The goal of this study was to identify a reliable GARCH model for modeling and forecasting each economic variable in Nigeria, including the price crude oil, consumer index, exchange rate, inflation rate. Monthly secondary data simulated sets were that used. Between January 2004 December 2020, are covered. Beta Volatility Coefficient (BVC) proposed detecting volatility research data. Using metho...

It is well known that as the time interval between two consecutive observations shrinks to zero, a properly constructed GARCH model will weakly converge to a bivariate diffusion. Naturally the European option price under the GARCH model will also converge to its bivariate diffusion counterpart. This paper investigates the convergence speed of the GARCH option price. We show that the European op...

This paper shows that, even if volatility is accurately predicted by correctly specified GARCH models, however such predictions are not very useful for traders when the conditional volatility does not vary "enough" over time, being therefore quite close to the unconditional one. It is shown that a low R in the Mincer-Zarnowitz regression implies flat (although correctly predicted) volatility, a...

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 ...

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter...

We address the IGARCH puzzle, by which we understand the fact that a GARCH(1,1) model fitted to virtually any financial dataset exhibit the property thatˆα + ˆ β is close to one. We do this by proving that if data is generated by a stochastic volatility model but fitted to a GARCH(1,1) model one would get thatˆα + ˆ β tends to one in probability as the sampling frequency is increased. We also d...