Stochastic Volatility In Mean Model Research Articles

Approximate Bayesian Estimation of Stochastic Volatility in Mean Models Using Hidden Markov Models: Empirical Evidence from Emerging and Developed Markets

Approximate Bayesian Estimation of Stochastic Volatility in Mean Models Using Hidden Markov Models: Empirical Evidence from Emerging and Developed Markets

Testing Data Cloning as the Basis of an Estimator for the Stochastic Volatility in Mean Model

Developed as a refinement of stochastic volatility (SV) models, the stochastic volatility in mean (SVM) model incorporates the latent volatility as an explanatory variable in both the mean and variance equations. It, therefore, provides a way of assessing the relationship between returns and volatility, albeit at the expense of complicating the estimation process. This study introduces a Bayesian methodology that leverages data-cloning algorithms to obtain maximum likelihood estimates for SV and SVM model parameters. Adopting this Bayesian framework allows approximate maximum likelihood estimates to be attained without the need to maximize pseudo likelihood functions. The key contribution this paper makes is that it proposes an estimator for the SVM model, one that uses Bayesian algorithms to approximate the maximum likelihood estimate with great effect. Notably, the estimates it provides yield superior outcomes than those derived from the Markov chain Monte Carlo (MCMC) method in terms of standard errors, all while being unaffected by the selection of prior distributions.

The Link Between Output Growth and Output Growth Volatility: Barbados

This article investigates the effect of output volatility on output growth in Barbados, a small island developing state located in the Caribbean, based on data from 1976 through 2018. I conduct the analysis using the Stochastic Volatility in Mean model with time-varying parameters. The evidence suggests that output growth volatility, measured by stochastic volatility, negatively links with output growth at the aggregate level. I also examine disaggregate output data in order to understand this link better. The sectoral evidence suggests a positive link for services, a negative link for manufacturing, and a weak link for agriculture and the industrial sectors.

Investigating the effect of climate uncertainty on global commodity markets

This study aims to investigate the effect of climate uncertainty on global commodity markets. To do so, I modify Mumtaz and Theodoridis's (2018) time-varying factor-augmented VAR (FAVAR) with stochastic volatility in mean model. By incorporating the information from a large data set with an efficiently constructed dynamic factor structure, I not only overcome the omitted variable problem but also maintain the efficiency of the estimator to identify the nonlinear climate effects. Moreover, I apply Chang et al.'s (2017) endogenous regime switching in mean model for the climate variable, to overcome the statistical problem generated by the periodicity. The main empirical results can be summarized as follows. First, climate uncertainty generates an inflationary pressure on agricultural food, non-energy, and energy commodities for the El Niño years. Second, individual items such as maize and soybeans are more sensitive than the aggregated commodity indices to the effect of climate uncertainty. Third, climate uncertainty generates a negative supply shock, whereas market uncertainty generates a negative demand shock on the individual agricultural items. • We estimate the effect of climate uncertainty on global commodity markets. • We employ a modified time-varying FAVAR with stochastic volatility in mean model. • We apply an endogenous regime switching in mean model for the climate variable. • El Ni n ~ o causes inflationary pressure on food, non-energy, and energy commodities. • Individual items are more sensitive than the aggregated commodity indices.

Heterogeneous dependence between crude oil price volatility and China’s agriculture commodity futures: Evidence from quantile-on-quantile regression

This paper investigates volatility dependence between global crude oil and China’s agriculture futures by employing a quantile-on-quantile approach. The time-varying parameter stochastic volatility in mean model is used to evaluate the conditional volatility. The empirical results demonstrate the heterogeneous dependence between crude oil volatility and volatility in China’s agricultural futures across quantiles. The absolute volatility spillover exhibits an overall increasing trend with higher quantiles of agricultural volatility, and the volatility dependence is asymmetric across violent/stable market situations. Moreover, extremely high or low quantiles of oil volatility exert a considerable influence, while crude oil volatility does not influence the agricultural volatility in the normal mode of the crude oil market. Furthermore, a high persistence is noted in the volatility dynamics, and the impacts of volatility on the returns exhibit substantial time variation. These findings could have important economic implications for portfolio managers and policymakers in different economic and financial circumstances.

The volatility effect on precious metals price returns in a stochastic volatility in mean model with time-varying parameters

The purpose of this study is to examine how volatility effects precious metals price returns. We use the time-varying parameter stochastic volatility in mean (TVP-SVM) model to estimate the volatility and incorporate strong time varying dynamics in commodity markets. The study employs monthly data on gold, silver, copper, platinum, and palladium from 1962 to 2017. We find evidence that volatility has a largely time-varying impact on the precious metal price returns. The results show that volatility has a significant negative impact on the precious metal price returns and the impact is more negative during higher volatility periods. The market volatility is also found to be extremely persistent, implying that strong policy measures might be required to restore equilibrium. The estimates also show that metal price returns have a positive and significant effect on the volatility and, thus, higher precious metal price returns generate increased future volatility.

Bayesian analysis of moving average stochastic volatility models: modeling in-mean effects and leverage for financial time series

We propose a moving average stochastic volatility in mean model and a moving average stochastic volatility model with leverage. For parameter estimation, we develop efficient Markov chain Monte Carlo algorithms and illustrate our methods, using simulated and real data sets. We compare the proposed specifications against several competing stochastic volatility models, using marginal likelihoods and the observed-data Deviance information criterion. We also perform a forecasting exercise, using predictive likelihoods, the root mean square forecast error and Kullback-Leibler divergence. We find that the moving average stochastic volatility model with leverage better fits the four empirical data sets used.

Time‐Varying Relationship between Inflation and Inflation Uncertainty

AbstractThis paper investigates whether the relationship between inflation and inflation uncertainty has changed and whether the change in this relationship has been gradual or abrupt. We extend the time‐varying parameter with stochastic volatility in mean model (TVP‐SVM) to include a mixture innovation disturbance in the time‐varying parameter process. The proposed model produces more reliable estimates and allows us to investigate the occurrence of breaks in the gradually evolving process of the time varying coefficients. Using data of US, Germany, Canada, New Zealand, UK, France, Italy, Spain and Australia, we find that: (i) the relationship between inflation and inflation uncertainty substantially varies over time; (ii) there is strong support for the existence of abrupt changes in the US inflation–inflation uncertainty relationship; (iii) our empirical results of Canada and New Zealand show that the correlation between inflation and inflation uncertainty has been much weaker since early 1990s, which coincides with the timing of the implementation of inflation targeting.

Stochastic volatility in mean model for capturing the conditional variance in volatile time series data

Stochastic volatility in mean model for capturing the conditional variance in volatile time series data

Assessing the effect of inflation uncertainty on inflation: further evidences for Latin America

PurposeThe purpose of this paper is to evaluate whether the effect of inflation uncertainty on inflation has changed over time in Latin America.Design/methodology/approachThe authors use a stochastic volatility in mean (SVM) model with time-varying parameters (TVP) as proposed by Chan (2017).FindingsConsidering inflation series for the last two decades, we report evidences of high uncertainty from 1996 to early 2000s. Moreover, despite being positive throughout the sample, the overall relationship between inflation uncertainty and inflation has changed over the years in Latin America, underscoring the importance of our time-varying specification.Practical/implicationThere are evidences of a greater volatile inflation behavior in the beginning of the sample period in comparison to the last few years. Overall, the considered Latin American economies seem to have endured relatively well the external adverse shocks from the 2008 global financial crisis.Originality/valueThe use of an SVM model with TVP in order to assess the effect of inflation uncertainty on inflation is new to the Latin America literature.

Bayesian Analysis of Moving Average Stochastic Volatility Models: Modelling in Mean Effects and Leverage for Financial Time Series

We propose a moving average stochastic volatility in mean model and a moving average stochastic volatility model with leverage. For parameter estimation, we develop efficient Markov chain Monte Carlo algorithms and illustrate our methods, using simulated data and a real data set. We compare the proposed specifications against several competing stochastic volatility models, using marginal likelihoods and the observed-data Deviance information criterion. We find that the moving average stochastic volatility model with leverage has better fit to our daily return series than various standard benchmarks.

Maximum likelihood estimation for stochastic volatility in mean models with heavy-tailed distributions.

In this article, we introduce a likelihood-based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions (Abanto-Valle et al., 2012). Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. The method is based on the proposal of Langrock et al. (2012) and makes explicit the useful link between HMMs and SVM models with SMN distributions. Likelihood-based estimation of the parameters of stochastic volatility models in general, and SVM models with SMN distributions in particular, is usually regarded as challenging as the likelihood is a high-dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, i.e., estimating the volatility of the process.

The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling

This article generalizes the popular stochastic volatility in mean model to allow for time-varying parameters in the conditional mean. The estimation of this extension is nontrival since the volatility appears in both the conditional mean and the conditional variance, and its coefficient in the former is time-varying. We develop an efficient Markov chain Monte Carlo algorithm based on band and sparse matrix algorithms instead of the Kalman filter to estimate this more general variant. The methodology is illustrated with an application that involves U.S., U.K., and Germany inflation. The estimation results show substantial time-variation in the coefficient associated with the volatility, highlighting the empirical relevance of the proposed extension. Moreover, in a pseudo out-of-sample forecasting exercise, the proposed variant also forecasts better than various standard benchmarks.

The time-varying effect of inflation uncertainty on inflation for Turkey

ABSTRACTWe investigate the effect of inflation uncertainty on inflation from January 1982 through March 2016 for Turkey by using the Stochastic Volatility in Mean model with time-varying parameters. Our empirical evidence from consumer price index (CPI) inflation suggests that the observed positive relationship between inflation and inflation uncertainty is not robust. This positive relationship diminishes after 2002. This finding is valid for all five subcomponents of CPI inflation; however, for Health Services, Transportation Services, and Recreational and Cultural Services, an inflation-positive association is reported after 2010.

Asymmetric risk and return: Evidence from the Australian Stock Exchange

This paper examines volatility asymmetry in a financial market using a stochastic volatility framework. We use the MCMC method for model estimations. There is evidence of volatility asymmetry in the data. Our asymmetric stochastic volatility in mean model, which nests both asymmetric stochastic volatility (ASV) and stochastic volatility in mean models (SVM), indicates ASV sufficiently captures the risk-return relationship; therefore, augmenting it with volatility in mean does not improve its performance. ASV fits the data better and yields more accurate out-of-sample forecasts than alternatives. We also demonstrate that asymmetry mainly emanates from the systematic parts of returns. As a result, it is more pronounced at the market level and the volatility feedback effect dominates the leverage effect.

The Stochastic Volatility in Mean Model with Time-Varying Parameters: An Application to Inflation Modeling

This paper generalizes the popular stochastic volatility in mean model of Koopman and Hol Uspensky (2002) to allow for time-varying parameters in the conditional mean. The estimation of this extension is nontrival since the volatility appears in both the conditional mean and the conditional variance, and its coefficient in the former is time-varying. We develop an efficient Markov chain Monte Carlo algorithm based on band and sparse matrix algorithms instead of the Kalman filter to estimate this more general variant. We illustrate the methodology with an application that involves US, UK and Germany inflation. The estimation results show substantial time-variation in the coefficient associated with the volatility, high-lighting the empirical relevance of the proposed extension. Moreover, in a pseudo out-of-sample forecasting exercise, the proposed variant also forecasts better than various standard benchmarks.

Stochastic volatility in mean models with heavy-tailed distributions

A stochastic volatility in mean (SVM) model using the class of symmetric scale mixtures of normal (SMN) distributions is introduced in this article. The SMN distributions form a class of symmetric thick-tailed distributions that includes the normal one as a special case, providing a robust alternative to estimation in SVM models in the absence of normality. A Bayesian method via Markov-chain Monte Carlo (MCMC) techniques is used to estimate parameters. The deviance information criterion (DIC) and the Bayesian predictive information criteria (BPIC) are calculated to compare the fit of distributions. The method is illustrated by analyzing daily stock return data from the Sao Paulo Stock, Mercantile & Futures Exchange index (IBOVESPA). According to both model selection criteria as well as out-of-sample forecasting, we found that the SVM model with slash distribution provides a significant improvement in model fit as well as prediction for the IBOVESPA data over the usual normal model.

Inflation and inflation uncertainty: A dynamic framework

This paper aims to investigate the direct relationship between inflation and inflation uncertainty by employing a dynamic method for the monthly country–region–place United States data for the time period 1976–2007. While the bulk of previous studies has employed GARCH models in investigating the link between inflation and inflation uncertainty, in this study Stochastic Volatility in Mean models are used to capture the shocks to inflation uncertainty within a dynamic framework. These models allow researchers to assess the dynamic effects of innovations in inflation as well as inflation volatility on inflation and inflation volatility over time, by incorporating the unobserved volatility as an explanatory variable in the mean (inflation) equation. Empirical findings suggest that innovations in inflation volatility increases inflation. This evidence is robust across various definitions of inflation and different sub-periods.

Stochastic volatility in mean models with scale mixtures of normal distributions and correlated errors: A Bayesian approach

A stochastic volatility in mean model with correlated errors using the symmetrical class of scale mixtures of normal distributions is introduced in this article. The scale mixture of normal distributions is an attractive class of symmetric distributions that includes the normal, Student-t, slash and contaminated normal distributions as special cases, providing a robust alternative to estimation in stochastic volatility in mean models in the absence of normality. Using a Bayesian paradigm, an efficient method based on Markov chain Monte Carlo (MCMC) is developed for parameter estimation. The methods developed are applied to analyze daily stock return data from the São Paulo Stock, Mercantile & Futures Exchange index (IBOVESPA). The Bayesian predictive information criteria (BPIC) and the logarithm of the marginal likelihood are used as model selection criteria. The results reveal that the stochastic volatility in mean model with correlated errors and slash distribution provides a significant improvement in model fit for the IBOVESPA data over the usual normal model.

The Growth-Volatility Relationship: New Evidence Based on Stochastic Volatility in Mean Models

This paper models the relationship between growth and volatility for G7 economies in the time period 1960-2009. It delivers for the first time estimates of this relationship based on a logarithm variant of stochastic volatility in mean (SV-M) models. The relationship appears significantly positive in Germany and Italy, but insignificant in other countries. We also show that output volatility has increased in all countries since the beginning of the financial crisis, which illustrates the end of the great moderation. For comparison, the paper also delivers estimates based on a logarithm variant of GARCH in mean (log-GARCH-M) models, the class of time series models previously used in the literature to estimate the growth-volatility relationship. We show that SV-M models deliver results preferable to those of log-GARCH-M models, despite the high computational cost of their estimation. SV-M models fit generally better data than log-GARCH-M ones. As their residuals do not violate distribution assumptions, they do not deliver dubious conclusions concerning the significance of the relationship, which is the case of the log-GARCH-model for France, the UK and the US. Finally, SV-M models suggest a positive impact of unexpected volatility on output growth, which is not taken into account by log-GARCH-M models.