Unbalanced Cointegration

Recently, increasing interest on the issue of fractional cointegration has emerged from theoretical and empirical viewpoints. Here, as opposite to the traditional prescription of unit root observables with weak dependent cointegrating errors, the orders of integration of these series are allowed to take real values, but, as in the traditional framework, equality of the orders of at least two observable series is necessary for cointegration. This assumption, in view of the real-valued nature of these orders could pose some difficulties, and in the present paper we explore some ideas related to this issue in a simple bivariate framework. First, in a situation of "nearcointegration", where the only difference with respect to the "usual" fractional cointegration is that the orders of the two observable series differ in an asymptotically negligible way, we analyse properties of standard estimates of the cointegrating parameter. Second, we discuss the estimation of the cointegrating parameter in a situation where the orders of integration of the two observables are truly different, but their corresponding balanced versions (with same order of integration) are cointegrated in the usual sense. A Monte Carlo study of finitesample performance and simulated series is included.

The Mexican border region after NAFTA: Attempting to surpass the assembly industry

In the last twenty years their has been an astonishing degree of industriali- zation on the Mexican border, in large part due to the arrival of foreign plants attracted by lower labor costs. This in keeping with the conception of the maquiladora program as a way to attract labor-intensive production to Mexico in order to provide more jobs and their benefits to the Mexican economy. At the end of the century a more balanced judgment has emerged. Foreign plants have invested in more intensive production processes, and more sophisticated organizational procedures: Advanced product manufacturing, just-in-time methods, and ISO9000 certification have become standard among a growing number of maquiladoras. As a consequence, knowledge of local engineers in industrial processes has remarkably increased in the last two decades. In our work we analyze those contradictory trends that make of the border region one of the most dynamic in the world. From the perspective of regional development it is necessary to asses if the industry will evolve into a more integrated network with old and new local industries, and if professional knowledge will be a more significant competitive advantage than low wages in the next few years. As Gereffi has stressed, there are different production roles among different countries;ranging from primary commodity exports to original brand-name manufacturing. Adopting the global commodity approach, we will assess whether the Mexican border region will be able to develop the ability to proceed to more sophisticated high-value industrial niches. ial niches.

Distribution-free tests of fractional cointegration

We propose tests of the null of spurious relationship against the alternative of fractional cointegration among the components of a vector of fractionally integrated time series. Our test statistics have an asymptotic chi-square distribution under the null and rely on generalized least squares–type of corrections that control for the short-run correlation of the weak dependent components of the fractionally integrated processes. We emphasize corrections based on nonparametric modelization of the innovations’ autocorrelation, relaxing important conditions that are standard in the literature and, in particular, being able to consider simultaneously (asymptotically) stationary or nonstationary processes. Relatively weak conditions on the corresponding short-run and memory parameter estimates are assumed. The new tests are consistent with a divergence rate that, in most of the cases, as we show in a simple situation, depends on the cointegration degree. Finite-sample properties of the tests are analyzed by means of a Monte Carlo experiment.Publicad

Taming the resistive switching in Fe/MgO/V/Fe magnetic tunnel junctions: An ab initio study

A possible mechanism for the resistive switching observed experimentally in Fe/MgO/V/Fe junctions is presented. Ab initio total energy calculations within the local density approximation and pseudopotential theory shows that by moving the oxygen ions across the MgO/V interface one obtains a metastable state. It is argued that this state can be reached by applying an electric field across the interface. In addition, the ground state and the metastable state show different electric conductances. The latter results are discussed in terms of the changes of the density of states at the Fermi level and the charge transfer at the interface due to the oxygen ion motion

Semiparametric Estimation of Fractional Cointegration

A semiparametric bivariate fractionally cointegrated system is considered, integrationorders possibly being unknown and I (0) unobservable inputs having nonparametricspectral density. Two kinds of estimate of the cointegrating parameter ? are considered,one involving inverse spectral weighting and the other, unweighted statistics with a spectralestimate at frequency zero. We establish under quite general conditions the asymptoticdistributional properties of the estimates of ?, both in case of "strong cointegration" (whenthe difference between integration orders of observables and cointegrating errors exceeds1/2) and in case of "weak cointegration" (when that difference is less than 1/2), whichincludes the case of (asymptotically) stationary observables. Across both cases, the sameWald test statistic has the same standard null ?2 limit distribution, irrespective of whetherintegration orders are known or estimated. The regularity conditions include unprimitiveones on the integration orders and spectral density estimates, but we check these undermore primitive conditions on particular estimates. Finite-sample properties are examined ina Monte Carlo study.Fractional cointegration, semiparametric model, unknown integration orders.

Cointegration in fractional systems with unknown integration orders.

Cointegrated bivariate nonstationary time series are considered in a fractional context, without allowance for deterministic trends. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is nested, but these values have typically been assumed known. We allow one or more of them to be unknown real values, in which case Robinson and Marinucci (1997,2001) have justified least squares estimates of the cointegrating vector, as well as narrow-band frequency-domain estimates, which may be less biased. While consistent, these estimates do not always have optimal convergence rates, and they have non-standard limit distributional behaviour. We consider estimates formulated in the frequency domain, that consequently allow for a wide variety of (parametric) autocorrelation in the short memory input series, as well as time-domain estimates based on autoregressive transformation. Both can be interpreted as approximating generalized least squares and Gaussian maximum likelihood estimates. The estimates share the same limiting distribution, having mixed normal asymptotics (yielding Wald test statistics with χ2 null limit distributions), irrespective of whether the integration orders are known or unknown, subject in the latter case to their estimation with adequate rates of convergence. The parameters describing the short memory stationary input series are √n-consistently estimable, but the assumptions imposed on these series are much more general than ones of autoregressive moving average type. A Monte Carlo study of finite-sample performance is included.

ROOT-N-CONSISTENT ESTIMATION OF WEAKFRACTIONAL COINTEGRATION

Empirical evidence has emerged of the possibility of fractional cointegration such that thegap, ß, between the integration order d of observable time series, and the integrationorder ? of cointegrating errors, is less than 0.5. This includes circumstances whenobservables are stationary or asymptotically stationary with long memory (so d 1/2, in particular=consistent - n andasymptotically normal estimation of the cointegrating vector ? is possible when ßFractional cointegration, Parametric estimation, Asymptotic normality.

Cointegration in Fractional Systems with Unknown Integration Orders

Cointegration of nonstationary time series is considered in a fractional context. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is nested, but these values have typically been assumed known. We allow one or more of them to be unknown real values, in which case Robinson and Marinucci (1997,2001) have justified least squares estimates of the cointegrating vector, as well as narrow-band frequencydomain estimates, which may be less biased. While consistent, these estimates do not always have optimal convergence rates, and they have non-standard limit distributional behaviour. We consider estimates formulated in the frequency domain, that consequently allow for a wide variety of (parametric) autocorrelation in the short memory input series, as well as time-domain estimates based on autoregressive transformation. Both can be interpreted as approximating generalized least squares and Gaussian maximum likelihood estimates. The estimates share the same limiting distribution, having mixed normal asymptotics (yielding Wald test statistics with null limit distributions), irrespective of whether the integration orders are known or unknown, subject in the latter case to their estimation with adequate rates of convergence. The parameters describing the short memory stationary input series are -consistently estimable, but the assumptions imposed on these series are much more general than ones of autoregressive moving average type. A Monte Carlo study of finite-sample performance and an empirical application to testing the PPP hypothesis are included.Fractional cointegration; Unknown integration orders; System estimates;Mixed normal asymptotics

Majorana bound states in open quasi-1D and 2D systems with transverse Rashba coupling

We study the formation of Majorana states in quasi-1D and 2D square lattices with open boundary conditions, with general anisotropic Rashba coupling, in the presence of an applied Zeeman field and in the proximity of a superconductor. For systems in which the length of the system is very large (quasi-1D) we calculate analytically the exact topological invariant, and we find a rich phase diagram which is strongly dependent on the width of the system. We compare our results with previous results based on a few-band approximation. We also investigate numerically open 2D systems of finite length in both directions. We use the recently introduced generalized Majorana polarization, which can locally evaluate the Majorana character of a given state. We find that the formation of Majoranas depends strongly on the geometry of the system and if the length and the width are comparable no Majorana states can form, however, one can show the formation of "quasi-Majorana" states that have a local Majorana character, but no global Majorana symmetry.Comment: 12 pages, 13 figure