Generalized autoregressive conditional heteroskedasticity

Bollerslev, Tim

doi:10.1016/0304-4076(86)90063-1

Cited by 17,654 publications

(10,741 citation statements)

References 13 publications

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“…Examples of autoregressive conditional parameter models include the generalised autoregressive conditional heteroscedasticity (GARCH) model of Bollerslev (1986), the autoregressive conditional duration (ACD) and intensity (ACI) models of Engle and Russell (1998), the autoregressive conditional Poisson model of Rydberg and Shephard (2000), the dynamic conditional correlation model of Engle (2002), specific autoregressive copulas in Patton (2006), and the HEAVY model of Shephard and Sheppard (2010). Due to their widespread use, the class of ACP models provides a useful benchmark to our analysis.…”

Section: Autoregressive Conditional Parameter Modelsmentioning

confidence: 99%

Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models

Koopman

Scharth

2012

SSRN Journal

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Section: Autoregressive Conditional Parameter Modelsmentioning

confidence: 99%

Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models

Koopman

Scharth

2012

SSRN Journal

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“…Many time series with such properties can be described by means of the generalized autoregressive conditional heteroscedasticity (GARCH) models proposed by Bollerslev (1986).…”

Section: Types Of Nonstationaritymentioning

confidence: 99%

Application of modern tests for stationarity to single-trial MEG data

et al. 2011

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Stationarity is a crucial yet rarely questioned assumption in the analysis of time series of magneto-(MEG) or electroencephalography (EEG). One key drawback of the commonly used tests for stationarity of encephalographic time series is the fact that conclusions on stationarity are only indirectly inferred either from the Gaussianity (e.g. the Shapiro-Wilk test or Kolmogorov-Smirnov test) or the randomness of the time series and the absence of trend using very simple time-series models (e.g. the sign and trend tests by Bendat and Piersol). We present a novel approach to the analysis of the stationarity of MEG and EEG time series by applying modern statistical methods which were specifically developed in econometrics to verify the hypothesis that a time series is stationary. We report our findings of the application of three different tests of stationarity-the Kwiatkowski-Phillips-Schmidt-Schin (KPSS) test for trend or mean stationarity, the Phillips-Perron (PP) test for the presence of a unit root and the White test for homoscedasticity-on an illustrative set of MEG data. For five stimulation sessions, we found already for short epochs of duration of 250 and 500 ms that, although the majority of the studied epochs of single MEG trials were usually mean-stationary (KPSS test and PP test), they were classified as nonstationary due to their heteroscedasticity (White test). We also observed that the presence of external auditory stimulation did not significantly affect the findings regarding the stationarity of the data. We conclude that the combination of these tests allows a refined analysis of the stationarity of MEG and EEG time series.

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“…The simple method that can consider two characteristics of financial asset returns, namely time-varying volatility and excess kurtosis, is the GARCH model by Engle (1982) and Bollerslev (1986). Researchers beginning with Black (1976) have demonstrated that stock returns are negatively correlated with changes in return volatility.…”

Section: Introductionmentioning

confidence: 99%

Improving Value-at-Risk Estimation from the Normal EGARCH Model

Mahsa

Sajjad

2017

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Returns in financial assets display consistent excess kurtosis and skewness, implying the presence of large fluctuations not forecasted by Gaussian models. This paper applies a resampling method based on the bootstrap and a bias-correction step to improve Value-at-Risk (VaR) forecasting ability of the n-EGARCH (normal EGARCH) model and correct the VaR for both long and short positions. Our aim is to utilize the advantages of this model, but still use the bootstrap resampling method to accurate for the tendency of the model tomiscalculate the VaR. Empirical results indicate that the bias-correction method can improve the n-GARCH and n-EGARCH VaR forecasts so much that the acquired VaR predictions are different from the proposed probability. Additionally, allowing asymmetry in the conditional variance using the EGARCH model with normal distribution instead of GARCH improves the performance of the bias-correction method in forecasting the VaR for almost all considered indices. Moreover, the bias-corrected n-EGARCH model performs better than the simple t-EGARCH model. Thus, it seems that this model can take account of both the asymmetry in the conditional variance and leptokurtosis in returns distribution. However, we find that the superiority of the bias-corrected n-EGARCH model over the t-EGARCH model is not completely confirmed for short positions based on the censored likelihood scoring rule. IntroductionSince the Basle Committee (1995; began allowing banks to implement internal VaR models for calculating capital requirements, various methods have been proposed to achieve this purpose. However, the theoretical and computational complexity of these methods has also been raised.

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Generalized autoregressive conditional heteroskedasticity

Cited by 17,654 publications

References 13 publications

Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models

Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models

Application of modern tests for stationarity to single-trial MEG data

Improving Value-at-Risk Estimation from the Normal EGARCH Model

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