Bayesian near-boundary analysis in basic macroeconomic time series models

Several lessons learnt from a Bayesian analysis of basic macroeconomic time series models are presented for the situation where some model parameters have substantial posterior probability near the boundary of the parameter region. This feature refers to near-instability within dynamic models, to forecasting with near-random walk models and to clustering of several economic series in a small number of groups within a data panel. Two canonical models are used: a linear regression model with autocorrelation and a simple variance components model. Several well-known time series models likeunit root and error correction models and further state space and panel data models are shown to be simple generalizations of these two canonical models for the purpose of posterior inference. A Bayesian model averaging procedure is presented in order to deal with models with substantial probability both near and at the boundary of the parameter region. Analytical, graphical and empirical results using U.S. macroeconomic data, in particular on GDP growth, are presented.MCMC;Bayesian model averaging;Gibbs sampler;autocorrelation;error correction models;nonstationarity;random effects panel data models;reduced rank models;state space models

Bayesian near-boundary analysis in basic macroeconomic time series models

Several lessons learnt from a Bayesian analysis of basic macroeconomic time series models are presented for the situation where some model parameters have substantial posterior probability near the boundary of the parameter region. This feature refers to near-instability within dynamic models, to forecasting with near-random walk models and to clustering of several economic series in a small number of groups within a data panel. Two canonical models are used: a linear regression model with autocorrelation and a simple variance components model. Several well-known time series models like unit root and error correction models and further state space and panel data models are shown to be simple generalizations of these two canonical models for the purpose of posterior inference. A Bayesian model averaging procedure is presented in order to deal with models with substantial probability both near and at the boundary of the parameter region. Analytical, graphical and empirical results using U.S. macroeconomic data, in particular on GDP growth, are presented

Impact of Investor's Varying Risk Aversion on the Dynamics of Asset Price Fluctuations

While the investors' responses to price changes and their price forecasts are well accepted major factors contributing to large price fluctuations in financial markets, our study shows that investors' heterogeneous and dynamic risk aversion (DRA) preferences may play a more critical role in the dynamics of asset price fluctuations. We propose and study a model of an artificial stock market consisting of heterogeneous agents with DRA, and we find that DRA is the main driving force for excess price fluctuations and the associated volatility clustering. We employ a popular power utility function, $U(c,\gamma)=\frac{c^{1-\gamma}-1}{1-\gamma}$ with agent specific and time-dependent risk aversion index, $\gamma_i(t)$, and we derive an approximate formula for the demand function and aggregate price setting equation. The dynamics of each agent's risk aversion index, $\gamma_i(t)$ (i=1,2,...,N), is modeled by a bounded random walk with a constant variance $\delta^2$. We show numerically that our model reproduces most of the ``stylized'' facts observed in the real data, suggesting that dynamic risk aversion is a key mechanism for the emergence of these stylized facts.Comment: 17 pages, 7 figure

Characteristic exponents of complex networks

We present a novel way to characterize the structure of complex networks by studying the statistical properties of the trajectories of random walks over them. We consider time series corresponding to different properties of the nodes visited by the walkers. We show that the analysis of the fluctuations of these time series allows to define a set of characteristic exponents which capture the local and global organization of a network. This approach provides a way of solving two classical problems in network science, namely the systematic classification of networks, and the identification of the salient properties of growing networks. The results contribute to the construction of a unifying framework for the investigation of the structure and dynamics of complex systems.Comment: 6 pages, 5 figures, 1 tabl