Estimation of conditional variance has lots of application reflecting economic, especially financial economics, social economics and political economics’ risk and volatility research. Therefore, obtaining accurate estimation of the conditional variance is especially important. Recently Hansen has modeled the conditional variance and realized volatility simultaneously which is known as Realized GARCH model. In this paper, we introduce a fuzzy coefficient in the Realized GARCH, and then compare this model with GARCH, EGARCH and GJR-GARCH methods as well as the RGARCH model with 2 different criteria of the realized volatility concerning Tehran Stock Exchange Index. The log likelihood value used to evaluate in-sample fitting. According to this criterion, our proposed model has a better fit than the rest of the models. To evaluate the accuracy of prediction of conditional variance, the rolling window method used with two MSE and QLIKE loss functions. The results indicate that our model, the Realized GARCH with fuzzy coefficient has the best performance with both loss functions.

Crude oil is the main source of energy and accounts for about a third of world energy production. Turmoil in this market will have far-reaching economic and financial consequences. Because of this, investors attach great importance to predicting volatility when investing in crude oil markets to hedge risk and portfolio diversification. However, their investment strategies are often strongly influenced by volatility because, in different periods of crude oil markets, there are high and low fluctuations that are attributed to the movement of economic cycles. Accordingly, the present study compares the Markov Regime Switching (MRS) and Hidden Markov (HM) volatility models with the GJR-GARCH asymmetric model on their forecasting capabilities in the WTI and Brent crude oil markets. Empirical results show that the MRS-GJRGARCH model performs better than the HM_GJRGARCH model in predicting volatility in both markets. Accordingly, using the two criteria of value at risk and the expected deficit, the minimum loss and the expected loss for December 2021 were predicted. The results show that the expected shortfall from investing in the WTI market is greater than the Brent oil market

In this paper we compare a set of different standard GARCH models with a group of Markov Regime-Switching GARCH (MRS-GARCH) in terms of their ability to forecast the petroleum futures markets volatility at horizons that range from one day to one month. To take into account the excessive persistence usually found in GARCH models that implies too smooth and too high volatility forecasts, MRS-GARCH models, where the parameters are allowed to switch between a low and a high volatility regime, are analyzed. Both gaussian and fat-tailed conditional distributions for the residuals are assumed, and the degrees of freedom can also be state-dependent to capture possible time-varying kurtosis. The forecasting performances of the competing models are evaluated with statistical loss functions. Under statistical losses, we use both tests of equal predictive ability of the Diebold-Mariano-type and test of superior predictive ability, such as White’s Reality Check and Hansen’s SPA test. The empirical analysis demonstrates that MRS-GARCH models do really outperform all standard GARCH models in forecasting volatility at shorter horizons according to a broad set of statistical loss functions. At longer horizons standard asymmetric GARCH models fare the best. All this tests reject the presence of a better model than the MRS-GARCH-t in this research.

In recent years, investment in gold has been remarkable for investors because of a recession in stock exchange. This increase in demand of gold caused increase in gold price. Because of increase in gold price, dealing of gold expanded and so volatility of gold price return increased intensly. So we have to use a model to predict volatility beside return to make decision for investment.Find a model that it can do a better forecast of price return volatility is a debatable topic in the finance literature. Around this topic some models have been presented and these models have some advantages and disadvantages. These models have been applied for predict of volatility of crude oil and exchange rate more than other fields. Between all models, GARCH models have been more applicable than others. So we use this group of models too, but in a different way. This way is a nonparametric approach to GARCH model that presented by Buhlman and McNeil for first time in 2002. In this research we use this approach to forecast volatility of gold price return and compare it with other GARCH models by two loss function (QLIKE-MSE). The result of this research shows that nonparametric GARCH has a better performance than the other GARCH models based on QLIKE loss function with a statistical significance, but based on MSE loss function we can’t judge.

forecasting the volatility of a financial asset has wide implications in finance. Conditional variance extracted from the GARCH framework could be a suitable proxy of financial asset volatility. Option pricing, portfolio optimization, and risk management are examples of implications of conditional variance forecasting. One of the most recent methods of volatility forecasting is Realized GARCH (RGARCH) that considers a simultaneous model for both realized volatility and conditional variance at the same time. In this article, we estimate conditional variance with GARCH, EGARCH, GIR-GARCH, and RGARCH with two realized volatility estimators using gold intraday data. We compared models, for in-sample fitting; by the log-likelihood value and used MSE and QLIKE lose functions to evaluate predicting accuracy. The results show that the RGARCH method for GOLD outperforms the other methods in both ways. So, using the RGARCH model in practical situations, like pricing and risk management would tend to better results.

In this paper, we propose a new model for additive noise based on GARCH time-series in array signal processing. Due to the some reasons such as complex implementation and computational problems, probability distribution function of additive noise is assumed Gaussian. In the different applications, scrutiny and measurement of noise shows that noise can sometimes significantly non-Gaussian and thus the methods based on Gaussian noise will degrade in an actual conditions. Heavy-tail probability density function (PDF) and time-varying statistical characteristics (e.g.; variance) are the most features of the additive noise process. On the other hand, GARCH process has important properties such as heavy-tail PDF (as excess kurtosis) and volatility modeling through feedback mechanism onto conditional variance so that it seems the GARCH model is a good candidate for the additive noise model in the array processing applications. In this paper, we propose a new method based on GARCH using the maximum likelihood approach in array processing and verify the performance of this approach in the estimation of the Direction-of-Arrivals of sources against the other methods and using the Cramer-Rao Bound.