A flexible parametric GARCH model with an application to exchange rates

Wang, Kaili; Fawson, Christopher; Barrett, Chris; McDonald, James B.

doi:10.1002/jae.606

Cited by 64 publications

(35 citation statements)

References 31 publications

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“…However, GARCH models with conditionally normal errors generally fail to sufficiently capture the leptokurtosis evident in asset returns. The increasing attention focused on distributional properties (particularly tail heavyness), when estimating exchange rates models, has led to the widespread adoption of non-Gaussian conditional error distributions, most commonly the Student-t [38,39,40]. The Student-t distribution models more extended tails than the normal distribution and is asymptotically a power law with an exponent κ equal to the number of its degrees of freedom.…”

Section: Numerical Resultsmentioning

confidence: 99%

Statistical Significance of Periodicity and Log-Periodicity With Heavy-Tailed Correlated Noise

Zhou

Sornette

2002

Int. J. Mod. Phys. C

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We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. The solution of this problem is already known for independent Gaussian distributed noise. We investigate more general situations with non-Gaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. A periodic component of a time series is usually detected by some sort of Fourier analysis. Here, we use the Lomb periodogram analysis which is suitable and outperforms Fourier transforms for unevenly sampled time series. We examine the false-alarm probability of the largest spectral peak of the Lomb periodogram in the presence of power-law distributed noises, of short-range and of long-range fractional-Gaussian noises. Increasing heavy-tailness (respectively correlations describing persistence) tends to decrease (respectively increase) the false-alarm probability of finding a large spurious Lomb peak. Increasing anti-persistence tends to decrease the false-alarm probability. We also study the interplay between heavy-tailness and long-range correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should in principle characterize the Lomb peak height, its width and its relations to other peaks in the complete spectrum. As a step towards this full characterization, we construct the jointdistribution of the frequency position (relative to other peaks) and of the height of the highest peak of the power spectrum. We also provide the distributions of the ratio of the second highest Lomb peak to the maximum peak. Using the insight obtained by the present statistical study, we re-examine previously reported claims of "log-periodicity" and find that the credibility for logperiodicity in 2D-freely decaying turbulence is weakened while it is strengthened for fracture, for the ion-signature prior to the Kobe earthquake and for financial markets.

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Section: Numerical Resultsmentioning

confidence: 99%

Statistical Significance of Periodicity and Log-Periodicity With Heavy-Tailed Correlated Noise

Zhou

Sornette

2002

Int. J. Mod. Phys. C

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“…Along with the Student's t (Bollerslev, 1987), two asymmetric generalizations are used, namely the non-central t distribution (Harvey and Siddique, 1999) and the so-called t 3 distribution used in . Further candidates include the hyperbolic (Eberlein and Keller, 1995;Küchler et al, 1999;Paolella, 1999), the generalized logistic (or EGB2) distribution (Paolella, 1997, Wang et al, 2001) and the asymmetric two-sided Weibull (Mittnik et al, 1998), abbreviated ADW. Table 1 reports the likelihood-based goodness-of-fit measures for the fitted models and the rankings of the models with respect to each of the criteria.…”

Section: Competing Modelsmentioning

confidence: 99%

Mixed Normal Conditional Heteroskedasticity

Haas

Mittnik

Paolella

2004

Journal of Financial Econometrics

168

173

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Abstract:Both unconditional mixed-normal distributions and GARCH models with fat-tailed conditional distributions have been employed for modeling financial return data. We consider a mixed-normal distribution coupled with a GARCH-type structure which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. An empirical application to NASDAQindex data indicates the appropriateness of the model class and illustrates that the approach can generate a plausible disaggregation of the conditional variance process, in which the components' volatility dynamics have a clearly distinct behavior that is, for example, compatible with the well-known leverage effect.JEL Classification: C22, C51, G10

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“…By comparing the sample moments by the moments predicted by the assumed distributions, we see that the models overestimate the skewness and underestimate the kurtosis. The implication is that more ßexible distributions may be needed, like the exponential generalized beta family in Wang et al (2001). …”

Section: Estimation Of the Auxiliary Modelmentioning

confidence: 99%

Estimation of an Adaptive Stock Market Model with Heterogeneous Agents

Amilon

2006

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. The Working Paper series presents reports on matters in the sphere of activities of the Riksbank that are considered to be of interest to a wider public. The papers are to be regarded as reports on ongoing studies and the authors will be pleased to receive comments. Terms of use: Documents inThe views expressed in Working Papers are solely the responsibility of the authors and should not to be interpreted as reflecting the views of the Executive Board of Sveriges Riksbank. Estimation of an Adaptive Stock Market Model with Heterogeneous AgentsHenrik Amilon * Sveriges Riksbank Working Paper Series No. 177 January 2005Abstract Standard economic models based on rational expectations and homogeneity have problems explaining the complex and volatile nature of Þnancial markets. Recently, boundedly rational and heterogeneous agent models have been developed and simulated returns are found to exhibit various stylized facts, such as volatility clustering and fat tails. Here, we are interested in how well the proposed models can explain all the properties seen in real data, not just one or a few at a time. Hence, we do a proper estimation of some simple versions of such a model by the use of efficient method of moments and maximum likelihood and compare the results to real data and more traditional econometric models. We discover two main Þndings. First, the similarities with observed data found in earlier simulations rely crucially on a somewhat unrealistic modeling of the noise term. Second, when the stochastic is more properly introduced we Þnd that the models are able to generate some stylized facts, but that the Þt generally is quite poor.

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A flexible parametric GARCH model with an application to exchange rates

Cited by 64 publications

References 31 publications

Statistical Significance of Periodicity and Log-Periodicity With Heavy-Tailed Correlated Noise

Statistical Significance of Periodicity and Log-Periodicity With Heavy-Tailed Correlated Noise

Mixed Normal Conditional Heteroskedasticity

Estimation of an Adaptive Stock Market Model with Heterogeneous Agents

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