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on Econometric Time Series |
| By: | Ajay Singh; Dinghai Xu |
| Abstract: | In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling price fluctuations as GARCH(1,1) process. The corresponding correlation matrix is constructed. It is found that the distribution of a significant number of eigenvalues of the volatility correlation matrix matches with the analytical result from the RMT. Furthermore, the empirical estimates of short and long-range correlations among eigenvalues, which are within the RMT bounds, match with the analytical results for Gaussian Orthogonal ensemble (GOE) of the RMT. To understand the information content of the largest eigenvectors, we estimate the contribution of GICS industry groups in each eigenvector. In comparison with eigenvectors of correlation matrix for price fluctuations, only few of the largest eigenvectors of volatility correlation matrix are dominated by a single industry group. We also study correlations among `volatility return' and get similar results. |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1310.1601&r=ets |
| By: | Matteo Barigozzi; Christian Brownlees |
| Abstract: | This work proposes novel network analysis techniques for multivariate time series. We dene the network of a multivariate time series as a graph where vertices denote the components of the process and edges denote non{zero long run partial correlations. We then introduce a two step lasso procedure, called nets, to estimate high{dimensional sparse Long Run Partial Correlation networks. This approach is based on a var approximation of the process and allows to decompose the long run linkages into the contribution of the dynamic and contemporaneous dependence relations of the system. The large sample properties of the estimator are analysed and we establish conditions for consistent selection and estimation of the non{zero long run partial correlations. The methodology is illustrated with an application to a panel of U.S. bluechips. |
| Keywords: | Networks, Multivariate Time Series, Long Run Covariance, Lasso |
| JEL: | C01 C32 C52 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:723&r=ets |
| By: | Yoonseok Lee (Dept. of Economics, Syracuse University); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | This paper considers model selection in nonlinear panel data models where incidental parameters or large-dimensional nuisance parameters are present. Primary interest typically centres on selecting a model that best approximates the underlying structure involving parameters that are common within the panel after concentrating out the incidental parameters. It is well known that conventional model selection procedures are often inconsistent in panel models and this can be so even without nuisance parameters (Han et al, 2012). Modifications are then needed to achieve consistency. New model selection information criteria are developed here that use either the Kullback-Leibler information criterion based on the profile likelihood or the Bayes factor based on the integrated likelihood with the robust prior of Arellano and Bonhomme (2009). These model selection criteria impose heavier penalties than those associated with standard information criteria such as AIC and BIC. The additional penalty, which is data-dependent, properly reflects the model complexity arising from the presence of incidental parameters. A particular example is studied in detail involving lag order selection in dynamic panel models with fixed individual effects. The new criteria are shown to control for over/under-selection probabilities in these models and lead to consistent order selection criteria. |
| Keywords: | (Adaptive) model selection, incidental parameters, profile likelihood, Kullback-Leibler information, Bayes factor, integrated likelihood, robust prior, model complexity, fixed effects, lag order |
| JEL: | C23 C52 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1919&r=ets |