Forecasting the volatility of a financial asset has wide implications in finance. Conditional variance extracted from GARCH framework could be a suitable proxy of financial asset volatility. Option pricing, portfolio optimization and risk management are examples for implications of conditional variance forecasting. One of the most recent methods of volatility forecasting is Realized GARCH (RGARCH) that considers 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 Tehran Exchange Price Index (TEPIX). 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 TEPIX outperforms the other methods in both ways. So, using RGARCH model in practical situations like pricing and risk management would tend to better results.

Long-range guided wave inspection systems are often used in low frequency– thickness ranges below the cut-off frequencies of higher wave modes to simplify data interpretation. In this paper, the potential of high-order guided wave modes for the inspection of plate structures is considered. The characteristics of high-order lamb wave modes and their corresponding sensitivity and detectability are investigated. Using a commercially available software package, finite element simulations are carried out to model the propagation of A1 and S1 wave modes in steel plate. Using a variable angle transducer, experimental pulse– echo measurements are also conducted to evaluate the measurement errors when implementing higher order modes A1 and S1 on a 2-mm thick steel plate at 4 MHz. mm. Experimental measurements show that when using S1 mode for short-range measurements, the relative error is less than 10%.

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.