Markov-switching GARCH Research Articles

Efficient Gibbs sampling for Markov switching GARCH models

Efficient simulation techniques for Bayesian inference on Markov-switching (MS) GARCH models are developed. Different multi-move sampling techniques for Markov switching state space models are discussed with particular attention to MS-GARCH models. The multi-move sampling strategy is based on the Forward Filtering Backward Sampling (FFBS) approach applied to auxiliary MS-GARCH models. A unified framework for MS-GARCH approximation is developed and this not only encompasses the considered specifications, but provides an avenue to generate new variants of MS-GARCH auxiliary models. The use of multi-point samplers, such as the multiple-try Metropolis and the multiple-trial metropolized independent sampler, in combination with FFBS, is considered in order to reduce the correlation between successive iterates and to avoid getting trapped by local modes of the target distribution. Antithetic sampling within the FFBS is also suggested to further improve the sampler’s efficiency. The simulation study indicates that the multi-point and multi-move strategies can be more efficient than other MCMC schemes, especially when the MS-GARCH is not strongly persistent. Finally, an empirical application to financial data shows the efficiency and effectiveness of the proposed estimation procedure.

Modeling carbon spot and futures price returns with GARCH and Markov switching GARCH models

This paper makes use of spot and futures market data to carry out a thorough analysis of the dynamics of carbon price returns in the European Union Emission Trading Scheme for the whole first commitment period from 2008 to 2012. Understanding the properties of carbon price returns is especially crucial for industries which have to comply with an emission trading system and other market participants such as risk managers and speculators. We therefore seek to develop accurate models which capture the behavior of carbon price returns comprehensively. We apply a broad spectrum of GARCH model specifications, using different distributions for model innovations. As both time series, spot and futures price returns, exhibit asymmetric behavior in their variance, we additionally take Markov regime switching models for the variance equation into consideration. Empirical results demonstrate that AGARCH, NARCH and GJR fit the data best. We further show that, in the error term of any model, fat-tailed distributions—in particular the generalized error distribution—significantly improve the fit. Additionally, as futures returns seem to carry informational content concerning subsequent spot returns, we propose a sound, yet parsimonious, spot returns model, well-suited to capturing the dynamics. Finally, the most appropriate models for spot and futures price returns are tested in an out-of-sample environment, and further checked for robustness in data subsets. Subsequently a model for each market is proposed.

Markov Switching GARCH Models for Bayesian Hedging on Energy Futures Markets

A new Bayesian multi-chain Markov Switching GARCH model for dynamic hedging in energy futures markets is developed by constructing a system of simultaneous equations for the return dynamics on the hedged portfolio and futures. More specifically, both the mean and variance of the hedged portfolio are assumed to be governed by two unobserved discrete state processes, while the futures dynamics is driven by a univariate hidden state process. The noise in both processes are characterized by a MS-GARCH model. This formulation has two main practical and conceptual advantages. First, the different states of the discrete processes can be identified as different volatility regimes. Secondly, the parameters can be easily interpreted as different hedging components. Our formulation also provides an avenue to analyze the contribution of the volatility dynamics and state probabilities to the optimal hedge ratio at each point in time. Moreover, the combination of the expected utility framework with regime-switching models allows the definition of a robust minimum variance hedging strategy to also account for parameter uncertainty. Evidence of changes in the optimal hedging strategies before and after the financial crisis is found when the proposed robust hedging strategy is applied to crude oil spot and futures markets.

Optimal portfolio selection in a Value-at-Risk framework: Markov-Switching GARCH Approach

The aim of this paper is to calculate VaR index with parametric Markov-Switching GARCH approach for accepted companies in Tehran Stock Exchange and also selecting the optimal portfolio of their stocks. To calculate the index, data and information of weekly stock price of 10 representative firms over the period 2008–2014 has been used which account for 332 working weeks. The results from estimation of VaR and determination of optimal stock portfolio in the non-linear programming framework showed that optimal portfolio of food-industry companies stock, in the context of VaR has higher returns in the first regime (Boom period) compared to the second regime (recession period), but had a lower risk. On the other hand, it has had lower weight in both stock portfolios that had lower average returns compared to the rest of the stocks and compared to the stocks which had lower VaR relative to other stocks that has higher weights.

Marginal likelihood for Markov-switching and change-point GARCH models

GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. Flexible alternatives are Markov-switching GARCH and change-point GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issue is the computation of their marginal likelihood, which is essential for determining the number of regimes or change-points. We solve the problem by using particle MCMC, a technique proposed by Andrieu et al. (2010). We examine the performance of this new method on simulated data, and we illustrate its use on several return series.

Forecasting electricity price volatility with the Markov-switching GARCH model: Evidence from the Nordic electric power market

In this paper, electricity price behavior in the Nordic electric power market is forecasted with both the Markov-switching generalized autoregressive conditional heteroskedasticity (MS-GARCH) model and a set of different volatility models. The MS-GARCH model is estimated with two regimes, representing periods of low and high volatility. This study shows that electricity price volatility is not only highly volatile but also strongly regime-dependent. The empirical results show that the MS-GARCH model enables more accurate forecasting than the standard GARCH models, according to tail loss and reality check tests for one- and multi-step ahead forecasts. The results suggest that both the electricity generation companies and consumers of electricity could carry out better price forecasts by using the proposed MS-GARCH model.

Financial fluctuations in the Tunisian repressed market context: a Markov-switching–GARCH approach

Small open economies are not immune to financial shocks. Fluctuations arising there interest more and more decision makers as they influence their policies’ effectiveness. A common belief is that opening the capital account is the primary source of financial instability. In this article we show that even if a capital account is not previously opened in Tunisia, the investor sentiment plays the role of the transmission channel of financial fluctuations. On monthly data (2000:01–2010:03) we filter financial business cycles via the Hodrick–Prescott procedure. Also we establish their turning points in Tunisian, Moroccan and French markets using the Bry–Boschan algorithm. Thus we build the investor sentiment index in Tunisia. Then we use it for the estimation of the financial volatility through a Markov switching–GARCH model. We show that business financial cycles in Tunisia are partially synchronized with those in France and the Tunisian investor’s sentiment is a significant explicative variable of the financial volatility. Therefore, we recommend a financial stabilization policy based on agent’s expectations for better macroeconomic effectiveness policies.

Maximum likelihood estimation of the Markov-switching GARCH model

The Markov-switching GARCH model offers rich dynamics to model financial data. Estimating this path dependent model is a challenging task because exact computation of the likelihood is infeasible in practice. This difficulty led to estimation procedures either based on a simplification of the model or not dependent on the likelihood. There is no method available to obtain the maximum likelihood estimator without resorting to a modification of the model. A novel approach is developed based on both the Monte Carlo expectation–maximization algorithm and importance sampling to calculate the maximum likelihood estimator and asymptotic variance–covariance matrix of the Markov-switching GARCH model. Practical implementation of the proposed algorithm is discussed and its effectiveness is demonstrated in simulation and empirical studies.

Geometric ergodicity of asymmetric volatility models with stochastic parameters

In this paper, we consider a general family of asymmetric volatility models with stationary and ergodic coefficients. This family can nest several non-linear asymmetric GARCH models with stochastic parameters into its ambit. It also generalizes Markov-switching GARCH and GJR models. The geometric ergodicity of the proposed process is established. Sufficient conditions for stationarity and existence of moments have also been investigated. Geometric ergodicity of various volatility models with stochastic parameters has been discussed as special cases.

Predicting volatility using the Markov-switching multifractal model: Evidence from S&P 100 index and equity options

In this paper, we evaluate the performance of the ability of Markov-switching multifractal (MSM), implied, GARCH, and historical volatilities to predict realized volatility for both the S&P 100 index and equity options. Some important findings are as follows. First, we find that the ability of MSM and GARCH volatilities to predict realized volatility is better than that of implied and historical volatilities for both the index and equity options. Second, equity option volatility is more difficult to be forecast than index option volatility. Third, both index and equity option volatilities can be better forecast during non-global financial crisis periods than during global financial crisis periods. Fourth, equity option volatility exhibits distinct patterns conditional on various equity and option characteristics and its predictability by MSM and implied volatilities depends on these characteristics. And finally, we find that MSM volatility outperforms implied volatility in predicting equity option volatility conditional on various equity and option characteristics.

Liquidity Needs, Private Information, Feedback Trading: Verifying Motives to Trade

We analyze investors' motives for trading on international stock markets and investigate whether evidence for these motives is robust when time-varying market volatility, changes between calm and turbulent periods, and existence of international financial spillovers are controlled for. Applying the Markov-switching GARCH specification of the standard model commonly used in the literature, we find that trades conducted due to liquidity needs or driven by private information cannot be identified unequivocally in any market, and positive feedback trading becomes predominant when return spillovers from the US market are taken into account.

A Family of Markov‐Switching Garch Processes

This paper develops a family of Markov‐switching GARCH (MSG) processes that not only encompasses some specifications in the literature, but also can be regarded as a Markov‐switching version of the family of GARCH processes introduced byHe and Teräsvirta (J. Econometrics, 1999, 92, 173–192). Some structural properties of this new family of MSG processes are considered. First, a sufficient and necessary condition for the existence of the strictly stationary solution of the family of MSG processes is presented. Moreover, we also give a sufficient and necessary condition for the existence of the strictly stationary solution of the family of MSG processes with finiteδ‐order moment. In particular, a definition of so‐called family of integrated MSG processes is introduced and its stationarity is also discussed. Next, the general conditions for the existence of any order moment of the family of MSG processes are derived. Finally, by means of a new renewal theorem, we describe the tail of the marginal distribution of the family of MSG processes.

Do short selling restrictions destabilize stock markets? Lessons from Taiwan

Short sellers have been routinely blamed for triggering, or exacerbating, stock market declines. The experience of Taiwan provides an interesting case study of the impact of short selling bans on stock returns volatility in a time series framework due to the length of time the short selling ban was in place there. Estimating several variants of an asymmetric GARCH model and a Markov switching GARCH model we find robust evidence that short selling restrictions raise stock returns volatility. The only qualifier is that the impact of short sale bans is a feature of the expansionary phase of business cycles. During recessions this effect dissipates.

Regime Switching GARCH Models and GARCH Models, in Stock Market of the Developing Countries'

This study is fore comparing GARCH models and Markov switching GARCH models in their ability to estimate and forecasting the volatility of Tehran stock market in some horizon of forecasting. This paper provides an analysis of regime switching in volatility and out-of-sample forecasting of the IRAN using daily data for the period 1995-2011. We first model volatility regime switching within a univariate Markov-Switching framework. Then We provide out-of-sample forecasts of the TEHRAN daily returns using two competing non-linear models, the GARCH Markov Switching model and the uniregime GARCH Model. The comparison of the out-of-sample forecasts is done on the basis of forecast accuracy, using the 7statistical loss function. The results, also, shows that SW-GARCH models can remove the high persistence of GARCH models and separately in each regime of volatility, the persistence are high. This shows the priority of SW-GARCH models. Another implication is that there is evidence of regime clustering.

Oil shock transmission to stock market returns: Wavelet-multivariate Markov switching GARCH approach

Since oil prices are typically governed by nonlinear and chaotic behavior, it’s become rather difficult to capture the dominant properties of their fluctuations. In recent years, unprecedented interest emerged on the decomposition methods in order to capture drifts or spikes relatively to this data. Together, our understanding of the nature of crude oil price shocks and their effects on the stock market returns has evolved noticeably. We accommodate these findings to investigate two issues that have been at the center of recent debates on the effect of crude oil shocks on the stock market returns of five developed countries (USA, UK, Japan, Germany and Canada). First, we analyze whether shocks and or volatility emanating from two major crude oil markets are transmitted to the equity markets. We do this by applying, the Haar A Trous Wavelet decomposition to monthly real crude oil series in a first step, and the trivariate BEKK Markov Switching GARCH model to analyze the effect of the smooth part on the degree of the stock market instability in a second step. The motivation behind the use of the former method is that noises and erratic behavior often appeared at the edge of the signal, can affect the quality of the shock and thus increase erroneous results of the shock transmission to the stock market. The proposed model is able to circumvent the path dependency problem that can influence the prediction’s robustness and can provide useful information for investors and government agencies that have largely based their views on the notion that crude oil markets affect negatively stock market returns. Second, under the hypothesis of common increased volatility, we investigate whether these states happen around the identified international crises. Indeed, the results show that the A Haar Trous Wavelet decomposition method appears to be an important step toward improving accuracy of the smooth signal in detecting key real crude oil volatility features. Additionally, apart from UK and Japanese cases, the responses of the stock market to an oil shock depend on the geographic area for the main source of supply whether from the North Sea or from the North America (as we take two oil benchmarks WTI and Brent respectively).

Marginal Likelihood for Markov-Switching and Change-Point GARCH Models

GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. Flexible alternatives are Markov-switching GARCH and change-point GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issue is the computation of their marginal likelihood, which is essential for determining the number of regimes or change-points. We solve the problem by using particle MCMC, a technique proposed by Andrieu, Doucet, and Holenstein (2010). We examine the performance of this new method on simulated data, and we illustrate its use on several return series.

Do Short Selling Restrictions Destabilize Stock Returns? Lessons from Taiwan

Short sellers have been routinely blamed for triggering, or exacerbating, stock market declines. The experience of Taiwan provides an interesting case study of the impact of short selling bans on stock returns volatility in a time series framework due to the length of time the short selling ban was in place there. Estimating several variants of an asymmetric GARCH model and a Markov switching GARCH model we find robust evidence that short selling restrictions raise stock returns volatility. The only qualifier is that the impact of short sale bans is a feature of the expansionary phase of business cycles. During recessions this effect dissipates.

Bayesian Forecasting for Financial Risk Management, Pre and Post the Global Financial Crisis

Value-at-Risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models are compared, including standard, threshold nonlinear and Markov switching GARCH specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student-t, skewed-t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia-Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models out-performed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre-crisis; while at the 1% level during and post-crisis, for a 1 day horizon, models with skewed-t errors ranked best, while IGARCH models were favoured at the 5% level; (iii) all models forecasted VaR less accurately and anti-conservatively post-crisis.

Forecasting hedge fund volatility: a Markov regime-switching approach

The article addresses forecasting volatility of hedge fund (HF) returns by using a non-linear Markov-Switching GARCH (MS-GARCH) framework. The in- and out-of-sample, multi-step ahead volatility forecasting performance of GARCH(1,1) and MS-GARCH(1,1) models is compared when applied to 12 global HF indices over the period of January 1990 to October 2010. The results identify different regimes with periods of high and low volatility for most HF indices. In-sample estimation results reveal a superior performance of the MS-GARCH model. The findings show that regime switching is related to structural changes in the market factor for most strategies. Out-of-sample forecasting shows that the MS-GARCH formulation provides more accurate volatility forecasts for most forecast horizons and for most HF strategies. Inclusion of MS dynamics in the GARCH specification highly improves the volatility forecasts for those strategies that are particularly sensitive to general macroeconomic conditions, such as Distressed Restructuring and Merger Arbitrage.

Forecasting Hedge Funds Volatility: A Markov Regime-Switching Approach

The article focuses on forecasting idiosyncratic hedge fund return volatility using a non-linear Markov switching GARCH (MS-GARCH) framework in which the conditional mean and volatility of systematic and idiosyncratic hedge fund return components may exhibit dynamic Markov switching behaviour. The article compares the out-of-sample and multi-step ahead forecasting performance of two competing conditional volatility specifications: GARCH(1,1) and MS-GARCH(1,1). The work employs data collected on 12 global hedge fund indices over January 1990 - October 2010 and produce volatility forecasts for the January 1999 - October 2010 period. The forecasting precision measure employed evidences superior forecasting performance of the MS volatility model for most hedge fund indices considered. The forecast encompassing robustness test results provide evidence that the MS-GARCH volatility forecasts significantly encompass the GARCH volatility forecasts for most Event-Driven and Relative Value hedge fund indices, whereas forecast encompassing is less significant for some Equity Hedge and Emerging Markets hedge fund indices.