Model Selection in Threshold Models

This paper considers information criteria as model evaluation tools for nonlinear threshold models. Results concerning the consistency of information criteria in selecting the lag order of linear autoregressive models are extended to nonlinear autoregressive threshold models. Extensive Monte Carlo evidence of the small sample performance of a number of criteria is presented

A new framework for extracting coarse-grained models from time series with multiscale structure

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales. In this work we consider the inference problem of identifying an appropriate coarse-grained model from a single time series of a multiscale system. It is known that estimators such as the maximum likelihood estimator or the quadratic variation of the path estimator can be strongly biased in this setting. Here we present a novel parametric inference methodology for problems with linear parameter dependency that does not suffer from this drawback. Furthermore, we demonstrate through a wide spectrum of examples that our methodology can be used to derive appropriate coarse-grained models from time series of partial observations of a multiscale system in an effective and systematic fashion

Entry and Exit Dynamics in Austrian Manufacturing

This article investigates the determinants of entry and exit in the Austrian manufacturing sector based on 1981 to 1994 data. We study the response of entry, exit and other indicators of firm dynamics to changes in average plant size, size heterogeneity, concentration, incentives and vertical integration. By applying Bayesian simulation methods we estimate random coefficient models and study the symmetry of the determinants of entry and exit. Our empirical analysis shows that entry and exit rates are driven by the same determinants. The impacts of these determinates are nearly homogeneous for both, entry rates and exits rates, respectively. Moreover, we find (i) that changes in average plant size, size heterogeneity and concentration are not symmetric with respect to entry and exit, (ii) that changes in the growth of sales is weakly symmetric and (iii) that the growth rate of employment is strongly asymmetric across industries in Austrian manufacturing. Furthermore, we infer from the data that the turnover of firms influences the changes in the number of competitors. Low entry rates go hand in hand with low net entryrates and a low turnover.Entry, Exit, Industry Turbulence, MCMC

Which graphical models are difficult to learn?

We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-complexity algorithms systematically fail when the Markov random field develops long-range correlations. More precisely, this phenomenon appears to be related to the Ising model phase transition (although it does not coincide with it)