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Timo Terasvirta - One of the best experts on this subject based on the ideXlab platform.
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Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH Model
Journal of Financial Econometrics, 2009Co-Authors: Annastiina Silvennoinen, Timo TerasvirtaAbstract:In this paper we propose a multivariate GARCH Model with a time-varying conditional correlation structure. The new Double Smooth Transition Conditional Correlation GARCH Model extends the Smooth Transition Conditional Correlation GARCH Model of Silvennoinen and Terasvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH Model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the Model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. The Model is applied to a selection of world stock indices, and it is found that time is an important factor affecting correlations between them.
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testing for volatility interactions in the constant conditional correlation GARCH Model
Econometrics Journal, 2009Co-Authors: Timo Terasvirta, Tomoaki NakataniAbstract:This thesis consists of four research papers. The main focus is on building the multivariate Conditional Correlation (CC-) GARCH Models. In particular, emphasis lies on considering an extension of CC-GARCH Models that allow for interactions or causality in conditional variances. In the first three chapters, misspecification testing and parameter restrictions in these Models are discussed. In the final chapter, a computer package for building major variants of the CC-GARCH Models is presented.The first chapter contains a brief introduction to the CC-GARCH Models as well as a summary of each research paper. The second chapter proposes a misspecification test for Modelling of the conditional variance part of the Extended Constant CC-GARCH Model. The test is designed for testing the hypothesis of no interactions in the conditional variances. If the null hypothesis is true, then the conditional variances may be described by the standard CCC-GARCH Model. The test is constructed on the Lagrange Multiplier (LM) principle that only requires the estimation of the null Model. Although the test is derived under the assumption of the constant conditional correlation, the simulation experiments suggest that the test is also applicable to building CC-GARCH Models with changing conditional correlations. There is no asymptotic theory available for these Models, which is why simulation of the test statistic in this situation has been necessary.The third chapter provides yet another misspecification test for Modelling of the conditional variance component of the CC-GARCH Models, whose parameters are often estimated in two steps. The estimator obtained through these two steps is a two-stage quasi-maximum likelihood estimator (2SQMLE). Taking advantage of the asymptotic results for 2SQMLE, the test considered in this chapter is formulated using the LM principle, which requires only the estimation of univariate GARCH Models. It is also shown that the test statistic may be computed by using an auxiliary regression. A robust version of the new test is available through another auxiliary regression. All of this amounts to a substantial simplification in computations compared with the test proposed in the second chapter. The simulation experiments show that, under both under both Gaussian and leptokurtic innovations, as well as under changing conditional correlations, the new test has reasonable size and power properties.When Modelling the conditional variance, it is necessary to keep the sequence of conditional covariance matrices positive definite almost surely for any time horizon. In the fourth chapter it is demonstrated that under certain conditions some of the parameters of the Model can take negative values while the conditional covariance matrix remains positive definite almost surely. It is also shown that even in the simplest first-order vector GARCH representation, the relevant parameter space can contain negative values for some parameters, which is not possible in the univariate Model. This finding makes it possible to incorporate negative volatility spillovers into the CC-GARCH framework.Many new GARCH Models and misspecification testing procedures have been recently proposed in the literature. When it comes to applying these Models or tests, however, there do not seem to exist many options for the users to choose from other than creating their own computer programmes. This is especially the case when one wants to apply a multivariate GARCH Model. The last chapter of the thesis offers a remedy to this situation by providing a workable environment for building CC-GARCH Models. The package is open source, freely available on the Internet, and designed for use in the open source statistical environment R. With this package can estimate major variants of CC-GARCH Models as well as simulate data from the CC-GARCH data generating processes with multivariate normal or Student's t innovations. In addition, the package is equipped with the necessary functions for conducting diagnostic tests such as those discussed in the third chapter of this thesis.
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testing for volatility interactions in the constant conditional correlation GARCH Model
Econometrics Journal, 2009Co-Authors: Timo Terasvirta, Tomoaki NakataniAbstract:In this paper, we propose a Lagrange multiplier test for volatility interactions among markets or assets. The null hypothesis is the Constant Conditional Correlation generalized autoregressive conditional heteroskedasticity (GARCH) Model in which volatility of an asset is described only through lagged squared innovations and volatility of its own. The alternative hypothesis is an extension of that Model in which volatility is Modelled as a linear combination not only of its own lagged squared innovations and volatility but also of those in the other equations while keeping the conditional correlation structure constant. This configuration enables us to test for volatility transmissions among variables in the Model. Monte Carlo experiments show that the proposed test has satisfactory finite-sample properties. The size distortions become negligible when the sample size reaches 2500. The test is applied to pairs of foreign exchange returns and individual stock returns. Results indicate that there seem to be volatility interactions in the pairs considered, and that significant interaction effects typically result from the lagged squared innovations of the other variables. Copyright The Author(s). Journal compilation Royal Economic Society 2009
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Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH Model
QUT Business School, 2009Co-Authors: Annastiina Silvennoinen, Timo TerasvirtaAbstract:In this paper, we propose a multivariate GARCH Model with a time-varying conditional correlation structure. The new double smooth transition conditional correlation (DSTCC) GARCH Model extends the smooth transition conditional correlation (STCC) GARCH Model of Silvennoinen and Terasvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH Model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the Model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. Applying the Model to the stock and bond futures data, we discover that the correlation pattern between them has dramatically changed around the turn of the century. The Model is also applied to a selection of world stock indices, and we find evidence for an increasing degree of integration in the capital markets.
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testing for volatility interactions in the constant conditional correlation GARCH Model
2008Co-Authors: Timo Terasvirta, Tomoaki NakataniAbstract:In this paper we propose a Lagrange multiplier test for volatility interactions among markets or assets. The null hypothesis is the Constant Conditional Correlation GARCH Model in which volatility of an asset is described only through lagged squared innovations and volatility of its own. The alternative hypothesis is an extension of that Model in which volatility is Modelled as a linear combination not only of its own lagged squared innovations and volatility but also of those in the other equations while keeping the conditional correlation structure constant. This configuration enables us to test for volatility transmissions among variables in the Model. Monte Carlo experiments show that the proposed test has satisfactory finite sample properties. The size distortions become negligible when the sample size reaches 2500. The test is applied to pairs of foreign exchange returns and individual stock returns. Results indicate that there seem to be volatility interactions in the pairs considered, and that significant interaction effects typically result from the lagged squared innovations of the other variables.
Michael Mcaleer - One of the best experts on this subject based on the ideXlab platform.
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A Portfolio Index GARCH Model
International Journal of Forecasting, 2008Co-Authors: Manabu Asai, Michael McaleerAbstract:Abstract This paper develops the structure of a parsimonious Portfolio Index (PI) GARCH Model. Unlike the conventional approach to Portfolio Index returns, which employs the univariate ARCH class, the PI-GARCH approach incorporates the effects on individual assets, leading to a better understanding of portfolio risk management, and achieves greater accuracy in forecasting Value-at-Risk (VaR) thresholds. For various asymmetric GARCH Models, a Portfolio Index Composite News Impact Surface (PI-CNIS) is developed to measure the effects of news on the conditional variances. The paper also investigates the finite sample properties of the PI-GARCH Model. The empirical example shows that the asymmetric PI-GARCH-t Model outperforms the GJR-t Model and the filtered historical simulation with a t distribution in forecasting VaR thresholds.
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forecasting value at risk with a parsimonious portfolio spillover GARCH ps GARCH Model
Journal of Forecasting, 2008Co-Authors: Michael Mcaleer, Bernardo Da VeigaAbstract:Accurate Modelling of volatility (or risk) is important in finance, particularly as it relates to the Modelling and forecasting of value-at-risk (VaR) thresholds. As financial applications typically deal with a portfolio of assets and risk, there are several multivariate GARCH Models which specify the risk of one asset as depending on its own past as well as the past behaviour of other assets. Multivariate effects, whereby the risk of a given asset depends on the previous risk of any other asset, are termed spillover effects. In this paper we analyse the importance of considering spillover effects when forecasting financial volatility. The forecasting performance of the VARMA-GARCH Model of Ling and McAleer (2003), which includes spillover effects from all assets, the CCC Model of Bollerslev (1990), which includes no spillovers, and a new Portfolio Spillover GARCH (PS-GARCH) Model, which accommodates aggregate spillovers parsimoniously and hence avoids the so-called curse of dimensionality, are compared using a VaR example for a portfolio containing four international stock market indices. The empirical results suggest that spillover effects are statistically significant. However, the VaR threshold forecasts are generally found to be insensitive to the inclusion of spillover effects in any of the multivariate Models considered. Copyright © 2008 John Wiley & Sons, Ltd.
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asymptotic theory for a vector arma GARCH Model
Econometric Theory, 2003Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper investigates the asymptotic theory for a vector ARMA-GARCH Model. The conditions for the strict stationarity, ergodicity, and the higherorder moments of the Model are established. Consistency of the quasi- maximum likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate ARCH and GARCH Models. Moreover, the asymptotic normality of the QMLE for the vector ARCH Model is obtained under only the second-order moment of the unconditional errors, and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH Models, as well as a consistent estimator of the asymptotic covariance.
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asymptotic theory for a vector arma GARCH Model
Econometric Theory, 2003Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) Model. The conditions for the strict stationarity, the ergodicity, and the higher order moments of the Model are established. Consistency of the quasi-maximum-likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate autoregressive conditional heteroskedasticity (ARCH) and GARCH Models. Moreover, the asymptotic normality of the QMLE for the vector ARCH Model is obtained under only the second-order moment of the unconditional errors and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH Models and also a consistent estimator of the asymptotic covariance. The authors thank the co-Editor, Bruce Hansen, and two referees for very helpful comments and suggestions and acknowledge the financial support of the Australian Research Council.
Marc S Paolella - One of the best experts on this subject based on the ideXlab platform.
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a non elliptical orthogonal GARCH Model for portfolio selection under transaction costs
Journal of Banking and Finance, 2021Co-Authors: Marc S Paolella, Pawel Polak, Patrick S WalkerAbstract:Abstract Covariance matrix forecasts for portfolio optimization have to balance sensitivity to new data points with stability in order to avoid excessive rebalancing. To achieve this, a new orthogonal GARCH Model for a multivariate set of non-Gaussian asset returns is proposed. The conditional return distribution is multivariate generalized hyperbolic and the dispersion matrix dynamics are driven by the leading factors in a principal component decomposition. Each of these leading factors is endowed with a univariate GARCH structure, while the remaining eigenvalues are kept constant over time. Joint maximum likelihood estimation of all Model parameters is performed via an expectation maximization algorithm, and is applicable in high dimensions. The new Model generates realistic correlation forecasts even for large asset universes and captures rising pairwise correlations in periods of market distress better than numerous competing Models. When applied to portfolio optimization, it generates strategies with lower turnover and maximum drawdown, and superior risk-adjusted returns net of transaction costs. Moreover, unlike its competitors, it performs well in the sudden market downturn triggered by the global COVID-19 pandemic.
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a non elliptical orthogonal GARCH Model for portfolio selection under transaction costs
Swiss Finance Institute Research Paper Series, 2019Co-Authors: Marc S Paolella, Pawel Polak, Patrick S WalkerAbstract:Covariance matrix forecasts for portfolio optimization have to balance sensitivity to new data points with stability in order to avoid excessive rebalancing. To achieve this, a new robust orthogonal GARCH Model for a multivariate set of non-Gaussian asset returns is proposed. The conditional return distribution is multivariate generalized hyperbolic and the dispersion matrix dynamics are driven by the leading factors in a principle component decomposition. Each of these leading factors is endowed with a univariate GARCH structure, while the remaining eigenvalues are kept constant over time. Joint maximum likelihood estimation of all Model parameters is performed via an expectation maximization algorithm, and is applicable in high dimensions. The new Model generates realistic correlation forecasts even for large asset universes and captures rising pairwise correlations in periods of market distress better than numerous competing Models. Moreover, it leads to improved forecasts of an eigenvalue-based financial systemic risk indicator. Crucially, it generates portfolios with much lower turnover and superior risk-adjusted returns net of transaction costs, outperforming the equally weighted strategy even under high transaction fees.
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accurate value at risk forecasting based on the normal GARCH Model
Computational Statistics & Data Analysis, 2006Co-Authors: Christoph Hartz, Stefan Mittnik, Marc S PaolellaAbstract:A resampling method based on the bootstrap and a bias-correction step is developed for improving the Value-at-Risk (VaR) forecasting ability of the normal-GARCH Model. Compared to the use of more sophisticated GARCH Models, the new method is fast, easy to implement, numerically reliable, and, except for having to choose a window length L for the bias-correction step, fully data driven. The results for several different financial asset returns over a long out-of-sample forecasting period, as well as use of simulated data, strongly support use of the new method, and the performance is not sensitive to the choice of L.
Shiqing Ling - One of the best experts on this subject based on the ideXlab platform.
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the zd GARCH Model a new way to study heteroscedasticity
Journal of Econometrics, 2018Co-Authors: Xingfa Zhang, Ke Zhu, Shiqing LingAbstract:This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) Model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH Model, ZD-GARCH(1, 1) Model is always non-stationary regardless of the sign of the Lyapunov exponent $\gamma_{0}$ , but interestingly when $\gamma_{0}$ = 0, it is stable with its sample path oscillating randomly between zero and infinity over time. Furthermore, this paper studies the generalized quasi-maximum likelihood estimator (GQMLE) of ZD-GARCH(1, 1) Model, and establishes its strong consistency and asymptotic normality. Based on the GQMLE, an estimator for $\gamma_{0}$, a test for stability, and a portmanteau test for Model checking are all constructed. Simulation studies are carried out to assess the finite sample performance of the proposed estimators and tests. Applications demonstrate that a stable ZD-GARCH(1, 1) Model is more appropriate to capture heteroscedasticity than a non-stationary GARCH(1, 1) Model, which suffers from an inconsistent QMLE of the drift term
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asymptotic theory for a vector arma GARCH Model
Econometric Theory, 2003Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper investigates the asymptotic theory for a vector ARMA-GARCH Model. The conditions for the strict stationarity, ergodicity, and the higherorder moments of the Model are established. Consistency of the quasi- maximum likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate ARCH and GARCH Models. Moreover, the asymptotic normality of the QMLE for the vector ARCH Model is obtained under only the second-order moment of the unconditional errors, and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH Models, as well as a consistent estimator of the asymptotic covariance.
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asymptotic theory for a vector arma GARCH Model
Econometric Theory, 2003Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) Model. The conditions for the strict stationarity, the ergodicity, and the higher order moments of the Model are established. Consistency of the quasi-maximum-likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate autoregressive conditional heteroskedasticity (ARCH) and GARCH Models. Moreover, the asymptotic normality of the QMLE for the vector ARCH Model is obtained under only the second-order moment of the unconditional errors and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH Models and also a consistent estimator of the asymptotic covariance. The authors thank the co-Editor, Bruce Hansen, and two referees for very helpful comments and suggestions and acknowledge the financial support of the Australian Research Council.
Juichung Hung - One of the best experts on this subject based on the ideXlab platform.
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adaptive fuzzy GARCH Model applied to forecasting the volatility of stock markets using particle swarm optimization
Information Sciences, 2011Co-Authors: Juichung HungAbstract:Fluctuations in the stock market follow the principle of volatility clustering in which changes are cataloged by similarity; as such, large changes tend to follow large changes, and small changes tend to follow small changes. This clustering is one of the major reasons why many generalized autoregression conditional heteroscedasticity (GARCH) Models do not forecast the stock market well. In this paper, an adaptive Fuzzy-GARCH Model with particle swarm optimization (PSO) is proposed to solve this problem. The adaptive Fuzzy-GARCH Model refers to both GARCH Models and the parameters of membership functions, which are determined by the characteristics of market itself. Here, we present an iterative algorithm based on PSO to estimate the parameters of the membership functions. The PSO method aims to achieve a global optimal solution with a rapid convergence rate. The three stock markets of Taiwan, Japan, and Germany were analyzed to illustrate the performance of the proposed method.
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applying a combined fuzzy systems and GARCH Model to adaptively forecast stock market volatility
Applied Soft Computing, 2011Co-Authors: Juichung HungAbstract:This paper studies volatility forecasting in the financial stock market. In general, stock market volatility is time-varying and exhibits clustering properties. Thus, this paper presents the results of using a fuzzy system method to analyze clustering in generalized autoregressive conditional heteroskedasticity (GARCH) Models. It also uses the adaptive method of recursive least-squares (RLS) to forecast stock market volatility. The fuzzy GARCH Model represents a joint estimation method; the membership function parameters together with the GARCH Model parameters make this problem of stock market is highly nonlinear and complicated. This study presents an iterative algorithm based on a genetic algorithm (GA) to estimate the parameters of the membership functions and the GARCH Models. In this paper, the GA method is employed to identify a global optimal solution with a fast convergence rate in the context of the fuzzy GARCH Model estimation problem studied here. Based on simulation results, we determined that both the estimation of in-sample and the forecasting of out-of-sample volatility performance are significantly improved when the GARCH Model considers both the clustering effect and the adaptive forecast.
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a fuzzy asymmetric GARCH Model applied to stock markets
Information Sciences, 2009Co-Authors: Juichung HungAbstract:In this paper, we derive a new class of flexible threshold asymmetric Generalized Autoregression Conditional Heteroskedasticity (GARCH) Models. We use this tool for analysis and Modeling of the properties that are apparent in many financial time series. In general, the transmission of volatility in the stock market is time-varying, nonlinear, and asymmetric with respect to both positive and negative results. Given this fact, we adopt the method of fuzzy logic systems to modify the threshold values for an asymmetric GARCH Model. Our simulations use stock market data from the Taiwan weighted index (Taiwan), the Nikkei 225 index (Japan), and the Hang Seng index (Hong Kong) to illustrate the performance of our proposed method. From the simulation results, we have determined that the forecasting of volatility performance is significantly improved if the leverage effect of clustering is considered along with the use of expert knowledge enabled by the GARCH Model.
