PRACTITIONERS CORNER: Tests for Cointegration in Models with Regime and Trend Shifts

ABSTRACT Recently Gregory and Hansen (1996) proposed a number of residual-based tests for cointegration in models with the possibility of a structural break. They considered three models: (i) level shift; (ii) level shift with trend; and (iii) regime shift (both level shift and slope coefficients can change). We introduce a more general model that permits a trend shift as well as a regime shift and we provide the critical values appropriate for testing this hypothesis.     

Density Forecasts With Midas Models

We propose a parametric block wild bootstrap approach to compute density forecasts for various types of mixed‐data sampling (MIDAS) regressions. First, Monte Carlo simulations show that predictive densities for the various MIDAS models derived from the block wild bootstrap approach are more accurate in terms of coverage rates than predictive densities derived from either a residual‐based bootstrap approach or by drawing errors from a normal distribution. This result holds whether the data‐generating errors are normally independently distributed, serially correlated, heteroskedastic or a mixture of normal distributions. Second, we evaluate density forecasts for quarterly US real output growth in an empirical exercise, exploiting information from typical monthly and weekly series. We show that the block wild bootstrapping approach, applied to the various MIDAS regressions, produces predictive densities for US real output growth that are well calibrated. Moreover, relative accuracy, measured in terms of the logarithmic score, improves for the various MIDAS specifications as more information becomes available. Copyright © 2016 John Wiley & Sons, Ltd.     

Cointegration in a historical perspective

We analyse the impact of the Engle and Granger (1987) article by means of its citations over time, and find evidence of a second life starting in the new millennium. Next, we propose a possible explanation of the success of this citation classic. We argue that the conditions for its success were just right at the time of its appearance, because of the growing emphasis on time series properties in econometric modelling, the empirical importance of stochastic trends, the availability of sufficiently long macroeconomic time series, and the availability of personal computers and econometric software for carrying out the new techniques.     

Cointegration in a macroeconomic system

This paper investigates the long-run relationships within a set of six quarterly time-series on the Austrian economy by means of cointegration. After analysing the univariate properties, especially with respect to the appropriate seasonal filter, the maximum-likelihood method proposed by Johansen (1988) is applied to estimate and test the cointegrating relationships. We found three such relations, implying that the system is driven by three independent stochastic time trends. In a next stage we investigate whether the empirically determined cointegrating relationships are compatible with implications derived from the neoclassical growth model with exogenous stochastic technical progress. It is found that the Austrian data strongly reject the propositions that the real interest rate and the log ratios of consumption to output, investment to output, and the real gross wage sum to output are stationary.     

Trends and Cycles in GDP

The recent experience in the UK of substantial growth in GDP following the recession of the early 1980s has led to renewed interest in the measurement and explanation of business cycles. Development of economic as well as econometric theory has improved our ability both to measure the cycle more accurately and to offer a better explanation of its behaviour. In this Briefing Paper we present an analysis of these two developments.     

Cointegration and distance between differenced processes

In this note, it is argued that cointegration augments the distance between the differenced series. If two series, x _t and y _t , are integrated of order one and cointegrated and v _t and w _t are integrated of order one but not cointegrated then, under certain conditions, the distance between ??x _t and ??y _t is more than the distance between ??v _t and ??w _t .     

Testing for Unit Roots and Cointegration in Spatial Cross-Section Data

Abstract

Spatial impulses are derived for SAR models containing a spatial unit root. Analytical solutions are obtained for lateral space where the number of spatial units tends to infinity. Numerical solutions are obtained for finite regular lattices where edge-effects are shown to influence spatial impulses, and for irregular lattices. Monte Carlo simulation methods are used to compute critical values for spatial unit root tests in SAR models estimated from spatial cross-section data for regular and irregular lattices. We also compute critical SAC values for spatial cointegration tests for cross-section data that happen to be spatially nonstationary. We show that parameter estimates in spatially cointegrated models are ‘superconsistent’.

RÉSUMÉ On dérive des impulsions spatiales de modèles SAR contenant une racine unité spatiale. On obtient des solutions analytiques pour l'espace latéral lorsque le nombre d'unités spatiales tend vers l'infini. On obtient des solutions numériques pour des réseaux réguliers finis, où l'on relève l'influence d’«?edge effects?» sur les impulsions spatiales, et pour des réseaux irréguliers. Des méthodes de simulation Monte Carlo sont utilisées pour calculer des valeurs critiques pour des tests de racine unité spatiale dans des modèles SAR estimés sur la base de données transversales spatiales pour réseaux réguliers et irréguliers. Nous calculons également des valeurs critiques de SAC pour essais de co-intégration spatiale, concernant des données transversales qui s'avèrent être spatialement non stationnaires. Nous démontrons que les estimations de paramètres dans des modèles spatialement co-intégrés sont «?ultra cohérentes?».

EXTRACTO Se derivan impulsos espaciales para modelos SAR que contienen una raíz unitaria espacial. Se obtienen soluciones analíticas para espacio lateral donde el número de unidades espaciales tiende al infinito. Se obtienen soluciones numéricas para retículos finitos regulares que demuestran que los efectos de borde influyen sobre los impulsos espaciales, así como para retículos irregulares. Se utilizan métodos de simulación de Monte Carlo para computar valores críticos destinados a las pruebas espaciales de raíces unitarias en modelos SAR, estimados a partir de datos espaciales de corte transversal para retículos regulares e irregulares. También computamos valores SAC críticos destinados a pruebas de cointegración espacial para datos de corte transversal que no son espacialmente estacionarios. Mostramos que las estimaciones de parámetros en modelos espacialmente cointegrados son ‘superconsistentes’.

     

自举法与协整参数的FMOLS估计

考虑静态和动态两类数据生成过程,利用蒙特卡罗模拟方法,从估计偏差、实际检验水平和检验功效三个方面对FMOLS(Full Modified Ordinary Least Square)估计的渐近分析和自举分析进行全面比较.结果表明,与渐近分析相比,自举分析可以减小实际检验水平对名义水平的偏差,但要以检验功效的降低为代价.严格意义上,自举分析是降低了拒真错误出现的概率.相对稳健的选择是结合两方面的信息,渐近检验通过则接受原假设,自举检验拒绝则接受备择假设,对于其他情况,具体结论取决于人们的研究态度.     

On the Role of Seasonal Intercepts in Seasonal Cointegration

In the paper we consider the role of seasonal intercepts in seasonal cointegration analysis. For the nonseasonal unit root, such intercepts can generate a stochastic trend with a drift common to all observations. For the seasonal unit roots, however, we show that unrestricted seasonal intercepts generate trends that are different across the seasons. Since such seasonal trends may not appear in economic data, we propose a modified empirical method to test for seasonal cointegration. We evaluate our method using Monte Carlo simulations and using a four-dimensional data set of Austrian macroeconomic variables.     

分形市场中的汇率协整关系

本文将混沌与分形运用到汇率研究中,运用R/S方法研究了外汇收益率的长记忆性,并将传统的协整理论推广到广义的分数维协整,研究了时间序列之间的长期均衡关系,并以外汇市场中的欧元和新加坡元兑美元的汇率为例进行了实证分析,指出这两种货币收益率服从分形分布,具有相同的分整阶数且二者存在分数维协整关系。     

Panel Data Unit Roots and Cointegration: An Overview

Recent developments in the field of the econometrics of panel data with non-stationary series are reviewed and interpreted. In particular, we discuss tests for unit roots and cointegration, and the roles of mean and variance correction, non-parametric correction and full modification for the construction of these tests and estimators. A discussion of the key contributions of the papers in this special issue is placed within the framework of the current literature and areas for further development are proposed.     

Accounting for Environmental Influences in Stochastic Frontier Models: With Application to International Airlines

The principal aim of this paper is to measure the efficiency of international airlines. We obtain measures of technical efficiency from stochastic frontier production functions which have been adjusted to account for environmental influences such as network conditions, geographical factors, etc. We observe that two alternative approaches to this problem have been proposed in the efficiency measurement literature. One assumes that the environmental factors influence the shape of the technology while the other assumes that they directly influence the degree of technical inefficiency. In this paper we compare the results obtained when using these two approaches. The two sets of results provide similar rankings of airlines but suggest differing degrees of technical inefficiency. Both sets of results also suggest that Asian/Oceanic airlines are technically more efficient than European and North American airlines but that the differences are essentially due to more favourable environmental conditions. Nevertheless, it is among Asian companies that the major improvements in managerial efficiency (technical efficiency with environmental factors netted out) took place over the sample period (1977–1990).     

中国省份产业经济周期的经验研究——基于贝叶斯潜在多动态因子模型的分析

本文利用基于吉本斯抽样估算的贝叶斯潜在多动态因子模型,估算出中国改革开放以来三次产业实际产出波动的全国、地区和省份动态因子,发现全国动态因子和区域动态因子较好得刻画了中国宏观经济波动的基本特征和基本区域经济事实。方差分解的结果表明,全国动态因子是省份第二产业实际产出波动最重要的驱动力,异质性成分是省份第一、第三产业实际产出波动的主要驱动力,区域动态因子影响力弱,省份动态因子对第一、第三产业有一定的影响。不同类型动态因子对各产业影响程度的省份差异在一定程度上和区域以及省份特征相关。     

广西固定资产投资与经济增长的协整性研究

本文基于广西1991-2008年数据,利用计量经济学中的协整检验、误差修正模型和格兰杰因果检验对广西固定资产投资和经济增长的关系进行分析。结果表明,广西固定资产投资与经济增长之间存在长期稳定的关系。取滞后期为1、3年时,广西固定资产投资是广西经济增长的格兰杰原因,取滞后期为2年时,广西固定资产投资与广西经济增长存在双向的因果关系,两者互相影响。     

在协整分析中如何处理截距和趋势

协整分析是经济时间序列分析中用到的重要工具,本文指出了国内进行协整分析时存在的不足,进而从理论和实证的角度,阐述了协整分析中处理截距和趋势的方法。     

Frequency Domain Tests for Residual Serial Correlation in Cointegration Regressions

This paper introduces tests for residual serial correlation in cointegrating regressions. The tests are devised in the frequency domain by using the spectral measure estimates. The asymptotic distributions of the tests are derived and test consistency is established. The asymptotic distributions are obtained by using the assumptions and methods that are different from those used in Grenander and Rosenblatt (1957) and Durlauf (1991). Small-scale simulation results are reported to illustrate the finite sample performance of the tests under various distributional assumptions on the data generating process. The distributions considered are normal and t-distributions. The tests are shown to have stable size at sample sizes as large as 50 or 100. Additionally, it is shown that the tests are reasonably powerful against the ARMA residuals. An empirical application of the tests to investigate the ‘weak-form’ efficiency in the foreign exchange market is also reported.