Testing volatility persistence on Markov switching stochastic volatility models

In the literature, some researchers found that the high persistence of the volatility can be caused by Markov regime switching. This concern can be reflected as a unit root problem on the basis of Markov switching models. In this paper, our main purpose is to provide a Bayesian unit root testing approach for Markov switching stochastic volatility (MSSV) models. We illustrate the developed approach using S&P 500 daily return covering the subprime crisis started in 2008.     

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.     

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。     

Volatility forecasting: long memory,regime switching and heteroscedasticity

In this article, we account for the first time for long memory, regime switching and the conditional time-varying volatility of volatility (heteroscedasticity) to model and forecast market volatility using the heterogeneous autoregressive model of realized volatility (HAR-RV) and its extensions. We present several interesting and notable findings. First, existing models exhibit significant nonlinearity and clustering, which provide empirical evidence on the benefit of introducing regime switching and heteroscedasticity. Second, out-of-sample results indicate that combining regime switching and heteroscedasticity can substantially improve predictive power from a statistical viewpoint. More specifically, our proposed models generally exhibit higher forecasting accuracy. Third, these results are widely consistent across a variety of robustness tests such as different forecasting windows, forecasting models, realized measures, and stock markets. Consequently, this study sheds new light on forecasting future volatility.     

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.     

A dynamic Nelson-Siegel yield curve model with Markov switching

This paper proposes a model to better capture persistent regime changes in the interest rates of the US term structure. While the previous literature on this matter proposes that regime changes in the term structure are due to persistent changes in the conditional mean and volatility of interest rates we find that changes in a single parameter that determines the factor loadings of the model better captures regime changes. We show that this model gives superior in-sample forecasting performance as compared to a baseline model and a volatility-switching model. In general, we find compelling evidence that the extracted factors from our term structure models are closely related with various economic variables. Furthermore, we investigate and find evidence that the effects of macroeconomic phenomena such as monetary policy, inflation expectations, and real economic activity differ according to the particular regime realized for the term structure. In particular, we identify the periods where monetary policy appears to have a greater effect on the yield curve, and the periods where inflation expectations seem to have a greater effect in yield determination. We also find convincing evidence of a relationship between the regimes estimated by the various switching models with economic activity and monetary policy.     

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.     

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.     

Interest Rate Volatility Regimes in Selected Asian Countries:A Univariate Markov Switching Analysis

Business cycle dynamics are determined by relatively large volatilities in output,consumption,and investment,which leads to cyclical fluctuations in interest rates.Using the Markov switching model,we model the nominal interest rate movements to explain the volatility regime shifts in a set of selected emerging Asian economies.The estimated results provide significant evidence of regime-dependent means,variances,and probabilities in both stable and volatile regimes in selected countries,confirming the existence of two distinct regimes in nominal interest rate movements.In addition,the smoothed probability results of switching autoregressive model show that the model is capable of capturing the two regimes for the corresponding nominal interest rate behaviors.Besides,the results reveal that the stables regimes have higher durations than the volatile regimes.This study also shows the advantage of Markov switching models over conventional regression models,allowing the identification of different regimes for the cyclical behavior of interest rates.     

Has the 2008 financial crisis and its aftermath changed the impact of inflation on inflation uncertainty in member states of the european monetary union?

We study to what extent the financial crisis of 2008 and its aftermath have changed the impact of inflation on inflation uncertainty in the 12 original member states of the European Monetary Union (EMU). We adopt a time‐varying coefficient regression model with stochastic volatility effects, and extract two measures of inflation uncertainty from our data, namely, (1) The conditional volatility of inflation, (2) The conditional volatility of steady‐state inflation. (1)–(2) represent short‐run and steady‐state inflation uncertainty, respectively. The time‐varying impact of inflation on inflation uncertainty is analyzed using Markov‐switching regressions, where switching between the low and high inflation uncertainty regime is determined via an unobserved Markov process. Results suggest that the 2008 financial crisis and its aftermath have changed the impact of inflation on (1) and (2) across the selected EMU member states. However, a uniform pattern cannot be detected. For some member states, we document a strong link, whereas for others, the impact of inflation on inflation uncertainty is relatively weaker.     

Uncertainty and Learning in Stochastic Macro Models

Limits on information have deep economic impact and affect the conduct of economic policy. In the present paper we explore the effect of substantive uncertainty in a macro model, from both an analytical and methodological point of view. Agents are boundedly rational and make their forecasts according to different techniques and try to learn the values of the various parameters. In this context, a Markov regime switching rule, a VAR system, and recursive least square are considered and compared. As a result, we obtain a model which is mostly keynesian in nature that can be compared with the new neoclassical synthesis models. Simulations are carried out and show the possible appearence of endogenous and persistent fluctuations.     

OPTIMAL FORECAST COMBINATION UNDER REGIME SWITCHING*

This article proposes a new forecast combination method that lets the combination weights be driven by regime switching in a latent state variable. An empirical application that combines forecasts from survey data and time series models finds that the proposed regime switching combination scheme performs well for a variety of macroeconomic variables. Monte Carlo simulations shed light on the type of data‐generating processes for which the proposed combination method can be expected to perform better than a range of alternative combination schemes. Finally, we show how time variations in the combination weights arise when the target variable and the predictors share a common factor structure driven by a hidden Markov process.     

Testing Markov switching models

In this article, we propose a new test for Markov switching models. Unlike the tests in the existing literature (e.g. Hansen, 1992; Garcia, 1998; Cho and White, 2007), we focus on testing the null of two regimes, instead of one single regime, in a switching framework. To implement our test, we propose a Markov switching model with absorbing states and examine whether the absorption probabilities are close to the boundary of the parameter space. We exploit recent advances by Andrews (2001) and conduct inference in the proposed model.     

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.     

The asymmetric effects of oil shocks on output growth: A Markov–Switching analysis for the G-7 countries

Oil shocks are generally acknowledged to have important effects on both economic activity and macroeconomic policy. The aim of this paper is to investigate how oil price shocks affect the growth rate of output of a subset of developed countries by comparing alternative regime switching models. Different Markov–Switching (MS) regime autoregressive models are, therefore, specified and estimated. In a successive step, univariate MS models are extended in order to verify if the inclusion of asymmetric oil shocks as an exogenous variable improves the ability of each specification to identify the different phases of the business cycle for each country under scrutiny. Following the wide literature on this topic, seven different definitions of oil shocks which are able to describe oil price changes, asymmetric transformations of oil price changes, oil price volatility, and oil supply conditions are considered.     

Asymmetric effect of advertising on the Chinese stock market

In this paper, we investigate whether investor attention to advertising has an asymmetric effect on Chinese stock returns by using a multivariate Markov switching model with time-varying regime transition probabilities. Using the Chinese stock market as a setting, we obtain lagged conditional volatility from generalized autoregressive conditional heteroskedasticity (GARCH) for modelling the time-varying transition probabilities of the regime-switching process to capture changes in the market regime. Our evidence documents that the high advertising portfolio does earn higher abnormal return than the low advertising portfolio in low-volatility periods. In high-volatility periods, however, the abnormal return is insignificant when the firm increases advertising spending. Our results support the behavioural model argument that in high-volatility period, advertising information diffuses slowly due to cognitive dissonance. Thus, the effect of advertising on stock returns is asymmetric, and it shows statistical significance in low-volatility periods.     

Co-movement and spillovers: empirical evidence from BRIC equity markets

A higher degree of co-movement and spillover effects among different asset classes undermine portfolio diversification benefits. In this regard, the present study attempts to capture dynamic co-movement and return-volatility spillover effects among the most promising emerging equity markets, i.e. Brazil, Russia, India and China in a multivariate framework by employing VAR-ABEKK and VAR-DCC-AGARCH (1,1) models. To further comprehend the behaviour of the correlation coefficients during the global financial crisis period (2007–2009), heat map and Markov regime switching model (two regimes with a switch at ‘mean’ level only) have been used. The results report that the BRIC equity markets do not share a common stochastic trend in the long run. There is strong evidence of market shocks to volatility, volatility to volatility and negative shocks to volatility spillover effects among the BRIC markets. Overall, the BRIC markets are partially integrated with each other, thereby making them stronger investment candidates.     

Examining the stochastic behavior of REIT returns: Evidence from the regime switching approach

In this paper the stochastic behavior of the returns on real estate investment trusts (REITs) is examined by using the unobserved component Markov switching (UC-MS) model. This approach endogenously permits the volatility to switch as the date and regime change and allows us to decompose the permanent and transitory components in REIT returns at monthly frequencies. The empirical evidence clearly shows that, for all of the REIT returns, the overall variance of the transitory component is significantly smaller than the corresponding variance for the permanent component. The durations of the high-variance regimes for both the fundamental and transitory components are short-lived and revert to normal levels quickly.     

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.     

A tale of two states: asymmetries in the UK small,value and momentum premiums

This article performs comparative analysis of the asymmetries in size, value and momentum premium and their macroeconomic determinants over the UK economic cycles, using Markov switching approach. We associate Markov switching regime 1 with economic upturn and regime 2 with economic downturn. We find clear evidence of cyclical variations in the three premiums, most notable being that in the size premium, which changes from positive in expansions to negative in recessions. Macroeconomic indicators prompting such cyclicality the most are variables that proxy credit market conditions, namely the interest rates, term structure and credit spread. Overall, macro factors tend to have more significant impact on the three premiums during economic downturns. The results are robust to the choice of information variable used in modelling transition probabilities of the two-stage Markov switching model. We show that exploiting cyclicality in premiums proves particularly profitable for portfolios featuring small cap stocks in recessions at a feasible level of transaction costs.