Ioannis D. Vrontos

Full Bayesian Inference for GARCH and EGARCH Models

A full Bayesian analysis of GARCH and EGARCH models is proposed consisting of parameter estimation, model selection, and volatility prediction. The Bayesian paradigm is implemented via Markov-chain Monte Carlo methodologies. We provide implementation details and illustrations using the General Index of the Athens stock exchange.

A Quantile Regression Approach to Equity Premium Prediction

We propose a quantile regression approach to equity premium forecasting. Robust point forecasts are generated by both fixed and time-varying weighting schemes, thus exploiting the entire distributional information associated with each predictor. Further gains are achieved by incorporating the forecast combination methodology in our quantile regression setting. Our approach using a time-varying weighting scheme delivers statistically and economically significant out-of-sample forecasts relative to the historical average benchmark and the combined mean predictive regression modeling approach.

Modelling nonlinearities and heavy tails via threshold normal mixture GARCH models

A new class of flexible threshold normal mixture GARCH models is proposed for the analysis and modelling of the stylized facts appeared in many financial time series. A Bayesian stochastic method is developed and presented for the analysis of the proposed model allowing for automatic model determination and estimation of the thresholds and their unknown number. A computationally feasible algorithm that explores the posterior distribution of the threshold models is designed using Markov chain Monte Carlo stochastic search methods. A simulation study is conducted to assess the performance of the proposed method, and an empirical application of the proposed model is illustrated using real data.

Modelling volatility asymmetries: a Bayesian analysis of a class of tree structured multivariate GARCH models

A new class of multivariate threshold GARCH models is proposed for the analysis and modelling of volatility asymmetries in financial time series. The approach is based on the idea of a binary tree where every terminal node parametrizes a (local) multivariate GARCH model for a specific partition of the data. A Bayesian stochastic method is developed and presented for the analysis of the proposed model consisting of parameter estimation, model selection and volatility prediction. A computationally feasible algorithm that explores the posterior distribution of the tree structure is designed using Markov chain Monte Carlo stochastic search methods. Simulation experiments are conducted to assess the performance of the proposed method, and an empirical application of the proposed model is illustrated using real financial time series. Copyright Royal Economic Society 2007

A markov chain monte carlo convergence diagnostic using subsampling

Abstract A new diagnostic procedure for assessing convergence of a Markov chain Monte Carlo (MCMC) simulation is proposed. The method is based on the use of subsampling for the construction of confidence regions from asymptotically stationary time series as developed in Politis, Romano, and Wolf. The MCMC subsampling diagnostic is capable of gauging at what point the chain has “forgotten” its starting points, as well as to indicate how many points are needed to estimate the parameters of interest according to the desired accuracy. Simulation examples are also presented showing that the diagnostic performs favorably in interesting cases.

A Bayesian Analysis of Unit Roots and Structural Breaks in the Level, Trend, and Error Variance of Autoregressive Models of Economic Series

In this article, a Bayesian approach is suggested to compare unit root models with stationary autoregressive models when the level, the trend, and the error variance are subject to structural changes (known as breaks) of an unknown date. Ignoring structural breaks in the error variance may be responsible for not rejecting the unit root hypothesis, even if allowance is made in the inferential procedures for breaks in the mean. The article utilizes analytic and Monte Carlo integration techniques for calculating the marginal likelihoods of the models under consideration, in order to compute the posterior model probabilities. The performance of the method is assessed by simulation experiments. Some empirical applications of the method are conducted with the aim to investigate if it can detect structural breaks in financial series, especially with changes in the error variance.

Out-of-Sample Equity Premium Prediction: A Complete Subset Quantile Regression Approach

This paper extends the complete subset linear regression framework to a quantile regression setting. We employ complete subset combinations of quantile forecasts in order to construct robust and accurate equity premium predictions. Our recursive algorithm that selects, in real time, the best complete subset for each predictive regression quantile succeeds in identifying the best subset in a time- and quantile-varying manner. We show that our approach delivers statistically and economically signi cant out-of-sample forecasts relative to both the historical average benchmark and the complete subset mean regression approach.

Evidence for hedge fund predictability from a multivariate Student's t full-factor GARCH model

Extending previous work on hedge fund return predictability, this paper introduces the idea of modelling the conditional distribution of hedge fund returns using Student-t full-factor multivariate GARCH models. This class of models takes into account the stylized facts of hedge fund return series, that is heteroskedasticity, fat tails and deviations from normality. For the proposed class of multivariate predictive regression models, we derive analytic expressions for the score and the Hessian matrix, which can be used within classical and Bayesian inferential procedures to estimate the model parameters, as well as to compare different predictive regression models. We propose a Bayesian approach to model comparison which provides posterior probabilities for various predictive models that can be used for model averaging. Our empirical application indicates that accounting for fat tails and time-varying covariances/correlations provides a more appropriate modelling approach of the underlying dynamics of financial series and improves our ability to predict hedge fund returns.

Communication Impacting Financial Markets

Since the attribution of the Nobel prize in 2002 to Kahneman for prospect theory, behavioral finance has become an increasingly important subfield of finance. However the main parts of behavioral finance, prospect theory included, understand financial markets through individual investment behavior. Behavioral finance thereby ignores any interaction between participants. We introduce a socio-financial model (Vitting Andersen J. and Nowak A., An Introduction to Socio-Finance (Springer, Berlin) 2013) that studies the impact of communication on the pricing in financial markets. Considering the simplest possible case where each market participant has either a positive (bullish) or negative (bearish) sentiment with respect to the market, we model the evolution of the sentiment in the population due to communication in subgroups of different sizes. Nonlinear feedback effects between the market performance and changes in sentiments are taken into account by assuming that the market performance is dependent on changes in sentiments (e.g., a large sudden positive change in bullishness would lead to more buying). The market performance in turn has an impact on the sentiment through the transition probabilities to change an opinion in a group of a given size. The idea is that if for example the market has observed a recent downturn, it will be easier for even a bearish minority to convince a bullish majority to change opinion compared to the case where the meeting takes place in a bullish upturn of the market. Within the framework of our proposed model, financial markets stylized facts such as volatility clustering and extreme events may be perceived as arising due to abrupt sentiment changes via ongoing communication of the market participants. The model introduces a new volatility measure which is apt of capturing volatility clustering and from maximum-likelihood analysis we are able to apply the model to real data and give additional long term insight into where a market is heading.

Performance evaluation of mutual fund investments: the impact of non-normality and time-varying volatility

Extending previous work on mutual fund pricing, this paper introduces the idea of modeling the conditional distribution of mutual fund returns using a fat tailed density and a time-varying conditional variance. This approach takes into account the stylized facts of mutual fund return series, that is heteroscedasticity and deviations from normality. We evaluate mutual fund performance using multifactor asset pricing models, with the relevant risk factors being identified through standard model selection techniques. We explore potential impacts of our approach by analyzing individual mutual funds and show that it can be economically important.