The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented GARCH(1,1) sequences and the asymptotic distribution of various ...

Autoregressive conditional heteroskedasticity (ARCH) models pioneered by Engle (1982) and their extended version have been proven to be very successful in modeling the volatility of financial time series; see Bollerslev et al. (1994). Bayesian inference on ARCH models has been implemented using the importance sampling technique proposed by Geweke (1989) and more recently using Markov chain Mont...

For a given time horizon ∆T , this article explores the relationship between the realized volatility (the volatility that will occur between t and t + ∆T ), the implied volatility (corresponding to at-the-money option with expiry at t+∆T ), and several forecasts for the volatility build from multi-scales linear ARCH processes. The forecasts are derived from the process equations, and the parame...

This paper performs an experiment to forecast stock market movement in India using Artificial Neural Network (ANN) and Genetic Algorithm (GA). This model is named Genetically optimized Neural Network (GNN). We have tested this newly created model against traditional ARCH/GARCH models using hypothesis testing (z-test).We have used different error metrics like Average Absolute Error (AAE), Mean A...

The role of price risk in sow farrowings is investigated by using bivariate ARCH-M and GARCH-M models and a nonparametric kernel estimator. To account for the relevant time horizon of irreversible supply decisions, predictions for mean price and conditional price variance are iterated forward. The empirical results vary markedly in terms of their implications for risk response in hog supply dec...

This research aims to analyze and to compare the ability of different mathematical models, such as artificial neural networks (ANN) and ARCH and GARCH models, to forecast the daily exchange rates Euro/U.S. dollar (USD), identifying which, among all the models applied, produces more accurate forecasts. By empirically comparing the different mathematical models developed in this research, the tra...

Abstract. Conventional streamflow models operate under the assumption of constant variance or season-dependent variances (e.g. ARMA (AutoRegressive Moving Average) models for deseasonalized streamflow series and PARMA (Periodic AutoRegressive Moving Average) models for seasonal streamflow series). However, with McLeod-Li test and Engle’s Lagrange Multiplier test, clear evidences are found for t...

In this paper we consider a general ...rst-order power ARCH process and, in particular, a special case in which the power parameter approaches zero. These considerations give us the autocorrelation function of the logarithms of the squared observations for ...rstorder exponential and logarithmic GARCH processes. These autocorrelations decay exponentially with the lag and may be used for checkin...

This research article aimed at modeling the variations in the dollar/cedi exchange rate. It examines the applicability of a range of ARCH/GARCH specifications for modeling volatility of the series. The variants considered include the ARMA, GARCH, IGARCH, EGARCH and M-GARCH specifications. The results show that the series was non stationary which resulted from the presence of a unit root in it. ...