Raíces unitarias, cointegración y cotendencias no lineales: Un análisis de la relación entre el tipo de interés y la inflación en Europa.

Abstract

[SPA] La determinación del orden de integrabilidad de las series temporales adquiere especial relevancia al tratarse de un paso necesario previo a otros análisis como el de causalidad, cointegración, etc., y al facilitar la determinación del tipo de modelo que debe ser utilizado en un determinado estudio, así como el procedimiento de inferencia que debe tenerse en cuenta en las últimas etapas del análisis de series temporales. Además, en la última década ha surgido un interés especial en el análisis de las relaciones de corto y largo plazo que surgen entre diferentes variables en la actividad económica, adquiriendo aún mayor interés la identificación del verdadero proceso generador de las series implicadas en dichas relaciones. La presencia de una raíz unitaria en una serie temporal implica que un shock que incide en la serie tendrá una elevada persistencia. La medición del impacto que ocasiona un cambio exógeno en una serie temporal en el largo plazo también ha suscitado un interés considerable en los últimos años, ya que algunos autores representan el proceso generador de datos de una serie temporal a través de diferentes modelos dependiendo de la magnitud de las consecuencias que genera el shock en las mismas.. Aunque el número de estudios relativos a los contrastes de raíces unitarias que tienen en cuenta la posible existencia de rupturas estructurales en las series son menos numerosos, no existe un consenso claro sobre cuál es el ”mejor” test que debe ser aplicado a una serie temporal, ya que las propiedades de la mayoría de estos tests dependen, entre otros factores, del tipo de ruptura (en la media o en la pendiente de la serie), de su magnitud, de la ubicación de la misma en la muestra, del número de rupturas que presenta la serie, de la determinación exógena o endógena de la misma e incluso del tamaño muestral. La no consideración de estas rupturas en las series lleva, por ejemplo, a que algunos autores consideren relaciones de cointegración entre variables para las que los contrastes de raíces unitarias que utilizan ponen de manifiesto que son procesos integrados de orden unitario (I (1)), mientras que otros autores, a través de diferentes contrastes, obtienen que estas series son estacionarias y, por tanto, no tendría sentido analizar relaciones de cointegración entre ellas. En el Capítulo 1 llevamos a cabo una recopilación estructurada de la información más relevante sobre las propiedades de diferentes contrastes de raíces unitarias y de estacionariedad cuando una serie temporal se ve afectada por cambios estructurales. Esta relación adquiere especial relevancia desde que Irving Fisher (1896, 1930) formulara la noción de tipo de interés real. La versión más clásica de la denominada”hipótesis de Fisher” o”efecto Fisher”.El objetivo del Capítulo 2 es determinar si en aquellos países para los que existe una cotendencia no lineal entre el tipo de interés y la tasa de inflación, se produce el fenómeno denominado como puzzle de precios, es decir, si en el entorno de los modelos VAR un shock que perturba al tipo de interés nominal tiene un efecto positivo en la tasa de inflación. En el Capítulo 3 proponemos un nuevo test de cointegración, basado en el test de raíces unitarias, que utiliza el procedimiento continuous path block bootstrap (CBB), desarrollado por Paparoditis y Politis (2001) y lo aplicamos a la tasa de inflación y tipo de interés nominal de los países considerados en el Capítulo 2. El procedimiento no paramétrico CBB permite generar pseudo-series integradas de orden unitario manteniendo las características más importantes de los datos. Por tanto, este trabajo orientado a la relación entre diferentes series temporales, como son el tipo de interés nominal y la tasa de inflación, pretende llamar la atención en la necesidad de seguir profundizando en el análisis de los contrastes de raíces unitarias, teniendo en cuenta que cuando se eligen series con un gran número de observaciones es difícil que no se hayan visto afectadas, en algún momento del tiempo, por algún shock exógeno. Ello origina una alteración de las propiedades de estos contrastes y, por ende, de las hipótesis de partida de los procedimientos utilizados para hallar relaciones entre varias series temporales.[ENG]Determining the order of integrability of the time series takes on special importance as it is a necessary step prior to other analysis and the causality, cointegration, etc.. And to facilitate the determination of the type of model to be used in a study and the inference procedure to be taken into account in the final stages of analyzing time series. Moreover, in the last decade has been a special interest in analyzing the relationship of short-and long-term disputes between different variables in the economy, gaining even greater interest is the identification of the true generating process of the series involved in these relationships. The presence of a unit root in a time series implies that a shock that affects the series will have a high persistence. Measuring the impact that causes a change in an exogenous time series in the long term has also generated considerable interest in recent years, as some authors represent the process generating a time series data across different models depending on the magnitude of the shock generated in the same .. Although the number of studies concerning the contrasts of unit roots that take into account the possible existence of structural breaks in the series are less numerous, there is no clear consensus on what the "best" test to be applied to a time series because the properties of most of these tests depend, among other factors, the type of break (in the average or the slope of the series), its magnitude, the location of the same in the sample, the number presents breakdowns of the series, the identification of endogenous or exogenous, and even from the same sample size. Lack of these breaks in the series leads, for example, that some authors consider cointegration relationships between variables for which contrasts using unit roots show that they are integrated processes of order unit (I (1)) while other authors, through different contrasts obtained that these series are stationary and therefore does not make sense to analyze cointegration relationships between them. In Chapter 1 we conducted a structured collection of the most relevant information about the properties of different contrasts of stationarity and unit roots when a time series is affected by structural changes. This relationship is especially relevant since Irving Fisher (1896, 1930) formulated the concept of real interest rate. The classic version of the "Fisher hypothesis" or "Fisher effect." The purpose of Chapter 2 is whether in those countries for which there is a nonlinear cotendencia interest rate and inflation rate, is the phenomenon known as the price puzzle, ie in the VAR models of a shock that disturbs the nominal interest rate has a positive effect on the rate of inflation. In Chapter 3 we propose a new cointegration test, based on the unit root test, using the procedure continuous path block bootstrap (CBB), developed by Paparoditis and Politis (2001) and apply it to the inflation rate and type of nominal interest of the countries considered in Chapter 2. The non-parametric procedure can generate pseudo-CBB series integrated of order unit to maintain the most important features of the data. Therefore, this work focused on the relationship between different time series, such as the nominal interest rate and inflation rate, to draw attention on the need to further deepen the analysis of the contrasting unit roots, taking into account when series are chosen with a large number of observations is difficult to have not been affected at some point in time, for some exogenous shock. This results in an alteration of the properties of these contrasts and, therefore, the assumptions made in the procedures used to find relationships between different time series.

[ENG] Determining the order of integrability of the time series takes on special importance as it is a necessary step prior to other analysis and the causality, cointegration, etc.. And to facilitate the determination of the type of model to be used in a study and the inference procedure to be taken into account in the final stages of analyzing time series. Moreover, in the last decade has been a special interest in analyzing the relationship of short-and long-term disputes between different variables in the economy, gaining even greater interest is the identification of the true generating process of the series involved in these relationships. The presence of a unit root in a time series implies that a shock that affects the series will have a high persistence. Measuring the impact that causes a change in an exogenous time series in the long term has also generated considerable interest in recent years, as some authors represent the process generating a time series data across different models depending on the magnitude of the shock generated in the same .. Although the number of studies concerning the contrasts of unit roots that take into account the possible existence of structural breaks in the series are less numerous, there is no clear consensus on what the "best" test to be applied to a time series because the properties of most of these tests depend, among other factors, the type of break (in the average or the slope of the series), its magnitude, the location of the same in the sample, the number presents breakdowns of the series, the identification of endogenous or exogenous, and even from the same sample size. Lack of these breaks in the series leads, for example, that some authors consider cointegration relationships between variables for which contrasts using unit roots show that they are integrated processes of order unit (I (1)) while other authors, through different contrasts obtained that these series are stationary and therefore does not make sense to analyze cointegration relationships between them. In Chapter 1 we conducted a structured collection of the most relevant information about the properties of different contrasts of stationarity and unit roots when a time series is affected by structural changes. This relationship is especially relevant since Irving Fisher (1896, 1930) formulated the concept of real interest rate. The classic version of the "Fisher hypothesis" or "Fisher effect." The purpose of Chapter 2 is whether in those countries for which there is a nonlinear cotendencia interest rate and inflation rate, is the phenomenon known as the price puzzle, ie in the VAR models of a shock that disturbs the nominal interest rate has a positive effect on the rate of inflation. In Chapter 3 we propose a new cointegration test, based on the unit root test, using the procedure continuous path block bootstrap (CBB), developed by Paparoditis and Politis (2001) and apply it to the inflation rate and type of nominal interest of the countries considered in Chapter 2. The non-parametric procedure can generate pseudo-CBB series integrated of order unit to maintain the most important features of the data. Therefore, this work focused on the relationship between different time series, such as the nominal interest rate and inflation rate, to draw attention on the need to further deepen the analysis of the contrasting unit roots, taking into account when series are chosen with a large number of observations is difficult to have not been affected at some point in time, for some exogenous shock. This results in an alteration of the properties of these contrasts and, therefore, the assumptions made in the procedures used to find relationships between different time series.