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Communication systems and network technologies
Published in Kennis Chan, Future Communication Technology and Engineering, 2015
Since the introduction of the ARCH model introduced by Engel, GARCH models, introduced by Bollerslev, generalized Engle’s earlier ARCH models to include Autoregressive (AR) as well as Moving Average (MA) terms. GARCH models can be more parsimonious (use fewer parameters), thereby increasing computational efficiency. After that, a numerous extension of GARCH models emerged to specify the conditional variance models. The class of GARCH models has become extremely popular for application to financial data over the past twenty years. In the following section, the GARCH class of models is explained as follows.
Beyond Linear Models
Published in Randal Douc, Eric Moulines, David S. Stoffer, Nonlinear Time Series, 2014
Randal Douc, Eric Moulines, David S. Stoffer
Some drawbacks of the GARCH model are that the likelihood tends to be flat unless n is very large, and the model tends to overpredict volatility because it responds slowly to large isolated returns. Returns are rarely conditionally normal or symmetric, so various extensions to the basic model have been developed to handle the various situations noticed empirically. Interested readers might find the general discussions in Bollerslev et al. (1994) and Shephard (1996) worthwhile reading. Also, Gouriéroux (1997) gives a detailed presentation of ARCH and related models with financial applications and contains an extensive bibliography. Excellent texts on financial time series analysis are Chan (2002), Teräsvirta et al. (2011), and Tsay (2005).
Modeling structural breakpoints in volatility of Philippine Peso-US Dollar currency exchange rate
Published in Yuli Rahmawati, Peter Charles Taylor, Empowering Science and Mathematics for Global Competitiveness, 2019
The Generalized Autoregressive Conditional Heteroskedasticity or GARCH, is a forecasting method proposed by (Bollerslev, 1986, Bollerslev et al, 1992) that generalizes the ARCH model of Engle in 1982. The GARCH (p, q) models the return yt () yt=C+ϵt,
Artificial Intelligence Methods: Toward a New Decision Making Tool
Published in Applied Artificial Intelligence, 2022
Ismail Lotfi, Abdelhamid El Bouhadi
Generally, GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models are used to model asset volatility as well as the asymmetry of the distribution (leptokurtic and platikurtic) of returns. It is with this objective in mind that studies of different assets work with returns and not with prices, for two essential points: Any modeling of the price history with the aim of projecting itself into the future will be incorrect, and this is because certain properties of price processes do not remain constant over time. Reference is made to non-stationarity, and thus one prefers to use yield processes that have stationarity as a characteristic.The notion of correlation stipulates the existence of a temporal dependence between an observation at the present moment and its past history.
DOA estimation for uncorrelated and coherent signals in non-stationary noise environments
Published in International Journal of Electronics, 2020
Atefeh Gholipour, Bijan Zakeri, Khalil Mafinezhad
All mentioned methods are based on uniform white noise that may be unrealistic in many applications, such as underwater systems. In this case, the estimation performance will be degraded especially in low SNR environment where the effect of noise is significant (Li & Vaccaro, 1992; Liu, Chen, Zhong, & Poor, 2010). Another general form for noise considers noise as an unknown coloured and spatially dependent process. In En, Lorenzelli, Hudson, and Yao (2008), Li and Lu (2008), Pesavento and Gershman (2001), Seghouane (2011) sensor’s noise has been modelled as a zero-mean spatially and temporally white Gaussian process with an unknown diagonal covariance matrix, but they did not consider multipath situation. A method in Qi, Chen, Wang, and Zhang (2007) is presented to solve DOA estimation in unknown non-uniform noise fields. All of these studies have been performed assuming a stationary noise model. In many applications the statistical behaviour of the environment change with time, in other words the noise behaves as non-stationary process. Generalised autoregressive conditional heteroskedasticity (GARCH) is a non-linear time series that represents the change of variance over the time (Bollerslev, 1986). Due to this property of GARCH and noise measurement result in Gholipour, Zakeri, and Mafinezhad (2016), GARCH time series is used for modelling the non-stationary additive noise. However, methods in Amiri, Amindavar, and Kirlin (2004) and Gholipour et al. (2016) presented for uncorrelated signals.
A dynamic target volatility strategy for asset allocation using artificial neural networks
Published in The Engineering Economist, 2018
Recently, institutional investors, such as insurance companies with long-term investments, have established an efficient risk control strategy known as target volatility (or risk control, constant volatility targeting) to maintain a predetermined level of volatility for a portfolio (Chew 2011; Xue 2012). There are a few empirical studies for an asset allocation based on the target volatility strategy. Hocquard et al. (2013) propose a constant volatility framework for managing tail risk using a cost-effective portfolio management approach. They use a simple generalized autoregressive conditional heteroskedasticity (GARCH) (1,1) model to estimate the volatility based on the daily returns of the underlying assets. They also price and derive the hedging strategy monthly to generate the desired payoff. Their analysis showed that the target volatility strategy helps to reduce tail risk. Perchet et al. (2016) analyze a target volatility strategy with different GARCH-type models applied to a portfolio consisting of the Standard & Poor's 500 Index (S&P 500) for a risky asset and the 3-month U.S. dollar LIBOR as a proxy for the risk-free rate. To validate the target volatility strategy, they apply the approach to other asset classes, such as government bonds, corporate bonds, and commodities. As a result, they show that the best way to forecast the volatility of risky assets was to use the I-GARCH model.