Theory and Inference for a Markov Switching GARCH Model

Bauwens, Luc; Preminger, Arie; Rombouts, Jeroen V.K.

doi:10.2139/ssrn.1011623

Cited by 55 publications

(89 citation statements)

References 49 publications

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“…Let us consider the following experiment. We assume that the P&L are generated from a Markov Switching GARCH model (Bauwens, Preminger and Rombouts, 2010). This particular model allows both the conditional mean and the volatility to change from one state to the next:…”

Section: < Insert Table 1 >mentioning

confidence: 99%

The Risk Map: A new tool for validating risk models

Colletaz

Hurlin

Pérignon

2013

Journal of Banking & Finance

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This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is dened as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR dened at an extremely low coverage probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.JEL classication: G21, G28, G32

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Section: < Insert Table 1 >mentioning

confidence: 99%

The Risk Map: A new tool for validating risk models

Colletaz

Hurlin

Pérignon

2013

Journal of Banking & Finance

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“…The strength of this approach is that it can be applied for the estimation of many variants of Markov-Switching models. Closer to our problem, Henneke et al [37], Chen et al [38], and Bauwens et al [39] proposed three different MCMC algorithms for the Bayesian estimation of MS-ARMA-GARCH, MS-ARX-GARCH and MS-GARCH models, respectively. Some other difficulties arise when estimating MS-GARCH models.…”

Section: Existing Markov Switching Models With Garch Errorsmentioning

confidence: 99%

“…Alternatively, it is possible to apply a MCMC algorithm for MS-GARCH models presented in [39] and include extra autoregressive terms in the mean equation, instead of a single intercept. The difference in those three algorithms lays in the sampler used for the estimation of the autoregressive and heteroscedastic coefficients.…”

Section: Ar and Garch Coefficient Samplingmentioning

confidence: 99%

“…This type of problems is avoided when estimating posterior distributions with a GG sampler because it does not require the posterior density to be known in closed form. Taking these considerations into account, it was chosen to follow the methodology presented in [39] which uses the GG sampler for estimating MS-GARCH models. Adding extra autoregressive terms for the estimation of MS-AR-GARCH models is then straightforward.…”

Section: Ar and Garch Coefficient Samplingmentioning

confidence: 99%

“…, m}, setting the parameters d kk > d ki with i = k is one way to reflect the prior knowledge that the probability of persistence (staying in the same regime) is larger than the probability of switching from regime k to i. For instance, a B(8, 2) distribution is used as prior in [38] whereas a uniform B(1, 1) is preferred in [39]. Several simulations with various values for the d ij parameters were run on synthetic time series with more than 1000 data points.…”

Section: Prior Distributionsmentioning

confidence: 99%

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Accurate wind power forecasts highly contribute to the integration of wind power into power systems. The focus of the present study is on large-scale offshore wind farms and the complexity of generating accurate probabilistic forecasts of wind power fluctuations at time-scales of a few minutes. Such complexity is addressed from three perspectives: (i) the modeling of a nonlinear and non-stationary stochastic process; (ii) the practical implementation of the model we proposed; (iii) the gap between working on synthetic data and real world observations. At time-scales of a few minutes, offshore fluctuations are characterized by highly volatile dynamics which are difficult to capture and predict. Due to the lack of adequate on-site meteorological observations to relate these dynamics to meteorological phenomena, we propose a general model formulation based on a statistical approach and historical wind power measurements only. We introduce an advanced Markov Chain Monte Carlo (MCMC) estimation method to account for the different features observed in an empirical time series of wind power: autocorrelation, heteroscedasticity and regime-switching. The model we propose is an extension of Markov-Switching Autoregressive (MSAR) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors in each regime to cope with the heteroscedasticity. Then, we analyze the predictive power of our model on a one-step ahead exercise of time series sampled over 10 min intervals. Its performances are compared to state-of-the-art models and highlight the interest of including a GARCH specification for density forecasts.

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Multivariate Volatility Modeling of Electricity Futures

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Pierret

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The deregulation of European electricity markets has led to an increasing need in understanding the volatility and correlation structure of electricity prices. We model a multivariate futures series of the European Energy Exchange (EEX) index, using an asymmetric GARCH model for volatilities and augmented dynamic conditional correlation (DCC) models for correlations. In particular, we allow for smooth changes in the unconditional volatilities and correlations through a multiplicative component that we estimate non-parametrically. We also introduce exogenous variables in our new multiplicative DCC model to account for congestion in short-term conditional volatilities. We find different correlation dynamics for long and short-term contracts and the new model achieves higher forecasting performance compared to a standard DCC model. AbstractThe deregulation of European electricity markets has led to an increasing need in understanding the volatility and correlation structure of electricity prices. We model a multivariate futures series of the European Energy Exchange (EEX) index, using an asymmetric GARCH model for volatilities and augmented dynamic conditional correlation (DCC) models for correlations. In particular, we allow for smooth changes in the unconditional volatilities and correlations through a multiplicative component that we estimate non-parametrically. We also introduce exogenous variables in our new multiplicative DCC model to account for congestion in short-term conditional volatilities. We find different correlation dynamics for long and short-term contracts and the new model achieves higher forecasting performance compared to a standard DCC model.

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Theory and Inference for a Markov Switching GARCH Model

Cited by 55 publications

References 49 publications

The Risk Map: A new tool for validating risk models

The Risk Map: A new tool for validating risk models

A General Probabilistic Forecasting Framework for Offshore Wind Power Fluctuations

Multivariate Volatility Modeling of Electricity Futures

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