Cointegration Rank Research Articles

Fractional Cointegration Rank Estimation

We consider cointegration rank estimation for a p-dimensional Fractional Vector Error Correction Model. We propose a new two-step procedure which allows testing for further long-run equilibrium relations with possibly different persistence levels. The first step consists in estimating the parameters of the model under the null hypothesis of the cointegration rank r=1,2,…,p-1. This step provides consistent estimates of the order of fractional cointegration, the cointegration vectors, the speed of adjustment to the equilibrium parameters and the common trends. In the second step we carry out a sup-likelihood ratio test of no-cointegration on the estimated p-r common trends that are not cointegrated under the null. The order of fractional cointegration is re-estimated in the second step to allow for new cointegration relationships with different memory. We augment the error correction model in the second step to adapt to the representation of the common trends estimated in the first step. The critical values of the proposed tests depend only on the number of common trends under the null, p-r, and on the interval of the orders of fractional cointegration b allowed in the estimation, but not on the order of fractional cointegration of already identified relationships. Hence this reduces the set of simulations required to approximate the critical values, making this procedure convenient for practical purposes. In a Monte Carlo study we analyze the finite sample properties of our procedure and compare with alternative methods. We finally apply these methods to study the term structure of interest rates.

Empirical Analysis of Twins’ Deficits in Bangladesh

Bangladesh represents a valuable case study for investing the dynamics of steadily high rates of budget and trade deficits. In this study an attempt has been made to empirically test the validity of Twin deficits hypothesis for Bangladesh using annual time series data from 1972-73 to 2011-12 fiscal year. Applying the VAR and Granger Causality after successfully running ADF and PP unit root test and cointegration rank test this paper reveals that budget deficit Granger cause trade deficit and vice versa but the relationship does not stand for the long-run dynamics. In fact, the long run relationship depends on overall macroeconomics environment and performances of other relevant variables. Policy implication is that Government should reduce budget deficit to improve the trade account balance.

Robust Cointegration Testing in the Presence of Weak Trends, with an Application to the Human Origin of Global Warming

Standard tests for the rank of cointegration of a vector autoregressive process present distributions that are affected by the presence of deterministic trends. We consider the recent approach of Demetrescu, Lutkepohl and Saikkonen (2009) who recommend testing a composite null. We assess this methodology in the presence of trends (linear or broken) whose magnitude is small enough not to be always detectable at conventional significance levels. We model them using local asymptotics and derive the properties of the test statistics. We show that whether the trend is orthogonal to the cointegrating vector has a major impact on the distributions but that the test combination approach remains valid. We apply of the methodology to the study of cointegration properties between global temperatures and the radiative forcing of human gas emissions. We find new evidence of Granger Causality.

Bootstrap Determination of the Co-Integration Rank in Heteroskedastic VAR Models

In a recent paper Cavaliere et al. (2012) develop bootstrap implementations of the (pseudo-) likelihood ratio (PLR) co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying vector autoregressive (VAR) model which obtain under the reduced rank null hypothesis. They propose methods based on an independent and individual distributed (i.i.d.) bootstrap resampling scheme and establish the validity of their proposed bootstrap procedures in the context of a co-integrated VAR model with i.i.d. innovations. In this paper we investigate the properties of their bootstrap procedures, together with analogous procedures based on a wild bootstrap resampling scheme, when time-varying behavior is present in either the conditional or unconditional variance of the innovations. We show that the bootstrap PLR tests are asymptotically correctly sized and, moreover, that the probability that the associated bootstrap sequential procedures select a rank smaller than the true rank converges to zero. This result is shown to hold for both the i.i.d. and wild bootstrap variants under conditional heteroskedasticity but only for the latter under unconditional heteroskedasticity. Monte Carlo evidence is reported which suggests that the bootstrap approach of Cavaliere et al. (2012) significantly improves upon the finite sample performance of corresponding procedures based on either the asymptotic PLR test or an alternative bootstrap method (where the short run dynamics in the VAR model are estimated unrestrictedly) for a variety of conditionally and unconditionally heteroskedastic innovation processes.

Bootstrap Determination of the Co-Integration Rank in Heteroskedastic VAR Models

In a recent paper Cavaliere et al. (2012) develop bootstrap implementations of the (pseudo-) likelihood ratio [PLR] co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying VAR model which obtain under the reduced rank null hypothesis. They propose methods based on an i.i.d. bootstrap re-sampling scheme and establish the validity of their proposed bootstrap procedures in the context of a co-integrated VAR model with i.i.d. innovations.In this paper we investigate the properties of their bootstrap procedures, together with analogous procedures based on a wild bootstrap re-sampling scheme, when time-varying behaviour is present in either the conditional or unconditional variance of the innovations. We show that the bootstrap PLR tests are asymptotically correctly sized and, moreover, that the probability that the associated bootstrap sequential procedures select a rank smaller than the true rank converges to zero. This result is shown to hold for both the i.i.d. and wild bootstrap variants under conditional heteroskedasticity but only for the latter under unconditional heteroskedasticity. Monte Carlo evidence is reported which suggests that the bootstrap approach of Cavaliere et al. (2012) significantly improves upon the nite sample performance of corresponding procedures based on either the asymptotic PLR test or an alternative bootstrap method (where the short run dynamics in the VAR model are estimated unrestrictedly) for a variety of conditionally and unconditionally heteroskedastic innovation processes.

The Long-run Causal Relationship Between Military Expenditure and Economic Growth in China: Revisited

This paper re-examines the long-run causal relationship between military expenditure and economic growth in China over the period 1952–2010. An empirical econometric analysis based on a Barro-style growth model is conducted. By employing the Bartlett corrected trace test, which provides better approximations of the finite sample distribution to determine the rank of cointegration, the results support the existence of a single long-run equilibrium relationship between the variables. Furthermore, it is confirmed that the cumulated shocks of military expenditure primarily originate from different components of shocks that relate to economic development rather than the other way round.

Wnioskowanie o rzędzie kointegracji dla modelu VEC ze składnikiem losowym z rozkładu SU Johnsona

Performance of small-sample cointegration rank tests is investigated within the framework of a VEC model with skewed fat-tailed error distribution. The Monte Carlo analysis is conducted for: asymptotic test, tests with degrees-of-freedom corrections, test with Bartlett correction, bootstrap test, and bootstrap test with Bartlett correction, as a surrogate of double bootstrap test. The results indicate that the smallsample cointegration rank tests are robust to skewed fat-tailed error distribution, approximated by SU Johnson distribution, with respect to size and power of these tests.

Właściwości wybranych metod małopróbkowego wnioskowania o rzędzie kointegracji

In the paper, properties of small sample cointegration rank tests are compared. The Monte Carlo experiments conducted for different data generating processes and areas in the parametric space indicate that (i) the likelihood ratio test with Bartlett correction usually have the best properties, (ii) bootstrapping the Bartlett corrected test does not lead to improvement of test properties, (iii) size of asymptotic test and tests with degrees-of-freedom correction is usually heavily distorted, (iv) the Bartlett correction can lead to a small improvement of power, (v) correlation of error terms between stationary and non-stationary component of canonical form lead to a signifi cant increase of power and size of test, but only size of Bartlett corrected test and bootstrapped test converge to nominal size.

The power of bootstrap tests of cointegration rank

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of asymptotic tests. The effect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymptotic test. The bootstrap test therefore estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.

Bootstrap Cointegration Rank Testing: The Role of Deterministic Variables and Initial Values in the Bootstrap Recursion

In this paper we investigate the role of deterministic components and initial values in bootstrap likelihood ratio type tests of cointegration rank. A number of bootstrap procedures have been proposed in the recent literature some of which include estimated deterministic components and nonzero initial values in the bootstrap recursion while others do the opposite. To date, however, there has not been a study into the relative performance of these two alternative approaches. In this paper we fill this gap in the literature and consider the impact of these choices on both ordinary least squares (OLS) and generalized least squares (GLS) detrended tests, in the case of the latter proposing a new bootstrap algorithm as part of our analysis. Overall, for OLS detrended tests our findings suggest that it is preferable to take the computationally simpler approach of not including estimated deterministic components in the bootstrap recursion and setting the initial values of the bootstrap recursion to zero. For GLS detrended tests, we find that the approach of Trenkler (2009), who includes a restricted estimate of the deterministic component in the bootstrap recursion, can improve finite sample behavior further.

Advantages of Non-Normality in Testing Cointegration Rank

Since the seminal work of Engle and Granger (1987) and Johansen (1988), testing for cointegration has become standard practice in analysing economic and - nancial time series data. Many of the techniques in cointegration analysis require the assumption of normality, which may not always hold. Although there is evidence that these techniques are robust to non-normality, most existing techniques do not seek additional information from non-normality. This is important in at least two cases. Firstly, the number of observations is typically small for macroeconomic time series data, the fact that the underlying distribution may not be normal provides important information that can potentially be useful in testing for cointegrating relationships. Secondly, high frequency nancial time series data often shows evidence of non-normal random variables with time-varying second moments and it is unclear how these char- acteristics aect the standard test of cointegration, such as Johansen's trace and max tests. This paper proposes a new framework derived from Independent Component Anal- ysis (ICA) to test for cointegration. The framework explicitly exploits processes with non-normal distributions and their independence. Monte Carlo simulation shows that the new test is comparable to the Johansen's trace and max tests when the number of observations is large and has a slight advantage over Johansen's tests if the number of observations is limited. Moreover, the computational requirement for this method is relatively mild, which makes this method practical for empirical research.

Optimal Pseudo-Gaussian and Rank-Based Tests of the Cointegrating Rank in Semiparametric Error-Correction Models

Optimal Pseudo-Gaussian and Rank-Based Tests of the Cointegrating Rank in Semiparametric Error-Correction Models

Cointegration: Bayesian Significance Test

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful and convincing results”. The present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used.

NUMERICAL DISTRIBUTION FUNCTIONS OF FRACTIONAL UNIT ROOT AND COINTEGRATION TESTS

SUMMARY We calculate, by simulations, numerical asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real-valued parameter b which must be estimated, simple tabulation is not feasible. Partly owing to the presence of this parameter, the choice of model specification for the response surface regressions used to obtain the numerical distribution functions is more involved than is usually the case. We deal with model uncertainty by model averaging rather than by model selection. We make available a computer program which, given the dimension of the problem, q, and a value of b, provides either a set of critical values or the asymptotic P-value for any value of the likelihood ratio statistic. Copyright © 2012 John Wiley & Sons, Ltd.

Is China compatible with ASEAN‐5? A gradual cointegration analysis

PurposeThe purpose of this paper to examine if there is continuous macroeconomic compatibility between ASEAN‐5 and China. Thus, in addition to the typical VECM test of the long run macroeconomic cointegration test, this paper examines the existence of an ongoing cointegration analysis.Design/methodology/approachThe degree of convergence during different sub‐sample period of the full sample is employed, via Johansen cointegration rank tests, to examine if there is evidence of ongoing and improved cointegrating relationship among the economies.FindingsA successful ASEAN‐China economic cooperation would only work if there is continuous macroeconomic interdependence between the partnership. Since a smooth transition of ACFTA will complement AFTA, the effective ASEAN‐China coordination plan is essential to endorse a successful ASEAN‐China coalition.Originality/valueThis paper suggests a quick yet effective verification on the continuous compatibility of economies intended to have a long‐term economic coordination.

A One-Step Test for the Presence of Multiple Cointegrating Vectors

Based on the Johansen's approach for cointegration tests, we offer critical values to test for the existence and rank of cointegration between first-order integrated variables. In this single-step procedure, the cointegrating rank is equal to the number of instances in which the test statistics are less than the respective proposed critical values.

Bootstrap Determination of the Co-Integration Rank in Vector Autoregressive Models

This paper discusses a consistent bootstrap implementation of the likelihood ratio (LR) co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying vector autoregressive (VAR) model that obtain under the reduced rank null hypothesis. A full asymptotic theory is provided that shows that, unlike the bootstrap procedure in Swensen (2006) where a combination of unrestricted and restricted estimates from the VAR model is used, the resulting bootstrap data are I(1) and satisfy the null co-integration rank, regardless of the true rank. This ensures that the bootstrap LR test is asymptotically correctly sized and that the probability that the bootstrap sequential procedure selects a rank smaller than the true rank converges to zero. Monte Carlo evidence suggests that our bootstrap procedures work very well in practice.

Improved Likelihood Ratio Tests for Cointegration Rank in the VAR Model

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but of course the asymptotic results apply more generally. The power gains relative to existing tests are due to two factors. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott, Rothenberg, and Stock (1996). Secondly, our tests incorporate a 'sign' restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.

Rank-Based Tests of the Cointegrating Rank in Semiparametric Error Correction Models

This paper introduces rank-based tests for the cointegrating rank in an Error CorrectionModel with i.i.d. elliptical innovations. The tests are asymptotically distribution-free,and their validity does not depend on the actual distribution of the innovations. Thisresult holds despite the fact that, depending on the alternatives considered, the model exhibitsa non-standard Locally Asymptotically Brownian Functional (LABF) and LocallyAsymptotically Mixed Normal (LAMN) local structure—a structure which we completelycharacterize. Our tests, which have the general form of Lagrange multiplier tests, dependon a reference density that can freely be chosen, and thus is not restricted to be Gaussianas in traditional quasi-likelihood procedures. Moreover, appropriate choices of the referencedensity are achieving the semiparametric efficiency bounds. Simulations show thatour asymptotic analysis provides an accurate approximation to finite-sample behavior.Our results are based on an extension, of independent interest, of two abstract resultson the convergence of statistical experiments and the asymptotic linearity of statistics tothe context of, possibly non-stationary, time series (This abstract was borrowed from another version of this item.)

Local-Explosive Approximations to Null Distributions of the Johansen Cointegration Test, with an Application to Cyclical Concordance in the Euro Area

This paper considers approximating the nite sample null-distribution of a test statistic as its asymptotic distribution under a local alternative. We focus on the Likelihood Ratio test for the rank of cointegration and use nonlinearities that represent some nite sample distributional features. Reliable approximations are obtained using a class of locally explosive models. An empirical evaluation of the concordance of European business cycles through cointegration shows that some standard corrections lead to underestimating the number of cointegrating relations and induce volatile results.