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Bayesian analysis of multivariate stochastic volatility with skew distribution  [PDF]
Jouchi Nakajima
Statistics , 2012,
Abstract: Multivariate stochastic volatility models with skew distributions are proposed. Exploiting Cholesky stochastic volatility modeling, univariate stochastic volatility processes with leverage effect and generalized hyperbolic skew t-distributions are embedded to multivariate analysis with time-varying correlations. Bayesian prior works allow this approach to provide parsimonious skew structure and to easily scale up for high-dimensional problem. Analyses of daily stock returns are illustrated. Empirical results show that the time-varying correlations and the sparse skew structure contribute to improved prediction performance and VaR forecasts.
Multivariate stochastic volatility using state space models  [PDF]
K. Triantafyllopoulos
Quantitative Finance , 2008,
Abstract: A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation structure between the observation and state innovation vectors and we extend the convolution between the Wishart and the multivariate singular beta distribution. A multiplicative model based on the generalized inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility and a flexible sequential volatility updating is employed. The proposed algorithm for the volatility is fast and computationally cheap and it can be used for on-line forecasting. The methods are illustrated with an example consisting of foreign exchange rates data of 8 currencies. The empirical results suggest that time-varying correlations can be estimated efficiently, even in situations of high dimensional data.
Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models  [PDF]
Efthymios G. Tsionas
Statistics , 2012,
Abstract: In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite location-scale mixtures and (ii) versions of approximate Bayesian computation (ABC) using the characteristic function and the asymptotic form of the likelihood function. In the context of multivariate stable distributions we propose several ways to perform statistical inference and obtain the spectral measure associated with the distributions, a quantity that has been a major impediment in using them in applied work. We extend the techniques to handle univariate and multivariate stochastic volatility models, static and dynamic factor models with disturbances and factors from general stable distributions, a novel way to model multivariate stochastic volatility through time-varying spectral measures and a novel way to multivariate stable distributions through copulae. The new techniques are applied to artificial as well as real data (ten major currencies, SP100 and individual returns). In connection with ABC special attention is paid to crafting well-performing proposal distributions for MCMC and extensive numerical experiments are conducted to provide critical values of the "closeness" parameter that can be useful for further applied econometric work.
The causal relationship between tourism and economic growth in Malaysia: Evidence from multivariate causality tests
Kadir,Norsiah; Nayan,Sabri; Abdullah,Mat Saad;
Revista Encontros Científicos - Tourism & Management Studies , 2010,
Abstract: tourism industry and economic growth of a particular country are to some extent, interrelated. the aim of this study is to investigate the presence as well as direction of (significant) causal relationship between the malaysian international tourism receipts and real growth in its national economy. based on the sample period of 1994 through 2004, the data are examined from the perspective of multivariate causality procedure. major finding of the study is twofold: first, international tourism receipts and real economic growth are found to be significantly cointegrated. secondly, multivariate causality test based on the error correction model reveals that the granger causality between international tourism receipts and real economic growth is unidirectional - running from real economic growth to international tourism receipts. the practical implication that could be conceived from this ?growth-led tourism? finding is that, as the malaysian economy is growing, accelerated growth of socio-economic activities as well as business opportunities in its tourism-related sectors could be expected.
Multivariate Nonparametric Volatility Density Estimation  [PDF]
Bert van Es,Peter Spreij
Statistics , 2009, DOI: 10.1016/j.jmva.2010.12.003
Abstract: We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the multivariate density of the finite dimensional distributions of which we aim to estimate. We assume that we observe the process at discrete instants in time. The sampling times will be equidistant with vanishing distance. A multivariate Fourier-type deconvolution kernel density estimator based on the logarithm of the squared processes is proposed to estimate the multivariate volatility density. An expansion of the bias and a bound on the variance are derived. Key words: stochastic volatility models, multivariate density estimation, kernel estimator, deconvolution, mixing
Multivariate volatility models  [PDF]
Ruey S. Tsay
Mathematics , 2007, DOI: 10.1214/074921706000001058
Abstract: Correlations between asset returns are important in many financial applications. In recent years, multivariate volatility models have been used to describe the time-varying feature of the correlations. However, the curse of dimensionality quickly becomes an issue as the number of correlations is $k(k-1)/2$ for $k$ assets. In this paper, we review some of the commonly used models for multivariate volatility and propose a simple approach that is parsimonious and satisfies the positive definite constraints of the time-varying correlation matrix. Real examples are used to demonstrate the proposed model.
Bayesian Testing for Asset Volatility Persistence on Multivariate Stochastic Volatility Models  [PDF]
Yong Li, Fang-Ping Peng, Hao-Feng Xu
Journal of Mathematical Finance (JMF) , 2012, DOI: 10.4236/jmf.2012.21010
Abstract: In empirical finance, it is well-known that the volatility of asset returns is highly persistent. The persistence of the volatility process may be checked by testing for a unit root on stochastic volatility models. In this paper, a Bayesian test statistic based on decision theory is developed for testing a unit root on multivariate stochastic volatility models. At last, the developed approach is applied to investigate the persistent effect of financial crisis on the two main stock markets in China.
Fast estimation of multivariate stochastic volatility  [PDF]
Kostas Triantafyllopoulos,Giovanni Montana
Quantitative Finance , 2007,
Abstract: In this paper we develop a Bayesian procedure for estimating multivariate stochastic volatility (MSV) using state space models. A multiplicative model based on inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility, and a flexible sequential volatility updating is employed. Being computationally fast, the resulting estimation procedure is particularly suitable for on-line forecasting. Three performance measures are discussed in the context of model selection: the log-likelihood criterion, the mean of standardized one-step forecast errors, and sequential Bayes factors. Finally, the proposed methods are applied to a data set comprising eight exchange rates vis-a-vis the US dollar.
Multivariate stochastic volatility with Bayesian dynamic linear models  [PDF]
K. Triantafyllopoulos
Quantitative Finance , 2008, DOI: 10.1016/j.jspi.2007.03.057
Abstract: This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distributions. A diagonal matrix of discount factors is employed in order to discount the variances element by element and therefore allowing a flexible and pragmatic variance modelling approach. Diagnostic tests and sequential model monitoring are discussed in some detail. The proposed estimation theory is applied to a four-dimensional time series, comprising spot prices of aluminium, copper, lead and zinc of the London metal exchange. The empirical findings suggest that the proposed Bayesian procedure can be effectively applied to financial data, overcoming many of the disadvantages of existing volatility models.
Multivariate Stochastic Volatility Estimation with Sparse Grid Integration  [PDF]
Halil Erturk Esen
Journal of Mathematical Finance (JMF) , 2016, DOI: 10.4236/jmf.2016.61009

Multivariate stochastic volatility (MSV) models are nonlinear state space models that require either linear approximations or computationally demanding methods for handling the high dimensional integrals arising in the estimation problems of the latent volatilities and model parameters. Markov Chain Monte Carlo (MCMC) methods, which are based on Monte Carlo simulations using special sampling schemes, are by far the most studied method with several extensions and versions in previous stochastic volatility estimation studies. Exact nonlinear filters and particularly numerical integration based methods, such as the method proposed in this paper, were neglected and not studied as extensively as MCMC methods especially in the multivariate settings of stochastic volatility models. Filtering, smoothing, prediction and parameter estimation algorithms based on the sparse grid integration method are developed and proposed for a general MSV model. The proposed algorithms for estimation are compared with an implementation of MCMC based algorithms in a simulation study followed by an illustration of the proposed algorithms on empirical data of foreign exchange rate returns of US dollars and Euro. Results showed that the proposed algorithms based on the sparse grid integration method can be promising alternatives to the MCMC based algorithms especially in practical applications with their appealing characteristics.

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