The popularity of Bitcoin increased significantly in 2021. is considered to deliver high returns a relatively short period, indicating that bitcoin has volatility. Data with volatility usually violates the Autoregresstive IntegratedinMovinginAverage (ARIMA)in homoscedasticity assumption. Autoregressive Conditional Heteroscedasticity (ARCH) and General (GARCH) model often used overcome problem h...

In this paper the value at risk (VaR) forecasts are compared using three different GARCH models; ARCH(1), GARCH(1,1) and EGARCH(1,1). The implemented method is a one-day ahead out of sample forecast of the VaR. The forecasts are evaluated using the Kupiec test with a five percent significance level. The focus is on three different markets; commodities, equities and exchange rates. The goal of t...

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...

In the light of regime switching and volatility clustering in the dynamics of SHIBOR, regime-switching CIR model (RSCIR) and regime-switching GARCH CIR model (RSCIR-GARCH) are established by introducing regime-switching and GARCH specifications into CIR model successively. Then, a contrast study among CIR, RSCIR and RSCIR-GARCH models is performed based on SHIBOR sample data, which indicates th...

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity ~ARMAGARCH! model+ The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established+ Consistency of the quasimaximum-likelihood estimator ~QMLE! is proved under only the second-order moment conditi...

We consider estimates of the parameters of GARCH models obtained using auxiliary information on latent variance which may be available from higher-frequency data, for example from an estimate of the daily quadratic variation such as the realized variance. We obtain consistent estimates of the parameters of the infinite ARCH representation via a regression using the estimated quadratic variation...

The well-known ARCH/GARCH models for financial time series have been criticized of late for their poor performance in volatility prediction, i.e., prediction of squared returns.1 Focusing on three representative data series, namely a foreign exchange series (Yen vs. Dollar), a stock index series (the S&P500 index), and a stock price series (IBM), the case is made that financial returns may not ...

We identify and estimate the mean and variance components of the daily closing share prices using ARIMA-GARCH type models by explaining the volatility structure of the residuals obtained under the best suited mean models for the said series. The parameters of ARIMA type simple specifications are routinely anticipated by applying the OLS methodology but it has two disadvantages when the volatili...

The log returns of financial time series are usually modeled by means of the stationary GARCH(1,1) stochastic process or its generalizations which can not properly describe the nonstationary deterministic components of the original series. We analyze the influence of deterministic trends on the GARCH(1,1) parameters using Monte Carlo simulations. The statistical ensembles contain numerically ge...

As a versatile investment tool in energy markets for speculators and hedgers, the Goldman Sachs Commodity Index (GSCI) futures are quite well known. Therefore, this paper proposes a hybrid model incorporating ARCH family models and ANN model to forecast GSCI futures price. Empirical results show that the hybrid ARCH(1)-M-ANN model is superior to ARIMA, ARCH(1),GARCH(1,1), EGARCH(1,1) and ARIMA-...