The conditional autoregressive wishart model for multivariate stock market volatility

We propose a Conditional Autoregressive Wishart (CAW) model for the analysis of realized covariance matrices of asset returns. Our model assumes a generalized linear autoregressive moving average structure for the scale matrix of the Wishart distribution allowing to accommodate for complex dynamic interdependence between the variances and covariances of assets. In addition, it accounts for symmetry and positive definiteness of covariance matrices without imposing parametric restrictions, and can easily be estimated by Maximum Likelihood. We also propose extensions of the CAW model obtained by including a Mixed Data Sampling (MIDAS) component and Heterogeneous Autoregressive (HAR) dynamics for long-run fluctuations. The CAW models are applied to time series of daily realized variances and covariances for five New York Stock Exchange (NYSE) stocks. --Component volatility models,Covariance matrix,Mixed data sampling,Observation-driven models,Realized volatility

Modeling and Forecasting of Multivariate Stock Market Volatility

This thesis contributes to recent developments in multivariate volatility modeling. The analysis focuses on stochastic volatility models and the direct modeling of realized (co)variances as precise measures of latent variances and covariances. Novel time-series models are proposed and analyzed in order to capture the complex serial and cross-sectional dynamics of daily and intra-daily asset return (co)variances and investigate the short-term information transmission on international financial markets as reflected by variance and covariance interdependencies. The proposed volatility models address both low-dimensional as well as high-dimensional volatility modeling. The models' in-sample properties are analyzed using model diagnostic tests while the out-of-sample forecasting performance is evaluated using comprehensive out-of-sample experiments including a range of prominent forecasting models from the relevant literature

Multivariate Wishart stochastic volatility and changes in regime

This paper generalizes the basic Wishart multivariate stochastic volatility model of Philipov and Glickman (J Bus Econ Stat 24:313-328, 2006) and Asai and McAleer (J Econom 150:182-192, 2009) to encompass regime-switching behavior. The latent state variable is driven by a first-order Markov process. The model allows for state-dependent (co)variance and correlation levels and state-dependent volatility spillover effects. Parameter estimates are obtained using Bayesian Markov Chain Monte Carlo procedures and filtered estimates of the latent variances and covariances are generated by particle filter techniques. The model is applied to five European stock index return series. The results show that the proposed regime-switching specification substantially improves the fit to persistent covariance dynamics relative to the basic model

A latent dynamic factor approach to forecasting multivariate stock market volatility

This paper proposes a latent dynamic factor model for high-dimensional realized covariance matrices of stock returns. The approach is based on the matrix logarithm and combines common latent factors driven by HAR processes and idiosyncratic autoregressive dynamics. The model accounts for positive definiteness of covariance matrices without imposing parametric restrictions. Simulated Bayesian parameter estimates are obtained using basic Markov chain Monte Carlo methods. An empirical application to 5-dimensional and 30-dimensional realized covariance matrices shows remarkably good forecasting results, in-sample and out-of-sample

Classical and Bayesian Inference for Income Distributions using Grouped Data

We propose a general framework for Maximum Likelihood (ML) and Bayesian estimation of income distributions based on grouped data information. The asymptotic properties of the ML estimators are derived and Bayesian parameter estimates are obtained by Monte Carlo Markov Chain (MCMC) techniques. A comprehensive simulation experiment shows that obtained estimates of the income distribution are very precise and that the proposed estimation framework improves the statistical precision of parameter estimates relative to the classical multinomial likelihood. The estimation approach is finally applied to a set of countries included in the World Bank databasePovcalNet

Dynamic principal component CAW models for high-dimensional realized covariance matrices

We propose a new dynamic principal component CAW model (DPC-CAW) for time-series of high-dimensional realized covariance matrices of asset returns (up to 100 assets). The model performs a spectral decomposition of the scale matrix of a central Wishart distribution and assumes independent dynamics for the principal components' variances and the eigenvector processes. A three-step estimation procedure makes the model applicable to high-dimensional covariance matrices. We analyze the finite sample properties of the estimation approach and provide an empirical application to realized covariance matrices for 100 assets. The DPC-CAW model has particularly good forecasting properties and outperforms its competitors for realized covariance matrices

Modeling and forecasting realized portfolio weights

We propose direct multiple time series models for predicting high dimensional vectors of observable realized global minimum variance portfolio (GMVP) weights computed based on high-frequency intraday returns. We apply Lasso regression techniques, develop a class of multiple AR(FI)MA models for realized GMVP weights, suggest suitable model restrictions, propose M-type estimators and derive the statistical properties of these estimators. In the empirical analysis for portfolios of 225 stocks from the S&P 500 we find that our direct models effectively minimize either statistical or economic forecasting losses both in- and out-of-sample as compared to relevant alternative approaches. (c) 2022 Elsevier B.V. All rights reserved

Estimating stochastic volatility models using realized measures

This paper extends the basic stochastic volatility (SV) model in order to incorporate the realized variance (RV) as an additional measure for the latent daily volatility. The particular model we use explicitly accounts for the dependency between daily returns and measurement errors of the realized volatility estimate. Within a simulation study we investigate the form of the dependency. In order to capture the long memory property of asset volatility, we explore different autoregressive dynamics for the latent volatility process, including heterogeneous autoregressive (HAR) dynamics and a two-component approach. We estimate the model using simulated maximum likelihood based on efficient importance sampling (EIS), producing numerically accurate parameter estimates and filtered state sequences. The model is applied to daily asset returns and realized variances of New York Stock Exchange (NYSE) traded stocks. Estimation results indicate that accounting for the dependency of returns and realized measures significantly affects the estimation results and improves the model fit for all autoregressive dynamics

A Mixed Frequency Stochastic Volatility Model for Intraday Stock Market Returns

We propose a mixed frequency stochastic volatility model for intraday returns. To account for long-memory type of dependence patterns we introduce a long-run component that changes daily and a short-run component that captures the remaining intraday volatility dynamics. We analyze the model's stochastic properties and extend it to capture leverage effects and overnight return information. The model is estimated by simulated maximum likelihood using efficient importance sampling. We apply the model to 30-min returns of 12 stocks. The results show that the model successfully accounts for the complex dynamic and distributional properties of asset returns both on the intraday and the daily frequency