Bayesian Conditional Cointegration

Cointegration is an important topic for time-series, and describes a relationship between two series in which a linear combination is stationary. Classically, the test for cointegration is based on a two stage process in which first the linear relation between the series is estimated by Ordinary Least Squares. Subsequently a unit root test is performed on the residuals. A well-known deficiency of this classical approach is that it can lead to erroneous conclusions about the presence of cointegration. As an alternative, we present a framework for estimating whether cointegration exists using Bayesian inference which is empirically superior to the classical approach. Finally, we apply our technique to model segmented cointegration in which cointegration may exist only for limited time. In contrast to previous approaches our model makes no restriction on the number of possible cointegration segments.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Bayesian approaches to cointegration

The degree of empirical support of a priori plausible structures on the cointegration vectors has a central role in the analysis of cointegration. Villani (2000) and Strachan and van Dijk (2003) have recently proposed finite sample Bayesian procedures to calculate the posterior probability of restrictions on the cointegration space, using the existence of a uniform prior distribution on the cointegration space as the key ingredient. The current paper extends this approach to the empirically important case with different restrictions on the individual cointegration vectors. Prior distributions are proposed and posterior simulation algorithms are developed. Consumers' expenditure data for the US is used to illustrate the robustness of the results to variations in the prior. A simulation study shows that the Bayesian approach performs remarkably well in comparison to other more established methods for testing restrictions on the cointegration vectors

Sparse cointegration

Cointegration analysis is used to estimate the long-run equilibrium relations between several time series. The coefficients of these long-run equilibrium relations are the cointegrating vectors. In this paper, we provide a sparse estimator of the cointegrating vectors. The estimation technique is sparse in the sense that some elements of the cointegrating vectors will be estimated as zero. For this purpose, we combine a penalized estimation procedure for vector autoregressive models with sparse reduced rank regression. The sparse cointegration procedure achieves a higher estimation accuracy than the traditional Johansen cointegration approach in settings where the true cointegrating vectors have a sparse structure, and/or when the sample size is low compared to the number of time series. We also discuss a criterion to determine the cointegration rank and we illustrate its good performance in several simulation settings. In a first empirical application we investigate whether the expectations hypothesis of the term structure of interest rates, implying sparse cointegrating vectors, holds in practice. In a second empirical application we show that forecast performance in high-dimensional systems can be improved by sparsely estimating the cointegration relations

Cointegration Analysis with State Space Models

This paper presents and exemplifies results developed for cointegration analysis with state space models by Bauer and Wagner in a series of papers. Unit root processes, cointegration and polynomial cointegration are defined. Based upon these definitions the major part of the paper discusses how state space models, which are equivalent to VARMA models, can be fruitfully employed for cointegration analysis. By means of detailing the cases most relevant for empirical applications, the I(1), MFI(1) and I(2) cases, a canonical representation is developed and thereafter some available statistical results are briefly mentioned.State space models, unit roots, cointegration, polynomial cointegration, pseudo maximum likelihood estimation, subspace algorithms

Testing the foreign aid-led growth hypothesis in West Africa

This paper assesses the foreign aid-led growth hypothesis in a panel of West African countries using panel cointegration techniques ( Pendroni Residual Cointegration Test, Error Correction Model, Johansen Fisher Panel Cointegration Test) and then on a country-by-country basis using time series cointegration techniques (Engle-Granger test, Error Correction Model , Johansen system cointegration test). The panel cointegration results indicate a long run relationship between aid and growth in the whole panel. For the individual countries, at least one test showed evidence of this long run relationship. Granger causality tests were done for the whole panel and then for each country individually to establish direction of causality between foreign aid and economic growth. There is evidence of unidirectional causality from foreign aid to economic growth, from economic growth to foreign aid and there are cases where both variables are independent. A simplified variation of the Chenery and Strout Two-Gap Model was estimated to test the impact of foreign aid and selected explanatory variables on economic growth in countries where aid was found to granger cause growth and this impact varied from country to country

A note on the power of panel conitegration tests - An application to health care expenditure and GDP

This paper enlarges on Gutierrez's (2003) results on the power of panel cointegration tests. By a comparison of power of panel cointegration tests, we show how the choice of most powerful test depends on the values of the sample statistics. Country - by - country and panel stationarity and cointegration tests are performed on a panel of 20 OECD countries over the period 1971 - 2004. Residual - based tests and a cointegration rank test in the system of health care expenditure and GDP are used to test cointegration. Asymptotic normal distribution of these tests allows a straightforward comparison: for some values of the sample statistics, residual - based and rank tests are not directly comparable as the power of the residual - based tests oscillates; for other values of the sample statistics, the rank test is more powerful than the residual - based tests. This suggests that a clear-cut conclusion on the most powerful test cannot be reached a priori

Non-Cointegration and Econometric Evaluation of Models of Regional Shift and Share

This paper tests for cointegration between regional output of an industry and national output of the same industry. An equilibrium economic theory is presented to argue for the plausibility of cointegration, however, regional economic forecasting using the shift and share framework often acts as if cointegration does not exist. Data analysis on broad industrial sectors for 20 states finds very little evidence for cointegration. Forecasting models with and without imposing cointegration are than constructed and used to forecast out of sample. The simplest, non-cointegrating models are the best.

Tests for cointegration in panels with regime shifts

In the paper we extend Gregory and Hansen’s (1996)ADF, Za, Zt cointegration tests to panel data, using the method proposed in Maddala and Wu (1999). We test the null hypothesis of no cointegration for all the units in the panel against the alternative hypothesis of cointegration, while allowing for a one-time regime shift of unknown timing for at least some regressions. We derive the panel tests for the ADF, Za, Zt tests , and compare these tests with Pedroni’s (1999) panel cointegration tests. We show that Gregory and Hansen’s (1996) panel tests have higher power to reject null when there is a structural change in the cointegration vector. We apply the statistics to the analysis of the well known Feldstein-Horioka puzzle for a sample of sixteen OCDE countries. After we allow for a structural break in the cointegration regression, we find strong evidence of cointegration between saving and investment rates.Panel data, Panel cointegration tests, Structural breaks, Feldstein-Horioka puzzle

Long-run Validity of Export-Led Growth: An Empirical Reinvestigation from Linear and Nonlinear Cointegration Test

This study is able to uncover long-run cointegration relationship for Singapore and South Korea, based on the Breitung (2001) rank test procedures. Breitung (2001) rank test can detect both linear and nonlinear cointegration relationships, added value to the literature with strong evidences of nonlinear cointegration on GDP growth and export.Export-led growth; Cointegration; Johansen; Nonlinear; Rank Tests