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Conditional Variance (conditional + variance)
Selected AbstractsIncome Variance Dynamics and HeterogeneityECONOMETRICA, Issue 1 2004Costas Meghir Recent theoretical work has shown the importance of measuring microeconomic uncertainty for models of both general and partial equilibrium under imperfect insurance. In this paper the assumption of i.i.d. income innovations used in previous empirical studies is removed and the focus of the analysis is placed on models for the conditional variance of income shocks, which is related to the measure of risk emphasized by the theory. We first discriminate amongst various models of earnings determination that separate income shocks into idiosyncratic transitory and permanent components. We allow for education- and time-specific differences in the stochastic process for earnings and for measurement error. The conditional variance of the income shocks is modelled as a parsimonious ARCH process with both observable and unobserved heterogeneity. The empirical analysis is conducted on data drawn from the 1967,1992 Panel Study of Income Dynamics. We find strong evidence of sizeable ARCH effects as well as evidence of unobserved heterogeneity in the variances. [source] Time series analysis of wind speed with time-varying turbulenceENVIRONMETRICS, Issue 2 2006Bradley T. Ewing Abstract The characterization of the time series properties of wind speed, in terms of the mean and variance, is important and relevant to both engineers and businesses. This research investigates the first and second moments of the Texas Tech WERFL wind speed data utilizing the ARMA-GARCH-in-mean framework. The methodology allows the conditional variance to depend on the size of past shocks (i.e. gusts) in the series. Results have important implications for wind energy production as well as for the operational and financial hedging strategies of companies exposed to wind-related risk. The findings can be summarized as follows: (i) mean wind speeds measured at different heights above ground exhibit persistence and are highly dependent on immediate past wind speed values; (ii) regardless of the height at which the data were collected, wind speed exhibits time-varying variance; (iii) persistence in conditional variance increases with height at which the data were collected; (iv) there is strong evidence that conditional volatility is positively correlated with mean wind speed while the magnitude of this relationship declines with height. Copyright © 2005 John Wiley & Sons, Ltd. [source] The intertemporal relationship between market return and variance: an Australian perspectiveACCOUNTING & FINANCE, Issue 3 2001Warren G. Dean In this paper we investigate the intertemporal relationship between the market risk premium and its conditional variance in an Australian setting. Using a bivariate EGARCH-M model combined with the dynamic conditional correlation (DCC) framework as proposed by Engle (2000), we find evidence of a positive relationship between the market risk premium and its variance and evidence of two distinct interest rate effects. Furthermore, while the bond market's own variance is not priced by investors, we find that the covariance between equity and bond markets is a significant risk factor that is priced in the market. [source] Market Price of Risk: A Comparison among the United States, United Kingdom, Australia and Japan,INTERNATIONAL REVIEW OF FINANCE, Issue 4 2009KENT WANG ABSTRACT This study examines and compares the market price of risk of the S&P 500, FTSE 100, All Ordinaries, and Nikkei 225 markets from 1984 to 2009 in the framework of Intertemporal Capital Asset Pricing Model (ICAPM). We follow the Vector Autoregressive instrumental variable approach in identifying the risk and hedge components of market returns and argue that in the context of market integration, covariance with a world market portfolio is a better measure of market risk than conditional market variance. Evidence is documented in support of using covariance as a risk measure in explaining market risk premiums in the Australian and Japanese markets. CAY, the consumption wealth ratio from the US market is found to be a robust state variable that helps to explain both conditional variance and covariance processes in the four markets. The market prices of risk, after controlling for the hedging demands, are positive and significant with the United States having the highest price of risk. The results are confirmed using a series of robustness tests that include varying the sampling interval. [source] Normal mixture GARCH(1,1): applications to exchange rate modellingJOURNAL OF APPLIED ECONOMETRICS, Issue 3 2006Carol Alexander Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both conditional skewness and kurtosis. A main focus of the paper is to provide evidence that, for modelling exchange rates, generalized two-component normal mixture GARCH(1,1) models perform better than those with three or more components, and better than symmetric and skewed Student's t -GARCH models. In addition to the extensive empirical results based on simulation and on historical data on three US dollar foreign exchange rates (British pound, euro and Japanese yen), we derive: expressions for the conditional and unconditional moments of all models; parameter conditions to ensure that the second and fourth conditional and unconditional moments are positive and finite; and analytic derivatives for the maximum likelihood estimation of the model parameters and standard errors of the estimates. Copyright © 2006 John Wiley & Sons, Ltd. [source] Stability of nonlinear AR-GARCH modelsJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2008Mika Meitz Abstract., This article studies the stability of nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a nonlinear autoregression of order p [AR(p)] with the conditional variance specified as a nonlinear first-order generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. Conditions under which the model is stable in the sense that its Markov chain representation is geometrically ergodic are provided. This implies the existence of an initial distribution such that the process is strictly stationary and , -mixing. Conditions under which the stationary distribution has finite moments are also given. The results cover several nonlinear specifications recently proposed for both the conditional mean and conditional variance, and only require mild moment conditions. [source] Prediction in ARMA Models with GARCH in Mean EffectsJOURNAL OF TIME SERIES ANALYSIS, Issue 5 2001Menelaos Karanasos This paper considers forecasting the conditional mean and variance from an ARMA model with GARCH in mean effects. Expressions for the optimal predictors and their conditional and unconditional MSEs are presented. We also derive the formula for the covariance structure of the process and its conditional variance. JEL. C22. [source] Robust modelling of DTARCH modelsTHE ECONOMETRICS JOURNAL, Issue 2 2005Yer Van Hui Summary, Autoregressive conditional heteroscedastic (ARCH) models and its extensions are widely used in modelling volatility in financial time series. One of the variants, the double-threshold autoregressive conditional heteroscedastic (DTARCH) model, has been proposed to model the conditional mean and the conditional variance that are piecewise linear. The DTARCH model is also useful for modelling conditional heteroscedasticity with nonlinear structures such as asymmetric cycles, jump resonance and amplitude-frequence dependence. Since asset returns often display heavy tails and outliers, it is worth studying robust DTARCH modelling without specific distribution assumption. This paper studies DTARCH structures for conditional scale instead of conditional variance. We examine L1 -estimation of the DTARCH model and derive limiting distributions for the proposed estimators. A robust portmanteau statistic based on the L1 -norm fit is constructed to test the model adequacy. This approach captures various nonlinear phenomena and stylized facts with desirable robustness. Simulations show that the L1 -estimators are robust against innovation distributions and accurate for a moderate sample size, and the proposed test is not only robust against innovation distributions but also powerful in discriminating the delay parameters and ARCH models. It is noted that the quasi-likelihood modelling approach used in ARCH models is inappropriate to DTARCH models in the presence of outliers and heavy tail innovations. [source] Uncovering the Risk,Return Relation in the Stock MarketTHE JOURNAL OF FINANCE, Issue 3 2006HUI GUO ABSTRACT There is ongoing debate about the apparent weak or negative relation between risk (conditional variance) and expected returns in the aggregate stock market. We develop and estimate an empirical model based on the intertemporal capital asset pricing model (ICAPM) that separately identifies the two components of expected returns, namely, the risk component and the component due to the desire to hedge changes in investment opportunities. The estimated coefficient of relative risk aversion is positive, statistically significant, and reasonable in magnitude. However, expected returns are driven primarily by the hedge component. The omission of this component is partly responsible for the existing contradictory results. [source] EXTENSIONS OF THE STANDARDIZED CROSS-SECTIONAL APPROACH TO SHORT-HORIZON EVENT STUDIESTHE JOURNAL OF FINANCIAL RESEARCH, Issue 4 2007Ronald Bremer Abstract Strong evidence indicates that short-horizon event-induced abnormal returns and volatility vary significantly over event days. Event-study methods that assume constant event-induced abnormal returns and volatility over event days have potentially inflated Type I error rates and poor test power. Our simple extensions of the Boehmer, Musumeci, and Poulsen (1991) approach scale abnormal returns with conditional variance, which is estimated with GARCH(1,1) and an indicator of the event in a two-stage estimation. Our method improves the Boehmer, Musumeci, and Poulsen approach on model specification and test power, even under challenging event-induced mean and volatility structures, and could standardize short-horizon event studies. [source] Nonlinear dynamics in high-frequency intraday financial data: Evidence for the UK long gilt futures marketTHE JOURNAL OF FUTURES MARKETS, Issue 11 2002David G. McMillan Recent research investigating the properties of high-frequency financial data has suggested that the stochastic nonlinearity widely present in such data may be characterized by heterogeneous components in conditional volatility, and nonlinear dependence of threshold autoregressive form due to market frictions. This article tests for the presence of such effects in intraday long gilt futures returns on the UK LIFFE market. Tests against the null of linearity indicate the significance of smooth transition autoregressive nonlinearities in such returns at the 5-min frequency, which entails a first-order autoregressive process with switching intercept. This nonlinear structure is robust to the presence of asymmetric and component structures in conditional variance, and consistent with the existence of heterogeneous traders facing different levels of transaction costs, noise trader risk, or capital constraints. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:1037,1057, 2002 [source] Return and Volatility Dynamics in the Spot and Futures Markets in Australia: An Intervention Analysis in a Bivariate EGARCH-X FrameworkTHE JOURNAL OF FUTURES MARKETS, Issue 9 2001Ramaprasad Bhar This article provides evidence of linkages between the equity market and the index futures market in Australia, where the futures market has experienced a major structural event due to the futures contract respecification. A bivariate Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model is developed that includes a cointegrating residual as an explanatory variable for both the conditional mean and the conditional variance. The conditional mean returns from both markets are influenced by the long-run equilibrium relationship, and these markets are informationally linked through the second moments. The crossmarket spillovers exhibit asymmetric behavior in that the volatility responses to past standardized innovations are different for market advances and market retreats. An intervention analysis shows that some of the parameters describing the return-generating process have shifted after the contract respecification by the futures exchange. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:833,850, 2001 [source] Assessment of uncertainty in computer experiments from Universal to Bayesian KrigingAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 2 2009C. Helbert Abstract Kriging was first introduced in the field of geostatistics. Nowadays, it is widely used to model computer experiments. Since the results of deterministic computer experiments have no experimental variability, Kriging is appropriate in that it interpolates observations at data points. Moreover, Kriging quantifies prediction uncertainty, which plays a major role in many applications. Among practitioners we can distinguish those who use Universal Kriging where the parameters of the model are estimated and those who use Bayesian Kriging where model parameters are random variables. The aim of this article is to show that the prediction uncertainty has a correct interpretation only in the case of Bayesian Kriging. Different cases of prior distributions have been studied and it is shown that in one specific case, Bayesian Kriging supplies an interpretation as a conditional variance for the prediction variance provided by Universal Kriging. Finally, a simple petroleum engineering case study presents the importance of prior information in the Bayesian approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] Estimating Systematic Risk Using Time Varying DistributionsEUROPEAN FINANCIAL MANAGEMENT, Issue 1 2002Gregory Koutmos This article proposes a dynamic vector GARCH model for the estimation of time-varying betas. The model allows the conditional variances and the conditional covariance between individual portfolio returns and market portfolio returns to respond asymmetrically to past innovations depending on their sign. Covariances tend to be higher during market declines. There is substantial time variation in betas but the evidence on beta asymmetry is mixed. Specifically, in 50% of the cases betas are higher during market declines and for the remaining 50% the opposite is true. A time series analysis of estimated time varying betas reveals that they follow stationary mean-reverting processes. The average degree of persistence is approximately four days. It is also found that the static market model overstates non-market or, unsystematic risk by more than 10%. On the basis of an array of diagnostics it is confirmed that the vector GARCH model provides a richer framework for the analysis of the dynamics of systematic risk. [source] Fractional integration in agricultural futures price volatilities revisitedAGRICULTURAL ECONOMICS, Issue 1 2009Peter S. Sephton Conditional volatility; Fractional integration; Long-memory Abstract Jin and Frechette (2004) examined the degree to which agricultural price volatilities exhibited evidence of fractional integration and concluded it was important to consider both long-run and short-run memory when modeling conditional variances. The purpose of this note is to revisit the issue using new methods and techniques which generally reaffirm the view that return volatilities are fractionally integrated and conditionally heteroskedastic, with many exhibiting significant leverage effects, a result not previously reported. [source] Second-Order Noncausality in Multivariate GARCH ProcessesJOURNAL OF TIME SERIES ANALYSIS, Issue 5 2000Fabienne Comte Typical multivariate economic time series may exhibit co-behavior patterns not only in the conditional means, but also in the conditional variances. In this paper we give two new definitions of variance noncausality in a multivariate setting a Granger-type noncausality and a linear Granger noncausality through projections on Hilbert spaces. Both definitions are related to a previous second-order noncausality concept defined by Granger et al. in a bivariate setting. The implications of second-order noncausality on multivariate ARMA processes with GARCH-type errors are investigated. We derive exact testable restrictions on the parameters of the processes considered, implied by this type of noncausality. Conditions for the finiteness of the fourth-order moment of the multivariate GARCH process are derived and related to earlier results in the univariate framework. We include an illustration of second-order noncausality in a trivariate model of daily financial returns. [source] A full-factor multivariate GARCH modelTHE ECONOMETRICS JOURNAL, Issue 2 2003I. D. Vrontos A new multivariate time series model with time varying conditional variances and covariances is presented and analysed. A complete analysis of the proposed model is presented consisting of parameter estimation, model selection and volatility prediction. Classical and Bayesian techniques are used for the estimation of the model parameters. It turns out that the construction of our proposed model allows easy maximum likelihood estimation and construction of well-mixing Markov chain Monte Carlo (MCMC) algorithms. Bayesian model selection is addressed using MCMC model composition. The problem of accounting for model uncertainty is considered using Bayesian model averaging. We provide implementation details and illustrations using daily rates of return on eight stocks of the US market. 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