P-values for non-standard distributions with an application to the DF test

The literature of unit roots and structural breaks has produced numerous tests that follow nonstandard asymptotic distributions. This paper by fitting a seminonparametric model to them proposes a new simple way of calculating the p-values

Large shocks vs. small shocks. (Or does size matter? May be so.)

What are the shocks that drive economic fluctuations? The answer to this question requires as a first step solving the shock identification issue. This paper proposes a new identification scheme based on two aspects: the long-run effect of the shock (permanent or transitory), and the size of the shock (Large or small). This is done by using a threshold integrated moving average model (TIMA) previously introduced in the literature by the authors. Based on this model we develop a testing strategy to determine whether Large and small shocks have different long-run effects, as well as whether one of them is purely transitory. The paper analyzes the impulse response function of both types of shocks, and provides the asymptotic results sufficient to implement the above testing strategy. Based on these results we develop a new nonlinear permanent–transitory decomposition, that is applied to US stock prices to analyze the quality ofthe stock market, and to US GNP to investigate the asymmetric behavior of its shocks.Publicad

A systematic framework for analyzing the dynamic effects of permanent and transitory shocks

This paper proposes a systematic framework for analyzing the dynamic effects of permanent and transitory shocks on a system of n economic variables. We consider a two-step orthogonolization on the residuals of a VECM with r cointegrating vectors. The first step separates the permanent from the transitory shocks, and the second step isolates n?r mutually uncorrelated permanent shocks and r transitory shocks. The decomposition is computationally straightforward and entails only a minor modification to the Choleski decomposition commonly used in the literature. We then show how impulse response functions can be constructed to trace out the propagating mechanism of shocks distinguished by their degree of persistence. In an empirical example, the dynamic responses to the identified permanent shocks have properties similar to shocks to productivity, the real interest rate, and money growth, even though no economic theory was used to achieve the identification. We highlight two numerical issues that could affect any identification of permanent and transitory shocks.Publicad

Transversely holomorphic flows and contact circles on spherical 3-manifolds

Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint. We describe a complex analogue of the classical Godbillon-Vey invariant, the so-called Bott invariant, and a logarithmic monodromy of closed leaves. The Bott invariant allows us to formulate a generalised Gau{\ss}-Bonnet theorem. We compute these invariants for the Poincar\'e foliations on the 3-sphere and derive rigidity statements, including a uniformisation theorem for orbifolds. These results are then applied to the classification of taut contact circles.Comment: 31 pages, 3 figures; v2: changes to the exposition, additional reference

Contagion versus flight to quality in financial markets

None doubts that financial markets are related (interdependent). What is not so clear is whether there exists contagion among them or not, its intensity, and its causal direction. The aim of this paper is to define properly the term contagion (different from interdependence) and to present a formal test for its existence, the magnitude of its intensity, and for its direction. Our definition of contagion lies on tail dependence measures and it is made operational through its equivalence with some copula properties. In order to do that, we define a NEW copula, a variant of the Gumbel type, that is sufficiently flexible to describe different patterns of dependence, as well as being able to model asymmetric effects of the analyzed variables (something not allowed with the standard copula models). Finally, we estimate our copula model to test the intensity and the direction of the extreme causality between bonds and stocks markets (in particular, the flight to quality phenomenon) during crises periods. We find evidence of a substitution effect between Dow Jones Corporate Bonds Index with 2 years maturity and Dow Jones Stock Price Index when one of them is through distress periods. On the contrary, if both are going through crises periods a contagion effect is observed. The analysis of the corresponding 30 years maturity bonds with the stock market reflects independent effects of the shocks

Threshold stochastic unit root models

This paper introduces a new class of stochastic unit root (STUR) processes, where the randomness of the autorregresive unit root is driven by a threshold variable. These new models, the threshold autorregresive stochastic unit root (TARSUR) models, are stationary in some regimes and mildly explosive in others. TARSUR models are not only an alternative to fixed unit root models but present interpretation, estimation and testing advantages with respect to the existent STUR models. The paper analyzes the stationarity properties of the TARSUR models and proposes a simple t -statistic for testing the null hypothesis of a fixed unit root versus a stochastic unit root hypothesis. It is shown that its asymptotic distribution (AD) depends on the knowledge we have about the threshold values: known, unknown but identified, and unknown and unidentified. In the first two cases the AD is a standard Normal distribution, while in the last one the AD is a functional of Brownian Motions and Brownian Sheets. Monte Carlo simulations show that the proposed tests behave very well in finite samples and that the Dickey-Fuller test cannot easily distinguish between an exact unit root and a threshold stochastic unit root. The paper concludes with applications to stock prices and interest rates where the hypothesis of a fixed unit root is rejected in favor of the threshold stochastic unit root

Subsampling inference in threshold autoregressive models

This paper discusses inference in self-exciting threshold autoregressive (SETAR) models. Of main interest is inference for the threshold parameter. It is well-known that the asymptotics of the corresponding estimator depend upon whether the SETAR model is continuous or not. In the continuous case, the limiting distribution is normal and standard inference is possible. In the discontinuous case, the limiting distribution is non-normal and it is not known how to estimate it consistently. We show that valid inference can be drawn by the use of the subsampling method. Moreover, the method can even be extended to situations where the (dis)continuity of the model is unknown. In this case, the inference for the regression parameters of the model also becomes difficult and subsampling can be used again. In addition, we consider an hypothesis test for the continuity of a SETAR model. A simulation study examines small sample performance and an application illustrates how the proposed methodology works in practice.Publicad