Some empirical evidence on the real effects of nominal volatility

It has been argued that volatility in nominal macroeconomic aggregates has had a negative effect on real output, in particular that such volatility contributed to slow output growth in the early 1980s. This paper reexamines the effects of volatility in nominal macroeconomic aggregates in the context of a modern simultaneous equation framework where the volatility of, nominal macroeconomic variables is modeled as the conditional variance of two variables of interest: the federal funds rate and inflation. The empirical framework is the recently developed multivariate GARCH-in-mean vector autoregressive model. We confirm evidence that inflation volatility and tight monetary policy have directly affected output growth, but find that volatility in the federal funds rate has not.     

Estimating and predicting multivariate volatility thresholds in global stock markets

We propose a general double tree structured AR‐GARCH model for the analysis of global equity index returns. The model extends previous approaches by incorporating (i) several multivariate thresholds in conditional means and volatilities of index returns and (ii) a richer specification for the impact of lagged foreign (US) index returns in each threshold. We evaluate the out‐of‐sample forecasting power of our model for eight major equity indices in comparison to some existing volatility models in the literature. We find strong evidence for more than one multivariate threshold (more than two regimes) in conditional means and variances of global equity index returns. Such multivariate thresholds are affected by foreign (US) lagged index returns and yield a higher out‐of‐sample predictive power for our tree structured model setting. Copyright © 2006 John Wiley & Sons, Ltd.     

Testing for co-integration in vector autoregressions with non-stationary volatility

Many key macroeconomic and financial variables are characterized by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in  and  are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identified inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, or to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very well in practice.     

Composite likelihood methods for large Bayesian VARs with stochastic volatility

Adding multivariate stochastic volatility of a flexible form to large vector autoregressions (VARs) involving over 100 variables has proved challenging owing to computational considerations and overparametrization concerns. The existing literature works with either homoskedastic models or smaller models with restrictive forms for the stochastic volatility. In this paper, we develop composite likelihood methods for large VARs with multivariate stochastic volatility. These involve estimating large numbers of parsimonious models and then taking a weighted average across these models. We discuss various schemes for choosing the weights. In our empirical work involving VARs of up to 196 variables, we show that composite likelihood methods forecast much better than the most popular large VAR approach, which is computationally practical in very high dimensions: the homoskedastic VAR with Minnesota prior. We also compare our methods to various popular approaches that allow for stochastic volatility using medium and small VARs involving up to 20 variables. We find our methods to forecast appreciably better than these as well.     

Uncertainty across volatility regimes

We propose a nonrecursive identification scheme for uncertainty shocks that exploits breaks in the volatility of macroeconomic variables and is novel in the literature on uncertainty. This approach allows us to simultaneously address two major questions in the empirical literature: Is uncertainty a cause or effect of decline in economic activity? Does the relationship between uncertainty and economic activity change across macroeconomic regimes? Results based on a small‐scale vector autoregression with US monthly data suggest that (i) uncertainty is an exogenous source of decline of economic activity, and (ii) the effects of uncertainty shocks amplify in periods of economic and financial turmoil.     

Testing for multivariate volatility functions using minimum volume sets and inverse regression

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii) of a bathtub shape, and (iii) in a given parametric form. The inference based on those tests may be further enhanced through associated diagnostic plots. Although the potential use of those ideas is much wider, we focus on the inference for multivariate volatility functions in this paper, i.e. we test for (i) heteroscedasticity, (ii) the so-called ‘smiling effect’, and (iii) some parametric volatility models. The asymptotic behavior of the proposed tests is investigated, and practical feasibility is shown via simulation studies. We further illustrate our methods with real financial data.     

Efficient estimation of Bayesian VARMAs with time‐varying coefficients

Empirical work in macroeconometrics has been mostly restricted to using vector autoregressions (VARs), even though there are strong theoretical reasons to consider general vector autoregressive moving averages (VARMAs). A number of articles in the last two decades have conjectured that this is because estimation of VARMAs is perceived to be challenging and proposed various ways to simplify it. Nevertheless, VARMAs continue to be largely dominated by VARs, particularly in terms of developing useful extensions. We address these computational challenges with a Bayesian approach. Specifically, we develop a Gibbs sampler for the basic VARMA, and demonstrate how it can be extended to models with time‐varying vector moving average (VMA) coefficients and stochastic volatility. We illustrate the methodology through a macroeconomic forecasting exercise. We show that in a class of models with stochastic volatility, VARMAs produce better density forecasts than VARs, particularly for short forecast horizons.     

Information flows and stock market volatility

This study examines how news is distributed across stocks. A model is developed that categorizes a stock's latent news into normal and nonnormal news, and allows both types of news to be filtered through to other stocks. This is achieved by formulating a model that jointly incorporates a multivariate lognormal‐Poisson jump process (for nonnormal news) and a multivariate GARCH process (for normal news), in addition to a news (or shock) transmission mechanism that allows the shocks from both processes to impact intertemporally on all stocks in the system. The relationship between news and the expected volatility surface is explored and a unique news impact surface is derived that depends on time, news magnitude, and news type. We find that the effect of nonnormal news on volatility expectations typically builds up before dissipating, with the news transmission mechanism effectively crowding‐out normal news and crowding‐in nonnormal news. Moreover, in contrast to the standard approach for measuring leverage effects using asymmetric generalized autoregressive conditional heteroskedasticity models, we find that leverage effects stem predominantly from nonnormal news. Finally, we find that the capacity to identify positively or negatively correlated stock returns is ambiguous in the short term, and depends heavily on the behavior of the nonnormal news component.     

Evolving United States stock market volatility: The role of conventional and unconventional monetary policies

Despite the econometric advances of the last 30 years, the effects of monetary policy stance during the boom and busts of the stock market are not clearly defined. In this paper, we use a structural heterogeneous vector autoregressive (SHVAR) model with identified structural breaks to analyse the impact of both conventional and unconventional monetary policies on U.S. stock market volatility. We find that contractionary monetary policy enhances stock market volatility, but the importance of monetary policy shocks in explaining volatility evolves across different regimes and is relative to supply shocks (and shocks to volatility itself). In comparison to business cycle fluctuations, monetary policy shocks explain a greater fraction of the variance of stock market volatility at shorter horizons, as in medium to longer horizons. Our basic findings of a positive impact of monetary policy on equity market volatility (being relatively stronger during calmer stock market periods) are also corroborated by analyses conducted at the daily frequency based on an augmented heterogeneous autoregressive model of realised volatility (HAR-RV) and a multivariate k-th order nonparametric causality-in-quantiles framework. Our results have important implications both for investors and policymakers.     

STRUCTURAL VECTOR AUTOREGRESSIONS: CHECKING IDENTIFYING LONG‐RUN RESTRICTIONS VIA HETEROSKEDASTICITY

Long‐run restrictions have been used extensively for identifying structural shocks in vector autoregressive (VAR) analysis. Such restrictions are typically just‐identifying but can be checked by utilizing changes in volatility. This paper reviews and contrasts the volatility models that have been used for this purpose. Three main approaches have been used, exogenously generated changes in the unconditional residual covariance matrix, changing volatility modelled by a Markov switching mechanism and multivariate generalized autoregressive conditional heteroskedasticity models. Using changes in volatility for checking long‐run identifying restrictions in structural VAR analysis is illustrated by reconsidering models for identifying fundamental components of stock prices.     

Multivariate volatility forecasts for stock market indices

Volatility forecasts aim to measure future risk and they are key inputs for financial analysis. In this study, we forecast the realized variance as an observable measure of volatility for several major international stock market indices and accounted for the different predictive information present in jump, continuous, and option-implied variance components. We allowed for volatility spillovers in different stock markets by using a multivariate modeling approach. We used heterogeneous autoregressive (HAR)-type models to obtain the forecasts. Based an out-of-sample forecast study, we show that: (i) including option-implied variances in the HAR model substantially improves the forecast accuracy, (ii) lasso-based lag selection methods do not outperform the parsimonious day-week-month lag structure of the HAR model, and (iii) cross-market spillover effects embedded in the multivariate HAR model have long-term forecasting power.     

Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting

We consider semiparametric frequency domain analysis of cointegration between long memory processes, i.e. fractional cointegration, allowing derivation of useful long-run relations even among stationary processes. The approach is due to Robinson (1994b. Annals of Statistics 22, 515–539) and uses a degenerating part of the periodogram near the origin to form a narrow-band frequency domain least squares (FDLS) estimator of the cointegrating relation, which is consistent for arbitrary short-run dynamics. We derive the asymptotic distribution theory for the FDLS estimator of the cointegration vector in the stationary long memory case, thus complementing Robinson's consistency result. An application to the relation between the volatility realized in the stock market and the associated implicit volatility derived from option prices is offered.     

An efficient Bayesian approach to multiple structural change in multivariate time series

This paper provides a feasible approach to estimation and forecasting of multiple structural breaks for vector autoregressions and other multivariate models. Owing to conjugate prior assumptions we obtain a very efficient sampler for the regime allocation variable. A new hierarchical prior is introduced to allow for learning over different structural breaks. The model is extended to independent breaks in regression coefficients and the volatility parameters. Two empirical applications show the improvements the model has over benchmarks. In a macro application with seven variables we empirically demonstrate the benefits from moving from a multivariate structural break model to a set of univariate structural break models to account for heterogeneous break patterns across data series.     

Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility

This paper compares alternative models of time‐varying volatility on the basis of the accuracy of real‐time point and density forecasts of key macroeconomic time series for the USA. We consider Bayesian autoregressive and vector autoregressive models that incorporate some form of time‐varying volatility, precisely random walk stochastic volatility, stochastic volatility following a stationary AR process, stochastic volatility coupled with fat tails, GARCH and mixture of innovation models. The results show that the AR and VAR specifications with conventional stochastic volatility dominate other volatility specifications, in terms of point forecasting to some degree and density forecasting to a greater degree. Copyright © 2014 John Wiley & Sons, Ltd.     

Robustifying multivariate trend tests to nonstationary volatility

This article studies inference of multivariate trend model when the volatility process is nonstationary. Within a quite general framework we analyze four classes of tests based on least squares estimation, one of which is robust to both weak serial correlation and nonstationary volatility. The existing multivariate trend tests, which either use non-robust standard errors or rely on non-standard distribution theory, are generally non-pivotal involving the unknown time-varying volatility function in the limit. Two-step residual-based i.i.d. bootstrap and wild bootstrap procedures are proposed for the robust tests and are shown to be asymptotically valid. Simulations demonstrate the effects of nonstationary volatility on the trend tests and the good behavior of the robust tests in finite samples.     

Time series copulas for heteroskedastic data

We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We suggest copulas for first‐order Markov series, and then extend them to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence, including co‐movement and spillover in multivariate series. In general, these depend upon the marginal distributions of the series. Using exchange rate returns, we show that the resulting copula models can capture their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models, and produce more accurate value‐at‐risk forecasts.     

Measuring Spot Variance Spillovers when (Co)variances are Time‐varying – The Case of Multivariate GARCH Models

We propose global and disaggregated spillover indices that allow us to assess variance and covariance spillovers, locally in time and conditionally on time‐t information. Key to our approach is the vector moving average representation of the half‐vectorized ‘squared’ multivariate GARCH process of the popular BEKK model. In an empirical application to a four‐dimensional system of broad asset classes (equity, fixed income, foreign exchange and commodities), we illustrate the new spillover indices at various levels of (dis)aggregation. Moreover, we demonstrate that they are informative of the value‐at‐risk violations of portfolios composed of the considered asset classes.     

Commodity Price Volatility and the Sources of Growth

This paper studies the impact of the growth and volatility of commodity terms of trade (CToT) on economic growth, total factor productivity, physical capital accumulation and human capital acquisition. We use the standard system generalized methods of moments (GMM) approach as well as the dynamic common correlated effects pooled mean group (CCEPMG) methodology for estimation to account for cross‐country heterogeneity, cross‐sectional dependence and feedback effects. Using both annual data for 1970–2007 and 5‐year non‐overlapping observations, we find that while CToT growth enhances real output per capita, CToT volatility exerts a negative impact on economic growth operating mainly through lower accumulation of physical and human capital. Productivity, however, is not affected by either the growth or the volatility of CToT. Our results also indicate that the negative growth effects of CToT volatility offset the positive impact of commodity booms. Therefore, we argue that volatility, rather than abundance per se, drives the ‘resource curse’ paradox. Copyright © 2014 John Wiley & Sons, Ltd.     

Following the leaders? A study of co-movement and volatility spillover in BRICS currencies

The paper investigates return co-movement and volatility spillover among the currencies of Brazil, Russia, India, China, and South Africa (the BRICS member countries) and four major developed countries from April 2006 to October 2019. Using Bloomberg daily data on exchange rates, the study employs a flexible multivariate generalized autoregressive conditional heteroskedasticity (MGARCH)–dynamic conditional correlation (DCC) model and a vector autoregressive (VAR)–based spillover index, as the empirical strategy. Along with evidence of exchange rate volatility in BRICS currencies, among which the Russian ruble and the Chinese yuan are explosive, the econometric estimation results show the presence of significant return co-movement and volatility spillover among the foreign exchange markets across different countries. The currency markets in developed countries, as leaders, are found to transmit volatility mostly to BRICS currency markets, which are net receivers. The degree of spillover, however, varies across countries, with Brazil and Russia passing on volatility to the developed countries whereas India, China, and South Africa receive volatility from their developed counterparts.