A Bayesian approach to model changes in volatility in the Mexican stock exchange index

We model the changes in volatility in the Mexican Stock Exchange Index using a Bayesian approach. We study the time series with a wide set of models characterized by a Markov switching heterogeneity. The advantage of this approach is that it allows for a broader spectrum of possible models since the estimation of the moments of the parameters is done using the finite mixture distribution MCMC method, without relying on assumptions about large sampling and mathematical optimization. This is particularly relevant for emerging markets’ financial data because of its special characteristics, like being more susceptible to jumps and changes in volatility caused by exchange rate swings, financial crises and oil and commodity prices. For model comparison, we use the marginal likelihood approach and the bridge sampling technique. The best representation of the data is given by a switching model with three states rather than any other autoregressive linear or non-linear model. The periods of volatility found by the model coincide with different financial crisis. Whereas other studies of volatility for the same market impose the Markovian model that captures changes in volatility, we let our model to be defined in an endogenous way.     

Regime-switching purchasing power parity in Latin America: Monte Carlo unit root tests with dynamic conditional score

We suggest a Monte Carlo simulation-based unit root test of the purchasing power parity theory for Latin American countries. Under the null hypothesis, we use a Markov regime-switching (MS) model with unit root in the conditional location and MS volatility dynamics. Under the alternative hypothesis, the proposed test incorporates Markov regime-switching autoregressive moving average (MS-ARMA) plus MS volatility dynamics. Under both the null and alternative hypotheses, one of the volatility models estimated is Beta-t-EGARCH, which is a recent dynamic conditional score volatility model. We use data on real effective exchange rate time series for 14 Latin American countries. For each country, we estimate by Monte Carlo simulation the critical values of the unit root test. We provide an economic discussion of the unit root test results and also study the robustness of MS-ARMA plus MS volatility with respect to smooth transition autoregressive models with Fourier function.     

S&P 500 volatility,volatility regimes,and economic uncertainty

We assess the relationship between regime-dependent volatility in S&P 500, economic policy uncertainty, the S&P 500 bull and bear sentiment spread (bb_sp), as well as the Chicago Board Options Exchange's VIX over the period 2000–2018. Our findings from two-covariate GARCH–MIDAS (GM) methodology, regime switching Markov Chain, and quantile regressions suggest that the association of realized volatility and sentiment varies across high- and low-volatility regimes and depends on investors’ sensitivity toward incidents of market uncertainties under these regimes. The findings suggest that these indicators may not be useful in volatility forecasting, especially under high-volatility regimes.     

Interest rate volatility and macroeconomic dynamics: Heterogeneity matters

We examine the relation between real interest rate volatility and aggregate fluctuations for a diverse sample of countries. Compiling a new dataset including emerging and advanced countries, the substantial variation in our data yields novel results: (a) stochastic volatility outperforms Markov‐switching in representing interest rates, (b) some advanced economies can be more volatile than emerging markets, and (c) creditors take on more debt following volatility shocks. We show how an equilibrium business cycle model with uncertainty shocks can generate these facts. Sample heterogeneity produces significant parameter differences, playing an important role in distinguishing the effects of volatility shocks.     

Conditional Markov regime switching model applied to economic modelling

In this paper we discuss the calibration issues of regime switching models built on mean-reverting and local volatility processes combined with two Markov regime switching processes. In fact, the volatility structure of these models depends on a first exogenous Markov chain whereas the drift structure depends on a conditional Markov chain with respect to the first one. The structure is also assumed to be Markovian and both structure and regime are unobserved. Regarding this construction, we extend the classical Expectation–Maximization (EM) algorithm to be applied to our regime switching model. We apply it to economic data (Euro/Dollar (USD) foreign exchange rate and Brent oil price) to show that such modelling clearly identifies both mean reverting and volatility regime switches. Moreover, it allows us to make economic interpretations of this regime classification as in some financial crises or some economic policies.     

Testing for a unit root in the presence of stochastic volatility and leverage effect

Previous studies have shown that the stationary and nonstationary time-varying volatilities have different implications on the unit root test. In this paper, we provide a Bayesian unit root test for an AR(1) model with stochastic volatility and leverage effect. Monte Carlo simulations show that the proposed Bayesian unit root test statistic achieves good finite sample properties and is robust to the stationarity of stochastic volatility.     

Crude oil price volatility dynamics and the great recession

Using a very simple econometric framework, we identify two major changes in the dynamics of crude oil price volatility based on data from 1997 to 2017. More precisely, we model weekly West Texas Intermediate (WTI) crude oil price realized volatility in a two-regime setting, one where realized volatility evolves as a plain autoregressive (AR) process (static), and the other where the level, persistence and innovation volatility of the AR process are subject to changes (dynamic). We use a Markov chain to model the probability that the process is in the static regime. The post Great Recession period sees a longer duration of the dynamic regime as well as smaller changes in the level and conditional volatility of realized volatility when switching actually occurs. Crude oil volatility also responds more aggressively to changes in economic variables, such as the t-bill rate and equity market volatility in the dynamic regime.     

Output volatility in Australia

A number of papers have documented a significant decline in real GDP volatility in several major OECD economies. Some authors have presented evidence to suggest that this is the outcome of a one-off structural break from a high to low volatility state whilst others have estimated regime switching models that indicate low volatility regime states have dominated in recent years. This article provides further evidence on the general properties of output volatility for Australia, including evidence of a significant moderation in output volatility for the country that occurred in the early 1980s. Estimates of various GARCH models of real GDP growth are also provided to further examine shorter term volatility features of the Australian economy that are associated with its business-cycle. A regime shift dummy is maintained in all models of the conditional variance in order to account for the regime shift in volatility and evidence is found of significant business-cycle effects, including leverage effects and asymmetries that suggest recessions are times of higher output volatility than economic expansions. Overall, it is concluded that the so-called ‘Great Moderation’ in macroeconomic instability, as documented here for Australia, is a result of a myriad of economic, institutional and policymaking changes.     

Improving GARCH volatility forecasts with regime-switching GARCH

Many researchers use GARCH models to generate volatility forecasts. Using data on three major U.S. dollar exchange rates we show that such forecasts are too high in volatile periods. We argue that this is due to the high persistence of shocks in GARCH forecasts. To obtain more flexibility regarding volatility persistence, this paper generalizes the GARCH model by distinguishing two regimes with different volatility levels; GARCH effects are allowed within each regime. The resulting Markov regime-switching GARCH model improves on existing variants, for instance by making multi-period-ahead volatility forecasting a convenient recursive procedure. The empirical analysis demonstrates that the model resolves the problem with the high single-regime GARCH forecasts and that it yields significantly better out-of-sample volatility forecasts. First Version Received: November 2000/Final Version Received: August 2001     

Forecasting volatility in the Chinese stock market under model uncertainty

Volatility forecasting is an important issue in empirical finance. In this paper, the main purpose is to apply the model averaging techniques to reduce volatility model uncertainty and improve volatility forecasting. Six GARCH-type models are considered as candidate models for model averaging. As to the Chinese stock market, the largest emerging market in the world, the empirical study shows that forecast combination using model averaging can be a better approach than the individual forecasts.     

Breaks or long range dependence in the energy futures volatility: Out-of-sample forecasting and VaR analysis

The aim of this paper is to propose an empirical strategy that allows the discrimination between true and spurious long memory behaviors. That strategy is based on the comparison between the estimated long memory parameter before and after filtering out the breaks. To date the breaks, we use the probability smoothing of the Markov Switching GARCH model of Haas et al. (2004). Application of this strategy to the crude oil, heating oil, RBOB regular gasoline and the propane futures energy with the one, two, three and four months maturities show strong evidence for the presence of long range dependence in all futures energy prices volatility¹ time series. This result of long range dependence in the volatility is confirmed by the superiority of the FIGARCH and FIEGARCH models compared with the Markov switching GARCH models in terms of out-of-sample forecasting and value at risk (VaR) performances. Moreover, we show that the proposed empirical strategy is robust to different data frequency. Practical implications of the results for market participants are proposed and discussed.     

Does purchasing power parity hold sometimes? Regime switching in real exchange rates

Standard unit root tests are not very powerful in drawing conclusions regarding the validity of Purchasing Power Parity (PPP). Rather than asking whether PPP holds throughout the whole sample period, we examine, in this study, if PPP holds sometimes by employing Hamilton-type (1989) Markov regime switching models. When at least one of multiple regimes is stationary, PPP holds locally within the regime. There are indeed various reasons that we should expect that the persistence of real exchange rates changes over time. Employing five real exchange rates spanning more than 100 years, we find herein strong evidence that the strength of PPP varies during the sample periods and that there exist stationary regimes in which PPP holds. Throughout the article, we also make comparisons to previous Markov regime switching estimation results by Kanas (2006) on the same data series. The new Markov switching model selection criterion of Smith et al. (2006), which is devised especially for discriminating Markov regime switching models, unambiguously indicates a preference for the Hamilton-type Markov regime switching model employed in this study. We also find that the evidence for PPP is not much different across different nominal exchange rate arrangements.     

An empirical analysis of the US stock market and output growth volatility spillover effects on three Anglo-Saxon countries

This paper examines the dynamic and switching effects of volatility spillovers arising from US stock market returns and GDP growth on those of Australia, Canada and the UK. For this purpose, we use quarterly data (1961q1–2013q1) and a constant probability Markov regime switching model. We found that the US stock market volatility significantly affects the stock market volatility of all three countries at least in one of the two specified regimes over time. However, the stock market volatilities in none of the three countries are contemporaneously influenced by the US output volatility even after allowing for two distinct regimes. On the other hand, the US stock market volatility exerts significant influences on the output volatilities of both Australia and the UK. Compared with Australia and the UK, Canada and the US show substantial output volatility co-movements, thereby confirming the close association between the two neighbouring economies through the NAFTA (North American Free Trade Agreement). We conclude that shocks emanating from the US stock market have unequivocal flow-on effects on the output and return volatilities of the other economies.     

A joint analysis of market indexes in credit default swap,volatility and stock markets

This paper analyses the joint dynamics of the CDS, volatility and stock markets using both VAR and Markov regime-switching VAR models with market index data. It shows that the joint behaviour of the three markets is better characterized by the Markov model with two regimes corresponding to low- and high-volatile market conditions. The relationship between changes in the market indexes under a regime is consistent with theory and persistent; the information transmission process of shocks to the markets is similar for the two regimes with a more important role for CDS shock; and the volatility in the money market is an important determinant of regime-switching. The findings have practical implications, particularly for hedging strategies with market indexes under different market conditions.     

Interest-rate volatility and volatility spillovers in emerging Europe

While many transition economies – particularly those that hope to join the Euro – have seen their economies converge to Europe’s, this process is by no means complete. Considerable macroeconomic volatility persists. This study examines the variability of the short-term nominal interest rates of ten transition economies, finding that eight of them exhibit time-varying volatility that can be modeled as a GARCH or Exponential GARCH process. Incorporating various measures of external volatility into the models, we find that those economies with fixed or managed exchange rates tend to experience more volatility spillovers, particularly from the Eurozone, regardless of the degree of transition. Only Estonia has a fixed exchange rate and remains free of international contagion.     

Linear time-varying regression with a DCC-GARCH model for volatility

This article provides a new linear state space model with time-varying parameters for forecasting financial volatility. The volatility estimates obtained from the model by using the US stock market data almost exactly match the realized volatility. We further compare our model with traditional volatility models in the ex post volatility forecast evaluations. In particular, we use the superior predictive ability and the reality check for data snooping. Evidence can be found supporting that our simple but powerful regression model provides superior forecasts for volatility.     

利率期限结构的马尔科夫区制转移模型与实证分析

本文在利率期限结构中通过纳入马尔科夫(Markov)区制转移,将传统CKLS模型推广到更为一般的状态相依的CKLS模型,并将之应用于对我国1996年1月至2006年3月银行间同业拆借市场六组不同到期日之月度加权平均利率的研究。通过模型估计和检验分析,我们发现在不同区制下不同到期日利率漂移函数和扩散函数均呈现非线性,其中漂移函数表现为强烈的随机游走过程或均值回归过程,而扩散函数表现为低波动状态或高波动状态。此外,结果表明不同到期日利率期限结构可由缩压的马尔科夫区制转移CKLS模型获得。     

Discerning trends in international metal prices in the presence of nonstationary volatility

In this paper, we develop an empirical framework that allows us to trace out a time path of metal prices. This framework shows that unpredictable shifts in demand, extraction costs and discovery of reserves, make estimation of the slope of this underlying trend an empirical question. Further, the low elasticity of demand and supply cause large volatility in the prices, which makes estimation of the trend difficult. We estimate the trend in metal prices employing econometric procedures that are robust to the underlying order of integration of the data and allow for nonstationary volatility, which we note is a characteristic feature of metal prices. We further analyse whether metal prices are characterised by stochastic trends by conducting unit root tests that allow for nonstationary volatility. Applying these procedures on metal prices for over a century, we draw conclusions that relate to policy.     

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.