On the properties of the Dickey-Pantula test against fractional alternatives

The limit properties of the testing sequence underlying the Dickey-Pantula test for a double unit root in a time series are derived when the true data generating process is assumed to be nonstationary fractionally integrated.Publicad

Instrumental Variable Interpretation of Cointegration with Inference Results for Fractional Cointegration

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The instrument is a delayed regressor obtained from the conditional bivariate system of nonstationary fractionally integrated processes with a weakly stationary error correction term. We prove the consistency of this estimator and derive its limiting distribution. We also show that, in the I(1) case, with a semiparametric correction simpler than the one required for the fully modified ordinary least squares (FM-OLS), our fully modified instrumental variables (FM-IV) estimator is median-unbiased, a mixture of normals, and asymptotically efficient. As a consequence, standard inference can be conducted with this new FM-IV estimator of the cointegrating parameter. We show by the use of Monte Carlo simulations that the small sample gains with the new IV estimator over OLS are remarkable.Publicad

How spurious features arise in case of fractional cointegration

It is well-known that a linear regression among the levels of independent highly persistent processes yields high values of the corresponding coefficient of determination along with divergent I-ratios and low values of the Durbin-Watson statistic. In fact, such a behaviour of the customary OLS statistics has become a sort of definition of the so-called spurious regressions in econometrics. In this paper, however, we show how these spurious stylized facts also arise among nonstationary (fractionally) cointegrated processes

Asymptotic inference results for multivariate long-memory processes

In this paper, we extend the well-known Sims, Stock and Watson (SSW)(Sims et al. 1990; Econometrica 56, 113?44), analysis on estimation and testing in vector autoregressive process (VARs) with integer unit roots and deterministic components to a more general set-up where non-stationary fractionally integrated (NFI) processes are considered. In particular, we focus on partial VAR models where the conditioning variables are NFI since this is the only finite-lag VAR model compatible with such processes. We show how SSW?s conclusions remain valid. This means that whenever a block of coefficients in the partial VAR can be written as coefficients on zero-mean I(0) regressors in models including a constant term, they will have a joint asymptotic normal distribution. Monte Carlo simulations and an empirical application of our theoretical results are also provided.Publicad

Fractal study of tumors

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Àlex HaroFractal geometry was first invented by mathematicians of the late 19th and early 20th century to study problems as abstract as the existence of continuous functions non derivable at any point, the continuum hypothesis, or the existence of topological spaces with strange properties. It was not until the second half of the 20th century that fractal geometry became popular, and it was applied to the study of natural phenomena by the hand of B. Mandelbrot. The study of tumor growth using fractal geometry is relatively recent. This study is based on the fractal character of tumor contours. One of their most important features is roughness, since its increase is related to the tumor growth. Tumor growth dynamic can be described by a function that depends on both time and position, known as local width function, as well as by some power law exponents, called critical exponents. The aim of this final degree project is to study all these concepts in connection with fractals. Elementary concepts of the theory of fractals will also be studied, as the iterated function systems, the fractal dimension and the fractal interpolation functions. Since fractal dimension can only be computed accurately for some specific mathematical objects, we will study some methods that estimate fractal dimension of tumors based on its fractal characteristics. Finally, we will develop some Matlab programs which will compute the fractal dimension of tumors, as well as the roughness of their contours. Furthermore, we will compare our results with the experimental data

Conceptual schemes and empiricism: what Davidson saw and McDowell missed

This paper is an examination and evaluation of McDowell’s criticisms of Davidson’s views on conceptual schemes and empiricism. I will argue that McDowell does not understand the real nature of Davidson’s arguments against the scheme-content dualism and that his new empiricist proposal fails to solve all the problems that old empiricism has traditionally raised. This is so because Davidson does not try to reject only a certain conception of experience by rejecting the dualism of scheme and content, but a way of thinking about meaning and knowledge that assumes a dualism that cannot be maintained

Cournot equilibria for socially responsible firms in an uncertain environment

This paper considers firms which compete under Cournot assumptions and in- corporate social responsibility to the evaluation of their results. In our model a socially responsible firm is one which takes into account not only its profits, but also it internalizes its own share of externality and is sensitive to consumer surplus. The analysis of the equilibria to which the firms will eventually arrive is ad- dressed in a framework where the results of the strategic decisions of the firms depend on a future uncertain event and no information about the probability distribution is available.En este trabajo se analiza el efecto de la inclusión de objetivos de responsabilidad social en un modelo de empresas que compiten bajo los supuestos de Cournot. En nuestro modelo una empresa socialmente responsable es aquella que no solo tiene en cuenta sus beneficios, sino que también tiene en cuenta las externalidades positivas generadas por el excedente del consumidor. El análisis de los equilibrios a los que pueden llegar las empresas se realiza en un contexto de incertidumbre. Los resultados de las decisiones estratégicas de las empresas dependen de la realización de un escenario futuro y no se dispone de información sobre las probabilidades de ocurrencia de los posibles escenarios