the GARCH(1,1) model has strong forecasting volatility and its usage under the truncated standard normal distribution (TSND) is more suitable than when it is under the normal and student-t distributions. On the contrary, no comparison was tried between the forecasting performance of volatility of the daily return series using the multi-step ahead forec...