
on Econometric Time Series 
By:  Marisa Faggini (Department of Economics and Statistics, University of Salerno) 
Abstract:  To show that a mathematical model exhibits chaotic behaviour does not prove that chaos is also present in the corresponding data. To convincingly show that a system behaves chaotically, chaos has to be identified directly from the data. From an empirical point of view, it is difficult to distinguish between fluctuations provoked by random shocks and endogenous fluctuations determined by the nonlinear nature of the relation between economic aggregates. For this purpose, chaos tests test are developed to investigate the basic features of chaotic phenomena: nonlinearity, fractal attractor, and sensitivity to initial conditions. The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in the data. More specifically, our attention will be devoted to reviewing the results reached by the application of these techniques to economic and financial time series and to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area. 
Keywords:  Economic dynamics, nonlinearity, tests for chaos, chaos 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:tur:wpaper:25&r=ets 
By:  Juan Carlos MartínezOvando; Stephen G. Walker 
Abstract:  In this paper we introduce two general nonparametric firstorder stationary timeseries models for which marginal (invariant) and transition distributions are expressed as infinitedimensional mixtures. That feature makes them the first Bayesian stationary fully nonparametric models developed so far. We draw on the discussion of using stationary models in practice, as a motivation, and advocate the view that flexible (nonparametric) stationary models might be a source for reliable inferences and predictions. It will be noticed that our models adequately fit in the Bayesian inference framework due to a suitable representation theorem. A stationary scalemixture model is developed as a particular case along with a computational strategy for posterior inference and predictions. The usefulness of that model is illustrated with the analysis of Euro/USD exchange rate logreturns. 
Keywords:  Stationarity, Markov processes, Dynamic mixture models, Random probability measures, Conditional random probability measures, Latent processes. 
JEL:  C11 C14 C15 C22 C51 
Date:  2011–09 
URL:  http://d.repec.org/n?u=RePEc:bdm:wpaper:201108&r=ets 
By:  Tómasson, Helgi (Faculty of Economics, University of Iceland, Reykjavik, Iceland) 
Abstract:  Representation of continuoustime ARMA, CARMA, models is reviewed. Computational aspects of simulating and calculating the likelihoodfunction of CARMA are summarized. Some numerical properties are illustrated by simulations. Some real data applications are shown. 
Keywords:  CARMA, maximumlikelihood, spectrum, Kalman filter, computation 
JEL:  C01 C10 C22 C53 C63 
Date:  2011–09 
URL:  http://d.repec.org/n?u=RePEc:ihs:ihsesp:274&r=ets 
By:  Christian Kascha; Carsten Trenkler 
Abstract:  We bring together some recent advances in the literature on vector autoregressive movingaverage models creating a relatively simple specification and estimation strategy for the cointegrated case. We show that in the cointegrated case with fixed initial values there exists a socalled final moving representation which is usually simpler but not as parsimonious than the usual Echelon form. Furthermore, we proof that our specification strategy is consistent also in the case of cointegrated series. In order to show the potential usefulness of the method, we apply it to US interest rates and find that it generates forecasts superior to methods which do not allow for movingaverage terms. 
Keywords:  Cointegration, VARMA models, forecasting 
JEL:  C32 C53 E43 E47 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:033&r=ets 
By:  Gospodinov, Nikolay; Lkhagvasuren, Damba 
Abstract:  This paper proposes a new method for approximating vector autoregressions by a finitestate Markov chain. The method is more robust to the number of discrete values and tends to outperform the existing methods over a wide range of the parameter space, especially for highly persistent vector autoregressions with roots near the unit circle. 
Keywords:  Markov Chain; Vector Autoregressive Processes; Functional Equation; Numerical Methods; Moment Matching; Numerical Integration 
JEL:  C10 C15 C60 
Date:  2011–06–08 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:33827&r=ets 
By:  Friederike Greb (GeorgAugustUniversity Göttingen); Tatyana Krivobokova (GeorgAugustUniversity Göttingen); Axel Munk (GeorgAugustUniversity Göttingen); Stephan von CramonTaubadel (GeorgAugustUniversity Göttingen) 
Abstract:  Estimation of threshold parameters in (generalized) threshold regression models is typically performed by maximizing the corresponding profile likelihood function. Also, certain Bayesian techniques based on noninformative priors are developed and widely used. This article draws attention to settings (not rare in practice) in which these standard estimators either perform poorly or even fail. In particular, if estimation of the regression coeffcients is associated with high uncertainty, the profile likelihood for the threshold parameters and thus the corresponding estimator can be highly affected. We suggest an alternative estimation method employing the empirical Bayes paradigm, which allows to circumvent deficiencies of standard estimators. The new estimator is completely datadriven and induces little additional numerical effort compared with the old one. Simulation results show that our estimator outperforms commonly used estimators and produces excellent results even if the latter show poor performance. The practical relevance of our approach is illustrated by a realdata example; we follow up the anlysis of crosscountry growth behavior detailed in Hansen (2000). 
Keywords:  threshold estimation; nuisance parameters; empirical Bayes 
Date:  2011–10–07 
URL:  http://d.repec.org/n?u=RePEc:got:gotcrc:099&r=ets 
By:  Tobias Adrian; Markus K. Brunnermeier 
Abstract:  We propose a measure for systemic risk: CoVaR, the value at risk (VaR) of the financial system conditional on institutions being under distress. We define an institution's contribution to systemic risk as the difference between CoVaR conditional on the institution being under distress and the CoVaR in the median state of the institution. From our estimates of CoVaR for the universe of publicly traded financial institutions, we quantify the extent to which characteristics such as leverage, size, and maturity mismatch predict systemic risk contribution. We also provide out of sample forecasts of a countercyclical, forward looking measure of systemic risk and show that the 2006Q4 value of this measure would have predicted more than half of realized covariances during the financial crisis. 
JEL:  G21 G22 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:17454&r=ets 
By:  McElroy, Tucker S; Politis, D N 
Abstract:  We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the Â¯rst diÂ®erence of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically. We also present asymptotic results for the case that the bandwidth is a Â¯xed proportion of sample size, extending known results to the case of Â°attop tapers. We adopt the Â¯xed proportion bandwidth perspective in our empirical section, presenting two methods for estimating the limiting critical values { both the subsampling method and a plugin approach. Extensive simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean. Both methods perform well { although the subsampling method appears to be better sized { and provide a viable framework for conducting inference for the mean. In summary, we supply a uniÂ¯ed asymptotic theory that covers all diÂ®erent types of memory under a single umbrella. 
Keywords:  kernel, lagwindows, overdifferencing, spectral estimation, subsampling, tapers, unitroot problem, Econometrics 
Date:  2011–09–01 
URL:  http://d.repec.org/n?u=RePEc:cdl:ucsdec:2265346&r=ets 