Copula-based multivariate GARCH model with uncorrelated dependent errors

Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conventional MGARCH model as a special case. The aim of this paper is to model MGARCH for non-normal multivariate distributions using copulas. We model the conditional correlation (by MGARCH) and the remaining dependence (by a copula) separately and simultaneously. We apply this idea to three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle [Engle, R.F., 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20, 339–350], the varying correlation (VC) model of Tse and Tsui [Tse, Y.K., Tsui, A.K., 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20, 351–362], and the BEKK model of Engle and Kroner [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150]. Empirical analysis with three foreign exchange rates indicates that the C-MGARCH models outperform DCC, VC, and BEKK in terms of in-sample model selection and out-of-sample multivariate density forecast, and in terms of these criteria the choice of copula functions is more important than the choice of the volatility models.     

The exchange rate and macroeconomic determinants: Time-varying transitional dynamics

In this paper, I consider modeling the effects of the macroeconomic determinants on the nominal exchange rate to be channeled through the transition probabilities in a Markovian process. The model posits that the deviation of the exchange rate from its fundamental value alters the market's belief in the probability of the process staying in certain regime next period. This paper further takes into account the ARCH effects of the volatility of the exchange rate. Empirical results generally confirm that fundamentals can affect the evolution of the dynamics of the exchange rate in a nonlinear way through the transition probabilities. In addition, I find that the volatility of the exchange rate is associated with significant ARCH effects which are subject to regime changes.     

Multivariate rotated ARCH models

This paper introduces a new class of multivariate volatility models which is easy to estimate using covariance targeting, even with rich dynamics. We call them rotated ARCH (RARCH) models. The basic structure is to rotate the returns and then to fit them using a BEKK-type parameterization of the time-varying covariance whose long-run covariance is the identity matrix. This yields the rotated BEKK (RBEKK) model. The extension to DCC-type parameterizations is given, introducing the rotated DCC (RDCC) model. Inference for these models is computationally attractive, and the asymptotics are standard. The techniques are illustrated using data on the DJIA stocks.     

The stochastic volatility in mean model: empirical evidence from international stock markets

In this paper we present an exact maximum likelihood treatment for the estimation of a Stochastic Volatility in Mean (SVM) model based on Monte Carlo simulation methods. The SVM model incorporates the unobserved volatility as an explanatory variable in the mean equation. The same extension is developed elsewhere for Autoregressive Conditional Heteroscedastic (ARCH) models, known as the ARCH in Mean (ARCH‐M) model. The estimation of ARCH models is relatively easy compared with that of the Stochastic Volatility (SV) model. However, efficient Monte Carlo simulation methods for SV models have been developed to overcome some of these problems. The details of modifications required for estimating the volatility‐in‐mean effect are presented in this paper together with a Monte Carlo study to investigate the finite sample properties of the SVM estimators. Taking these developments of estimation methods into account, we regard SV and SVM models as practical alternatives to their ARCH counterparts and therefore it is of interest to study and compare the two classes of volatility models. We present an empirical study of the intertemporal relationship between stock index returns and their volatility for the United Kingdom, the United States and Japan. This phenomenon has been discussed in the financial economic literature but has proved hard to find empirically. We provide evidence of a negative but weak relationship between returns and contemporaneous volatility which is indirect evidence of a positive relation between the expected components of the return and the volatility process. Copyright © 2002 John Wiley & Sons, Ltd.     

Time series properties of ARCH processes with persistent covariates

We investigate the time series properties of a volatility model, whose conditional variance is specified as in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated or nearly integrated process, with its effect on volatility given by a wide class of nonlinear volatility functions. In the paper, such a model is shown to generate many important characteristics that are commonly observed in financial time series. In particular, the model yields persistence in volatility, and also well predicts leptokurtosis. This is true for any type of volatility functions considered in the paper, as long as the covariate is integrated or nearly integrated. Stationary covariates cannot produce important characteristics observed in many financial time series. We present two empirical applications of the model, which show that the default premium (the yield spread between Baa and Aaa corporate bonds) affects stock return volatility and the interest rate differential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that the model generally outperforms GARCH and FIGARCH at relatively lower frequencies.     

Simultaneous stochastic volatility transmission across American equity markets

Information flows across international financial markets typically occur within hours, making volatility spillovers appear contemporaneously in daily data. Such simultaneous transmission of variances is featured by the stochastic volatility model developed in this paper, in contrast to usually employed multivariate ARCH processes. The arising identification problem is solved by considering heteroscedasticity of the structural volatility innovations. Estimation takes place in an appropriately specified state space setup. In the empirical application, unidirectional volatility spillovers from the US stock market to three American countries are revealed. The impact is strongest for Canada, followed by Mexico and Brazil, which are subject to idiosyncratic crisis effects.     

Model‐free evaluation of directional predictability in foreign exchange markets

We examine directional predictability in foreign exchange markets using a model‐free statistical evaluation procedure. Based on a sample of foreign exchange spot rates and futures prices in six major currencies, we document strong evidence that the directions of foreign exchange returns are predictable not only by the past history of foreign exchange returns, but also the past history of interest rate differentials, suggesting that the latter can be a useful predictor of the directions of future foreign exchange rates. This evidence becomes stronger when the direction of larger changes is considered. We further document that despite the weak conditional mean dynamics of foreign exchange returns, directional predictability can be explained by strong dependence derived from higher‐order conditional moments such as the volatility, skewness and kurtosis of past foreign exchange returns. Moreover, the conditional mean dynamics of interest rate differentials contributes significantly to directional predictability. We also examine the co‐movements between two foreign exchange rates, particularly the co‐movements of joint large changes. There exists strong evidence that the directions of joint changes are predictable using past foreign exchange returns and interest rate differentials. Furthermore, both individual currency returns and interest rate differentials are also useful in predicting the directions of joint changes. Several sources can explain this directional predictability of joint changes, including the level and volatility of underlying currency returns. Copyright © 2007 John Wiley & Sons, Ltd.     

Evidence of nonlinear speculative bubbles in pacific-rim stock markets

Increased volatility of many stock markets in recent years has sometimes been associated with rapid increases or decreases in asset values that may contain elements of speculative bubbles not justified by the underlying fundamentals. This paper studies the behavior of daily stock returns from ten pacific-rim countries by using a regime switching model to detect trends. Residuals from a VAR model of daily stock indices and presumed fundamentals like exchange rates, Far East and the World stock indices used in a regime switching model point to the existence of bubbles. The ARCH and BDS statistics also indicate strong evidence of non-linearities in all of these countries.     

The common and specific components of dynamic volatility

This paper develops a dynamic approximate factor model in which returns are time-series heteroskedastic. The heteroskedasticity has three components: a factor-related component, a common asset-specific component, and a purely asset-specific component. We develop a new multivariate GARCH model for the factor-related component. We develop a univariate stochastic volatility model linked to a cross-sectional series of individual GARCH models for the common asset-specific component and the purely asset-specific component. We apply the analysis to monthly US equity returns for the period January 1926 to December 2000. We find that all three components contribute to the heteroskedasticity of individual equity returns. Factor volatility and the common component in asset-specific volatility have long-term secular trends as well as short-term autocorrelation. Factor volatility has correlation with interest rates and the business cycle.     

On loss functions and ranking forecasting performances of multivariate volatility models

The ranking of multivariate volatility models is inherently problematic because when the unobservable volatility is substituted by a proxy, the ordering implied by a loss function may be biased with respect to the intended one. We point out that the size of the distortion is strictly tied to the level of the accuracy of the volatility proxy. We propose a generalized necessary and sufficient functional form for a class of non-metric distance measures of the Bregman type which ensure consistency of the ordering when the target is observed with noise. An application to three foreign exchange rates is provided.     

Nonstationary nonlinear heteroskedasticity

In this paper, we consider time series with the conditional heteroskedasticities that are given by nonlinear functions of integrated processes. Such time series are said to have nonlinear nonstationary heteroskedasticity (NNH), and the functions generating conditional heterogeneity are called heterogeneity generating functions (HGF's). Various statistical properties of time series with NNH are investigated for a wide class of HGF's. For NNH models with a variety of HGF's, volatility clustering and leptokurtosis, which are common features of ARCH type models, are manifest. In particular, it is shown that the sample autocorrelations of their squared processes vanish only very slowly, or do not even vanish at all, in the limit. Volatility clustering is therefore well expected. The NNH models with certain types of HGF's indeed have sample characteristics that are very similar to those of ARCH type models. Moreover, the sample kurtosis of the NNH model either diverges or has a stable limiting distribution with support truncated on the left by the kurtosis of the innovations. This would well explain the presence of leptokurtosis in many observed time series data. To illustrate the empirical relevancy of our model, we analyze the spreads between the forward and spot rates of USD/DM exchange rates. It is found that the conditional variances of the spreads can be well modelled as a nonlinear function of the levels of the spot rates.     

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.     

Time-series properties and predictability of Greek exchange rates

This paper explores the time-series properties and predictability of weekly percentage changes in the Greek drachma exchange rates with respect to the currencies of major trading-partner countries, such as the USA, Germany, the UK, France, Italy and Japan. The analysis is carried out using the EGARCH-M model along with the power exponential distribution. Percentage changes in the Greek drachma with respect to the German mark, the French franc, the Italian lira and Japanese yen are predictable using past information. The volatility of Greek exchange rates is best represented by an EGARCH process and as such is predictable using past volatility measures. Moreover, volatility of the Greek drachma with respect to the German mark and Italian lira positively influences future movements in these exchange rates. The hypothesis that volatility is an asymmetric function of past innovations is rejected in all cases. Following the inclusion of the Greek drachma in the ECU currency basket, its value has been depreciating at a higher rate with respect to the German mark and Italian lira and at a lower rate with respect to the US dollar. Also, its volatility with respect to the German mark, the French franc, and the Italian lira has decreased, whereas its volatility with respect to the US dollar has increased.     

Estimation of variance of housing prices using spatial conditional heteroskedasticity (SARCH) model with an application to Boston housing price data

In this paper we investigate housing price volatility within a spatial econometrics setting. We propose an extended spatial regression model of the real estate market that includes the effects of both conditional heteroskedasticity and spatial autocorrelation. Our suggested model has features similar to those of autoregressive conditional heteroskedasticity (ARCH) in the time-series context. We utilize the spatial ARCH (SARCH) model to analyze Boston housing price data used by Harrison and Rubinfeld (1978) and Gilley and Pace (1996). We show that measuring the variability of housing prices is an important issue and our SARCH model captures the conditional spatial variability of Boston housing prices. We argue that there is a different source of spatial variation, which is independent of traditional housing and neighborhood characteristics, and is captured by the SARCH model.     

Monetary integration in the Southern Cone

The effect of exchange-rate volatility on the domestic economy depends in part on the importance of trade in total economic activity. Unlike the European Union (EU), trade among the Mercosur countries is less highly integrated, so that movements in intra-area exchange rates are less important than exchange rates vis-à-vis the dollar and the euro. This paper analyzes the impact of exchange-rate and interest-rate volatility on investment and labor markets in the Southern Cone and finds that both volatility against the dollar and the euro and variability of interest rates have significant dampening effects on employment and investment.     

Forecasting exchange rates with elliptically symmetric principal components

We extract elliptically symmetric principal components from a panel of 17 OECD exchange rates and use the deviations from the components to forecast future exchange rate movements, following the method in Engel et al. (2015). Instead of using standard factor models, we apply elliptically symmetric principal component analysis (ESPCA), introduced by Solat and Spanos (2018), which captures both contemporaneous and temporal co-variation among the exchange rates. We find that ESPCA is more accurate than forecasts generated by existing standard methods and the random walk model, with or without including macroeconomic fundamentals.     

“汇改”后汇率变动对股票市场的影响——基于具体行业股票收益率的实证分析

使用GARCH和分位数回归模型,以11个具体行业上市公司为样本,对2005年7月＂汇改＂后人民币汇率变动与股票市场中行业股票收益率波动的相关性进行分析,研究结果表明：相对于即期汇率,以远期汇率为代表的汇率预期对行业股票收益率影响更为明显;预期汇率对行业股票收益率的影响具有明显的阶段性特征;在第一阶段,受远期汇率影响的行业主要对远期汇率的升值比较关注,而在第三阶段,不同行业对即期汇率和远期汇率的反应呈现多样化。     

Exchange rate misalignments,capital flows and volatility

This study investigates the effect of three dimensions of exchange rate misalignments—(i) distance (absolute misalignments), (ii) direction (overvaluation or undervaluation), and (iii) degree (small or large misalignments)—on the overall as well as short-cycle exchange rate volatility. Using data from 1988 to 2014, we find that relative PPP-based exchange rate misalignments increase exchange rate volatility. For developed and developing countries, this increase in volatility is driven mainly by large undervalued misalignments of the U.S. dollar. This finding might be linked to interventions targeting the loss in domestic producers’ competitiveness in global markets. Interestingly, in the case of developed countries, we find this adverse effect on exchange rate volatility also for small absolute misalignments; exchange rate movements close to equilibrium may be associated with ambiguity with respect to future movements in developed countries, which can result in higher exchange rate volatility. Further, the results suggest that, when the dollar is highly undervalued, capital flows have a stabilizing effect on exchange rate volatility in developed countries but a destabilizing effect in developing countries. The finding is consistent with investors’ strategy of taking exchange rate overvaluation and undervaluation into account when engaging in cross-border investments.     

Forecasting exchange rate volatility using high-frequency data: Is the euro different?

We assess the performances of alternative procedures for forecasting the daily volatility of the euro’s bilateral exchange rates using 15 min data. We use realized volatility and traditional time series volatility models. Our results indicate that using high-frequency data and considering their long memory dimension enhances the performance of volatility forecasts significantly. We find that the intraday FIGARCH model and the ARFIMA model outperform other traditional models for all exchange rate series.     

Balance sheet effects and original sinners’ risk premiums

This paper describes an empirical model of country risk premiums and their determinants, relying on recent theories of balance sheet effects. We approach the latter by introducing a novel approach to country risk premiums that assumes that nominal exchange rates can move away from or towards equilibrium exchange rates, which allows exchange rate movements towards equilibrium to stimulate favourable competitiveness effects as opposed to adverse balance sheet effects. We investigate eight European emerging economies that suffer from “original sin” over the period 2001–2013, using the pooled mean group estimator of the dynamic panel error correction model. This methodology improves estimation efficiency and model performance, but also allows differentiation between long- and short-run country risk premium determinants. We find that, in the long run, country risk premiums increase in response to higher inflation and a higher total debt-to-GDP ratio, while they move in the opposite direction when the real GDP growth rate rises. Our results suggest that, in the short run, higher external debt service caused by exchange rate depreciation, i.e. the balance sheet effect, and market volatility tends to raise risk premiums, while higher international reserves and the federal funds rate tend to decrease them. Moreover, we show that the negative balance sheet effect is much stronger than the potentially favourable competitiveness effect, and that the rise in risk premiums is not due to the increase in the size of external debt, but to the larger debt burden represented by balance sheet effects.