Normal Mixture GARCH(1,1): Applications to Exchange Rate Modelling

Alexander, Carol; Lazar, Emese

doi:10.2139/ssrn.557362

Cited by 60 publications

(98 citation statements)

References 70 publications

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“…Similarly, the intercept in the conditional variance equation also displays a bias that is in general inversely related to the values of the corresponding mixing parameter. The result is largely in line with those reported in, for example, Alexander and Lazar (2006).…”

Section: Simulation Resultssupporting

confidence: 92%

“…Further, the off-diagonal elements of β i 's are set to zeros. Alexander and Lazar (2006) and others find that substantial estimation biases appear when k > 2 and allowing for non-zero off-diagonal elements in β i 's does not improve the empirical performance of NM-GARCH models they considered. Thus, for brevity, we consider the simplified version in the empirical part of our exercise.…”

Section: Estimation Resultsmentioning

confidence: 96%

“…Otherwise, it is asymmetric. Following, say, Alexander and Lazar (2006), we consider both the symmetric and asymmetric NM-GARCH processes; that is processes with the restriction λ 1 = λ 2 = · · · = λ k = 0 and without it. See Alexander and Lazar (2006) and Haas et al (2004a) for additional discussions of the properties of NM-GARCH processes and the related economic interpretations.…”

Section: The Modelmentioning

confidence: 99%

“…For the normal mixture GARCH component, the simplified empirical model has a mixture of two normal distributions (that is, k = 2) and the off-diagonal elements of β i 's are set to zeros. Alexander and Lazar (2006) and others find that substantial estimation biases appear when k > 2 and the empirical performance of NM-GARCH models they considered is not improved with non-zero off-diagonal elements in β i 's. Thus, for brevity, we consider the simplified version in the empirical part of our exercise.…”

Section: The Modelmentioning

confidence: 99%

“…The basic formulation has been modified in various directions, but more studies are still needed to accommodate the time varying structure of skewness and kurtosis. One recent extension is based on the notion of a normal mixture GARCH innovation process which is a linear combination of GARCH processes with their weights determined by data (see Alexander and Lazar 2006;Haas et al 2002Haas et al , 2004a. Several authors have already studied different versions of normal mixture GARCH models (see Bai et al 2003;Ding and Granger 1996;Roberts 2001;Vlaar and Palm 1993).…”

mentioning

confidence: 99%

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Section: Simulation Resultssupporting

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Section: The Modelmentioning

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Stochastic covariance models have been explored in recent research to model the interdependence of assets in financial time series. The approach uses a single stochastic model to capture such interdependence. However, it may be inappropriate to assume a single coherence structure at all time t . In this paper, we propose the use of a mixture of stochastic covariance models to generalize the approach and offer greater flexibility in real data applications. Parameter estimation is performed by Bayesian analysis with Markov chain Monte Carlo sampling schemes. We conduct a simulation study on three different model setups and evaluate the performance of estimation and model selection. We also apply our modeling methods to high-frequency stock data from Hong Kong. Model selection favors a mixture rather than non-mixture model. In a real data study, we demonstrate that the mixture model is able to identify structural changes in market risk, as evidenced by a drastic change in mixture proportions over time.

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On equity risk prediction and tail spillovers

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This paper studies the impact of modelling time-varying variances of stock returns in terms of risk measurement and extreme risk spillover. Using a general class of regime-dependent models, we find that volatility can be disaggregated into distinct components: a persistent stable process with low sensitivity to shocks and a high volatility process capturing rather short-lived rare events.Out-of-sample forecasts show that, once regime shifts are accounted for, accuracy is improved compared to the standard generalized autoregressive conditional heteroscedasticity or the historical volatility model. Volatility plays an important role in controlling and monitoring financial risks. Therefore, by means of a risk management application, we illustrate the economic value and the practical implications of risk control ability of the models in terms of value at risk. Finally, tests for predictability in co-movements in the tails of stock index returns suggest that large losses are strongly correlated, supporting asymmetric transmission processes for financial contagion in the left tail of return distributions, whereas contagion in reverse direction (gains) is weak. KEYWORDS causality in risk, forecasting, regime volatility, risk spillover, stock markets, value at risk Int J Fin Econ. 2017;22:379-393.wileyonlinelibrary.com/journal/ijfe

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Normal Mixture GARCH(1,1): Applications to Exchange Rate Modelling

Cited by 60 publications

References 70 publications

A Long Memory Model with Normal Mixture GARCH

A Long Memory Model with Normal Mixture GARCH

Stochastic Multivariate Mixture Covariance Model

On equity risk prediction and tail spillovers

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