Volatility Modeling with a Generalized <i>t</i> Distribution

Harvey, Andrew; Lange, Rutger‐Jan

doi:10.1111/jtsa.12224

Cited by 51 publications

(30 citation statements)

References 18 publications

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“…Further generalizations are possible. For example the generalized t ‐distribution may be used, as in the ARCH‐M model of Theodossiou and Savva (), and this may be extended to allow for different degrees of freedom in the upper and lower tails, as in Harvey and Lange (). Adding an ARCH‐M vector to a multivariate DCS volatility model of the kind proposed by Creal et al () is also possible, yielding a model which is much closer to the specification of Bekaert and Wu () than that of Bollerslev et al ().…”

Section: Resultsmentioning

confidence: 99%

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Modeling the Interactions between Volatility and Returns using EGARCH‐M

Harvey

Lange

2018

Journal Time Series Analysis

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An EGARCH-M model, in which the logarithm of scale is driven by the score of the conditional distribution, is shown to be theoretically tractable as well as practically useful. A two-component extension makes it possible to distinguish between the short-and long-run effects of returns on volatility, and the resulting short-and long-run volatility components are then allowed to have different effects on returns, with the long-run component yielding the equity risk premium. The EGARCH formulation allows for more flexibility in the asymmetry of the volatility response (leverage) than standard GARCH models and suggests that, for weekly observations on two major stock market indices, the short-term response is close to being anti-symmetric. component, as found by Engle and Lee (1999) and others. Indeed, short-run volatility may even decrease after a good day, because it calms the market. Standard GARCH models are unable to identify this effect.Adrian and Rosenberg (2008) proposed a two-component exponential GARCH-M (EGARCH-M) model. They showed that it captures the asymmetric response of short-and long-term volatility to returns, and that the long-run component is positively correlated with the equity risk premium. Here we demonstrate that letting the dynamics be driven by the score of the conditional distribution yields a model that is theoretically tractable as well as practically useful. Models constructed using the conditional score were introduced into the literature by Creal et al. (2011Creal et al. ( , 2013, where they are called Generalized Autoregressive Score (GAS) models, and Harvey (2013), where they are called Dynamic Conditional Score (DCS) models. The classic EGARCH specification in Nelson (1991), which is the one used by Adrian and Rosenberg, is sensitive to outliers and it has the unfortunate theoretical property that unconditional moments do not exist when the conditional distribution is Student's t. The DCS model resolves these problems and, in doing so, yields a specification which is open to the development of a full asymptotic theory for the distribution of the maximum likelihood estimator. This contrasts with standard formulations of ARCH-M models, where the asymptotic theory appears to be intractable.Section 2 sets out the DCS formulation of the basic EGARCH-M model with a conditional Student's t-distribution and outlines the associated statistical theory, including an easily implemented condition for invertibility. This is followed by subsections on the asymmetric response of volatility to returns (leverage), two components, skewness and splines. In Section 3 various models are fitted to weekly data on NASDAQ and NIKKEI returns. The risk-free rate of return is then introduced as an explanatory variable, as in Scruggs (1998), and the model is fitted to weekly excess returns on S&P500 over a 60-year period. Section 4 reports the results of a small forecasting study to provide reassurance on the predictive performance of DCS models. Section 5 concludes. Appendices A to C are provided online as Ap...

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Section: Resultsmentioning

confidence: 99%

“…Following the discussion in Blasques et al (), a sufficient condition for invertibility can be found by generalizing the result in Harvey and Lange (, p. 182). The proposition below is for the Beta‐t‐EGARCH‐M model, to , but with the ARCH‐M score term dropped from .…”

Section: Model Formulationmentioning

confidence: 86%

Modeling the Interactions between Volatility and Returns using EGARCH‐M

Harvey

Lange

2018

Journal Time Series Analysis

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“…The critical value is 3.64 for a single parameter restriction at a 5% level of significance. 13 The asymmetric skew generalized t model of Harvey and Lange (2017) was also estimated for all series and compared via LRTs. The tests failed to reject the simpler AST DCS model at a 10% level for the FTSE, NASDAQ, Kospi and Bovespa series, though improvements were found for the S&P 500 and DJIA.…”

Section: In-sample Estimation Resultsmentioning

confidence: 99%

Modeling the conditional distribution of financial returns with asymmetric tails

Thiele

2019

J of Applied Econometrics

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Summary This paper proposes a conditional density model that allows for differing left/right tail indices and time‐varying volatility based on the dynamic conditional score (DCS) approach. The asymptotic properties of the maximum likelihood estimates are presented under verifiable conditions together with simulations showing effective estimation with practical sample sizes. It is shown that tail asymmetry is prevalent in global equity index returns and can be mistaken for skewness through the center of the distribution. The importance of tail asymmetry for asset allocation and risk premia is demonstrated in‐sample. Application to portfolio construction out‐of‐sample is then considered, with a representative investor willing to pay economically and statistically significant management fees to use the new model instead of traditional skewed models to determine their asset allocation.

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“…For example, as = 2, it becomes Student-t with degrees of freedom. On the other hand, with →∞, the limiting case is GED( ), the generalized error distribution; see Harvey and Lange (2017) for a more detailed discussion. The distribution is quite flexible and therefore capable of capturing many empirically relevant situations, especially related with the occurrence of rare events.…”

Section: Methodsmentioning

confidence: 99%

Probabilistic predictive analysis of business cycle fluctuations in Polish economy

Mazur

2017

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Research background: The probabilistic setup and focus on evaluation of uncertainties and risks has become more widespread in modern empirical macroeconomics, including the analysis of business cycle fluctuations. Therefore, forecast-based indicators of future economic conditions should be constructed using density forecasts rather than point forecasts, as the former provide description of forecast uncertainty. Purpose of the article: We discuss model-based probabilistic inference on business cycle fluctuations in Poland. In particular, we consider model comparison for probabilistic prediction of growth rates of the Polish industrial production. We also develop a class of indicators of future economic conditions constructed using probabilistic information on the rates (that make use of joint predictive distribution over several forecast horizons). Methods: We use Bayesian methods (in order to capture the estimation uncertainty) and consider two groups of models. The first group consists of Dynamic Conditional Score models with the generalized t conditional distribution (with conditional heteroskedasticity and heavy tails, being important for modelling of extreme observations). Another group of models relies on deterministic cycle modelling using Flexible Fourier Form. Ex-post density forecasting performance of the models is compared using the criteria for probabilistic pre-diction: Log-Predictive Score (LPS) and Continuous Ranked Probability Score (CRPS). Findings & value added: The pre-2013 data support the deterministic cycle models whereas more recent observations can be explained by a simple mean-reverting Gaussian AR(4) process. The results indicate a structural change affecting Polish business cycle fluctuations after 2013. Hence, forecast pooling strategies are recommended as a tool for further research. We find rather limited support in favor of the first group of models. The probabilistic indicator of future economic conditions considered here leads actual phases of the growth cycle quite well, though the effect is less obvious after 2013.

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Volatility Modeling with a Generalized t Distribution

Cited by 51 publications

References 18 publications

Modeling the Interactions between Volatility and Returns using EGARCH‐M

Modeling the Interactions between Volatility and Returns using EGARCH‐M

Modeling the conditional distribution of financial returns with asymmetric tails

Probabilistic predictive analysis of business cycle fluctuations in Polish economy

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