It is shown empirically that mixed autoregressive moving average regression models with generalized autoregressive conditional heteroskedasticity (Reg-ARMA-GARCH models) can have multimodality in the likelihood that is caused by a dummy variable in the conditional mean. Maximum likelihood estimates at the local and global modes are investigated and turn out to be qualitatively different, leadin...

Enhancing forecasting performance in terms of both the expected mean value and variance has been a critical challenging issue for energy industry. In this paper, novel methodology finite mixture Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) approach with Expectation–Maximization (EM) algorithm is introduced. The applicability comprehensively evaluated related time series inc...

The objective of the current study is to present a comparison techniques for forecasting low-frequency climate oscillation indices with focus on Great Lakes system. A number time series models have been tested including traditional autoregressive moving average (ARMA) model, dynamic linear model (DLM), generalized conditional heteroskedasticity (GARCH) as well nonstationary resampling (NSOR) te...

Stocks are investment instruments that provide returns but tend to be risky. The most important component of investing is volatility, where volatility identical the standard conditional deviation stock price return. thing in addition return a risk. Value-at-Risk (VaR) statistical method estimating maximum losses. To evaluate quality VaR estimates, models should always back-tested with appropria...