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Journal articles on the topic 'Cointegration models'

Author: Grafiati

Published: 28 May 2022

Last updated: 18 July 2025

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1

Aue, Alexander, Lajos Horváth, Clifford Hurvich, and Philippe Soulier. "LIMIT LAWS IN TRANSACTION-LEVEL ASSET PRICE MODELS." Econometric Theory 30, no. 3 (2013): 536–79. http://dx.doi.org/10.1017/s0266466613000406.

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We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such effects as intraday seasonal patterns in volatility and nontrading periods that may be different for the two assets. We also allow for asymmetries (leverage effects). We obtain the asymptotic distribution of the log-price process. For the weak fractional cointegration case, we obtain the asymptotic distribution of the ordinary least squares estimator of the cointegrating parameter based on data sampled from an equally spaced discretization of calendar time, and we justify a feasible method of hypothesis testing for the cointegrating parameter based on the correspondingt-statistic. In the strong fractional cointegration case, we obtain the limiting distribution of a continuously averaged tapered estimator as well as other estimators of the cointegrating parameter, and we find that the rate of convergence can be affected by properties of intertrade durations. In particular, the persistence of durations (hence of volatility) can affect the degree of cointegration. We also obtain the rate of convergence of several estimators of the cointegrating parameter in the standard cointegration case. Finally, we consider the properties of the ordinary least squares estimator of the regression parameter in a spurious regression, i.e., in the absence of cointegration.

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2

Hwan Seo, Myung. "ESTIMATION OF NONLINEAR ERROR CORRECTION MODELS." Econometric Theory 27, no. 2 (2010): 201–34. http://dx.doi.org/10.1017/s026646661000023x.

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Asymptotic theory for the estimation of nonlinear vector error correction models that exhibit regime-specific short-run dynamics is developed. In particular, regimes are determined by the error correction term, and the transition between regimes is allowed to be discontinuous, as in, e.g., threshold cointegration. Several nonregular problems are resolved. First of all, consistency—square rootnconsistency for the cointegrating vectorβ—is established for the least squares estimation of this general class of models. Second, the convergence rates are obtained for the least squares of threshold cointegration, which aren3/2andnforβandγ, respectively, whereγdenotes the threshold parameter. This fast rate forβin itself is of practical relevance because, unlike in smooth transition models, the estimation error inβdoes not affect the estimation of short-run parameters. We also derive asymptotic distributions for the smoothed least squares estimation of threshold cointegration.

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3

Olaniran, Saidat Fehintola, Oyebayo Ridwan Olaniran, Jeza Allohibi, and Abdulmajeed Atiah Alharbi. "A Novel Approach for Testing Fractional Cointegration in Panel Data Models with Fixed Effects." Fractal and Fractional 8, no. 9 (2024): 527. http://dx.doi.org/10.3390/fractalfract8090527.

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Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series was fairly robust to a moderate degree of heterogeneity across sections of the six tests considered. Therefore, this paper advances a customized version of the Chen and Hurvich methodology to detect cointegrating connections in panels with unobserved fixed effects. Specifically, we develop a test statistic that accommodates variation in the long-term cointegrating vectors and fractional cointegration parameters across observational units. The behavior of our proposed test is examined through extensive Monte Carlo experiments under various data-generating processes and circumstances. The findings reveal that our modified test performs quite well comparatively and can successfully identify fractional cointegrating relationships in panels, even in the presence of idiosyncratic disturbances unique to each cross-sectional unit. Furthermore, the proposed modified test procedure established the presence of long-run equilibrium between the exchange rate and labor wage of 36 countries’ agricultural markets.

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4

Black, Angela J., David G. McMillan, and Fiona J. McMillan. "Cointegration between stock prices, dividends, output and consumption." Review of Accounting and Finance 14, no. 1 (2015): 81–103. http://dx.doi.org/10.1108/raf-09-2013-0103.

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Purpose – This paper aims to empirically test for multiple cointegrating vectors in a holistic manner. Theoretical developments imply bivariate cointegration among stock prices, dividends, output and consumption where independent models identify key theoretical cointegration vectors. Design/methodology/approach – This paper considers both Johansen and Horvath–Watson testing approaches for cointegration. This paper also examines the forecasting power of these cointegrating relationships against alternate forecast variables. Findings – The results suggest evidence of a long-run cointegrating relationship between stock prices, dividends, output and consumption, although not necessarily linked by a single common stochastic trend; each series responds to disequilibrium with greater evidence of a reaction from dividends and consumption – of note, output responds to changes in stock market equilibrium; and there is forecast power from the joint stock market–macro cointegrating vector for stocks returns and consumption growth over the historical average. Of particular note, other forecast models that include consumption perform well and suggest a key role for this variable in stock return and consumption growth forecasts. Originality/value – This is the first paper to combine the cointegrating relationships between stocks, dividends, output and consumption. Thus, the empirical validity of stated theoretical hypotheses can be analysed. The forecast results also demonstrate the usefulness of this. They also show that forecast models that include consumption perform well and suggest a key role for this variable in stock return and consumption growth forecasts.

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5

Xiao, Zhijie. "Functional-coefficient cointegration models." Journal of Econometrics 152, no. 2 (2009): 81–92. http://dx.doi.org/10.1016/j.jeconom.2009.01.008.

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6

Jumah, Adusei, and Robert M. Kunst. "Prediction of Consumption and Income in National Accounts: Simulation-Based Forecast Model Selection." Engineering Proceedings 5, no. 1 (2021): 55. http://dx.doi.org/10.3390/engproc2021005055.

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Simulation-based forecast model selection considers two candidate forecast model classes, simulates from both models fitted to data, applies both forecast models to simulated structures, and evaluates the relative benefit of each candidate prediction tool. This approach, for example, determines a sample size beyond which a candidate predicts best. In an application, aggregate household consumption and disposable income provide an example for error correction. With panel data for European countries, we explore whether and to what degree the cointegration properties benefit forecasting. It evolves that statistical evidence on cointegration is not equivalent to better forecasting properties by the implied cointegrating structure.

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7

Elliott, Graham, and Elena Pesavento. "TESTING THE NULL OF NO COINTEGRATION WHEN COVARIATES ARE KNOWN TO HAVE A UNIT ROOT." Econometric Theory 25, no. 6 (2009): 1829–50. http://dx.doi.org/10.1017/s026646660999034x.

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A number of tests have been suggested for the test of the null of no cointegration. Under this null, correlations are spurious in the sense of Granger and Newbold (1974) and Phillips (1986). We examine a set of models local to the null of no cointegration and derive tests with optimality properties in order to examine the efficiency of available tests. We find that, for a sufficiently tight weighting over potential cointegrating vectors, commonly employed full system tests have power that can, in some situations, be quite far from the power bounds for the models examined.

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8

Biondini, Riccardo, Yan-Xia Lin, and Michael Mccrae. "A case study of the residual-based cointegration procedure." Journal of Applied Mathematics and Decision Sciences 7, no. 1 (2003): 29–48. http://dx.doi.org/10.1155/s1173912603000038.

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The study of long-run equilibrium processes is a significant component of economic and finance theory. The Johansen technique for identifying the existence of such long-run stationary equilibrium conditions among financial time series allows the identification of all potential linearly independent cointegrating vectors within a given system of eligible financial time series. The practical application of the technique may be restricted, however, by the pre-condition that the underlying data generating process fits a finite-order vector autoregression (VAR) model with white noise. This paper studies an alternative method for determining cointegrating relationships without such a pre-condition. The method is simple to implement through commonly available statistical packages. This ‘residual-based cointegration’ (RBC) technique uses the relationship between cointegration and univariate Box-Jenkins ARIMA models to identify cointegrating vectors through the rank of the covariance matrix of the residual processes which result from the fitting of univariate ARIMA models. The RBC approach for identifying multivariate cointegrating vectors is explained and then demonstrated through simulated examples. The RBC and Johansen techniques are then both implemented using several real-life financial time series.

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9

Skrobotov, A. A. "Structural breaks in cointegration models." Applied Econometrics 63 (2021): 117–41. http://dx.doi.org/10.22394/1993-7601-2021-63-117-141.

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10

Deistler, Manfred, and Martin Wagner. "Cointegration in singular ARMA models." Economics Letters 155 (June 2017): 39–42. http://dx.doi.org/10.1016/j.econlet.2017.03.001.

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11

Lin, Yingqian, and Yundong Tu. "On transformed linear cointegration models." Economics Letters 198 (January 2021): 109686. http://dx.doi.org/10.1016/j.econlet.2020.109686.

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12

Skrobotov, Anton. "Structural breaks in cointegration models: Multivariate case." Applied Econometrics 64, no. 4 (2021): 83–106. http://dx.doi.org/10.22394/1993-7601-2021-64-83-106.

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This review discusses methods of testing for a cointegration rank in a multivariate time series in the presence of structural breaks. The review covers both the methods with known and unknown break date. Multiple breaks are also considered. The issues of testing for cointegration with a possible change in the cointegration rank over time are discussed separately.

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13

Chang, Yoosoon, and Peter C. B. Phillips. "Time Series Regression with Mixtures of Integrated Processes." Econometric Theory 11, no. 5 (1995): 1033–94. http://dx.doi.org/10.1017/s0266466600009968.

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The paper develops a statistical theory for regressions with integrated regressors of unknown order and unknown cointegrating dimension. In practice, we are often unsure whether unit roots or cointegration is present in time series data, and we are also uncertain about the order of integration in some cases. This paper addresses issues of estimation and inference in cases of such uncertainty. Phillips (1995, Econometrica 63, 1023–1078) developed a theory for time series regressions with an unknown mixture of 1(0) and 1(1) variables and established that the method of fully modified ordinary least squares (FM-OLS) is applicable to models (including vector autoregressions) with some unit roots and unknown cointegrating rank. This paper extends these results to models that contain some I(0), I(1), and I(2) regressors. The theory and methods here are applicable to cointegrating regressions that include unknown numbers of I(0), I(1), and I(2) variables and an unknown degree of cointegration. Such models require a somewhat different approach than that of Phillips (1995). The paper proposes a residual-based fully modified ordinary least-squares (RBFMOLS) procedure, which employs residuals from a first-order autoregression of the first differences of the entire regressor set in the construction of the FMOLS estimator. The asymptotic theory for the RBFM-OLS estimator is developed and is shown to be normal for all the stationary coefficients and mixed normal for all the nonstationary coefficients. Under Gaussian assumptions, estimation of the cointegration space by RBFM-OLS is optimal even though the dimension of the space is unknown.

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14

Barigozzi, Matteo, Marco Lippi, and Matteo Luciani. "Cointegration and Error Correction Mechanisms for Singular Stochastic Vectors." Econometrics 8, no. 1 (2020): 3. http://dx.doi.org/10.3390/econometrics8010003.

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Large-dimensional dynamic factor models and dynamic stochastic general equilibrium models, both widely used in empirical macroeconomics, deal with singular stochastic vectors, i.e., vectors of dimension r which are driven by a q-dimensional white noise, with q < r . The present paper studies cointegration and error correction representations for an I ( 1 ) singular stochastic vector y t . It is easily seen that y t is necessarily cointegrated with cointegrating rank c ≥ r − q . Our contributions are: (i) we generalize Johansen’s proof of the Granger representation theorem to I ( 1 ) singular vectors under the assumption that y t has rational spectral density; (ii) using recent results on singular vectors by Anderson and Deistler, we prove that for generic values of the parameters the autoregressive representation of y t has a finite-degree polynomial. The relationship between the cointegration of the factors and the cointegration of the observable variables in a large-dimensional factor model is also discussed.

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15

Bhat, Fayaz Ahmad, Shazia Hussain, and Effat Yasmin. "How Does Taxation Affect the Economy in the Long-Run? A Study of Indian States through Panel ARDL Approach." Statistika: Statistics and Economy Journal 105, no. 2 (2025): 245–56. https://doi.org/10.54694/stat.2024.43.

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This study examines the long-term impact of taxation on economic prosperity across 20 major Indian states and union territories from 1993 to 2017. To estimate the long-term relationships, various panel autoregressive distributed lag (P-ARDL) models, including pooled mean group (PMG), mean group (MG), and dynamic fixed effect (DFE) models, are employed. Unit root tests reveal that the variables exhibit a mixed order of integration at the level and first difference. Panel cointegration tests confirm a high likelihood of a long-term cointegrating relationship among economic growth, direct taxes, indirect taxes, and social expenditure. The PMG results indicate a long-term relationship between economic growth and these variables, significant at the 5 percent level, with a cointegration rate of 1.03. In contrast, the MG and DFE estimations show cointegration rates of 1.09 and 1.07, respectively, also significant at the 5 percent level. The findings highlight a significant impact of taxation and social expenditure on economic growth in India.

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16

Muscatelli, Vito Antonio, and Stan Hurn. "COINTEGRATION AND DYNAMIC TIME SERIES MODELS." Journal of Economic Surveys 6, no. 1 (1992): 1–43. http://dx.doi.org/10.1111/j.1467-6419.1992.tb00142.x.

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17

da Silva, Afonso Gonçalves, and Peter M. Robinson. "FRACTIONAL COINTEGRATION IN STOCHASTIC VOLATILITY MODELS." Econometric Theory 24, no. 5 (2008): 1207–53. http://dx.doi.org/10.1017/s0266466608080481.

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Asset returns are frequently assumed to be determined by one or more common factors. We consider a bivariate factor model where the unobservable common factor and idiosyncratic errors are stationary and serially uncorrelated but have strong dependence in higher moments. Stochastic volatility models for the latent variables are employed, in view of their direct application to asset pricing models. Assuming that the underlying persistence is higher in the factor than in the errors, a fractional cointegrating relationship can be recovered by suitable transformation of the data. We propose a narrow band semiparametric estimate of the factor loadings, which is shown to be consistent with a rate of convergence, and its finite-sample properties are investigated in a Monte Carlo experiment.

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18

Löf, Mårten, and Johan Lyhagen. "Forecasting performance of seasonal cointegration models." International Journal of Forecasting 18, no. 1 (2002): 31–44. http://dx.doi.org/10.1016/s0169-2070(01)00105-4.

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19

Hassler, Uwe, and Jürgen Wolters. "Autoregressive distributed lag models and cointegration." Allgemeines Statistisches Archiv 90, no. 1 (2006): 59–74. http://dx.doi.org/10.1007/s10182-006-0221-5.

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20

Wagner, Martin. "Cointegration analysis with state space models." AStA Advances in Statistical Analysis 94, no. 3 (2010): 273–305. http://dx.doi.org/10.1007/s10182-010-0138-x.

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21

Fukuda, Kosei. "Cointegration Detection Using Dynamic Factor Models." Communications in Statistics - Simulation and Computation 37, no. 1 (2007): 143–53. http://dx.doi.org/10.1080/03610910701723997.

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22

Horvath, Michael T. K., and Mark W. Watson. "Testing for Cointegration When Some of the Cointegrating Vectors are Prespecified." Econometric Theory 11, no. 5 (1995): 984–1014. http://dx.doi.org/10.1017/s0266466600009944.

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Many economic models imply that ratios, simple differences, or “spreads” of variables are I(0). In these models, cointegrating vectors are composed of 1's, 0's, and —1's and contain no unknown parameters. In this paper, we develop tests for cointegration that can be applied when some of the cointegrating vectors are prespecified under the null or under the alternative hypotheses. These tests are constructed in a vector error correction model and are motivated as Wald tests from a Gaussian version of the model. When all of the cointegrating vectors are prespecified under the alternative, the tests correspond to the standard Wald tests for the inclusion of error correction terms in the VAR. Modifications of this basic test are developed when a subset of the cointegrating vectors contain unknown parameters. The asymptotic null distributions of the statistics are derived, critical values are determined, and the local power properties of the test are studied. Finally, the test is applied to data on foreign exchange future and spot prices to test the stability of the forward–spot premium.

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23

Johansen, Søren. "Cointegration and Adjustment in the CVAR(∞) Representation of Some Partially Observed CVAR(1) Models." Econometrics 7, no. 1 (2019): 2. http://dx.doi.org/10.3390/econometrics7010002.

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A multivariate CVAR(1) model for some observed variables and some unobserved variables is analysed using its infinite order CVAR representation of the observations. Cointegration and adjustment coefficients in the infinite order CVAR are found as functions of the parameters in the CVAR(1) model. Conditions for weak exogeneity for the cointegrating vectors in the approximating finite order CVAR are derived. The results are illustrated by two simple examples of relevance for modelling causal graphs.

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24

Olaniran, Saidat Fehintola, and Mohd Tahir Ismail. "A Comparative Analysis of Semiparametric Tests for Fractional Cointegration in Panel Data Models." Austrian Journal of Statistics 51, no. 4 (2022): 96–119. http://dx.doi.org/10.17713/ajs.v51i4.1170.

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Several authors have studied fractional cointegration in time series data, but little or no consideration has been extended to panel data settings. Therefore, in this paper, we compare the finite sample behaviour of existing fractional cointegration time-series test procedures in panel data settings. This comparison is performed to determine the best tests that can be adapted to fractional cointegration in panel data settings. Specifically, simulation studies and real-life data analysis were performed to study the changes in the empirical type I error rate and power of six semiparametric fractional cointegration tests in panel settings. The various results revealed the limitations of the tests in the nonstationary and low or high correlation of the residual errors conditions. Also, two of the test procedures were recommended for testing the null hypothesis of no fractional cointegration in both time series and panel data settings.

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25

Gregory, Allan W. "Testing for Cointegration in Linear Quadratic Models." Journal of Business & Economic Statistics 12, no. 3 (1994): 347. http://dx.doi.org/10.2307/1392091.

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26

Davidson, James. "THE COINTEGRATION PROPERTIES OF VECTOR AUTOREGRESSION MODELS." Journal of Time Series Analysis 12, no. 1 (2008): 41–62. http://dx.doi.org/10.1111/j.1467-9892.1991.tb00067.x.

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27

Gregory, Allan W. "Testing for Cointegration in Linear Quadratic Models." Journal of Business & Economic Statistics 12, no. 3 (1994): 347–60. http://dx.doi.org/10.1080/07350015.1994.10524550.

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28

Benth, Fred Espen, and Andre Süss. "Cointegration in continuous time for factor models." Mathematics and Financial Economics 13, no. 1 (2018): 87–114. http://dx.doi.org/10.1007/s11579-018-0221-8.

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29

John, Nimitha, and Balakrishna Narayana. "Cointegration models with non Gaussian GARCH innovations." METRON 76, no. 1 (2017): 83–98. http://dx.doi.org/10.1007/s40300-017-0133-z.

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30

Baillie, Richard T., and David D. Selover. "Cointegration and models of exchange rate determination." International Journal of Forecasting 3, no. 1 (1987): 43–51. http://dx.doi.org/10.1016/0169-2070(87)90077-x.

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31

Kleibergen, Frank, and Herman K. van Dijk. "Direct cointegration testing in error correction models." Journal of Econometrics 63, no. 1 (1994): 61–103. http://dx.doi.org/10.1016/0304-4076(93)01561-y.

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32

Cui, Kai, and Wenshan Cui. "Bayesian Markov Regime-Switching Models for Cointegration." Applied Mathematics 03, no. 12 (2012): 1892–97. http://dx.doi.org/10.4236/am.2012.312259.

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33

Campbell, John Y., and Robert J. Shiller. "Cointegration and Tests of Present Value Models." Journal of Political Economy 95, no. 5 (1987): 1062–88. http://dx.doi.org/10.1086/261502.

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34

Juhl, Ted, and Zhijie Xiao. "Testing for cointegration using partially linear models." Journal of Econometrics 124, no. 2 (2005): 363–94. http://dx.doi.org/10.1016/j.jeconom.2004.02.007.

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35

Phillips, Peter C. B., Degui Li, and Jiti Gao. "Estimating smooth structural change in cointegration models." Journal of Econometrics 196, no. 1 (2017): 180–95. http://dx.doi.org/10.1016/j.jeconom.2016.09.013.

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36

Galvão, Ana Beatriz C. "Multivariate Threshold Models: TVARs and TVECMs." Brazilian Review of Econometrics 23, no. 1 (2003): 143. http://dx.doi.org/10.12660/bre.v23n12003.2734.

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In this paper, I review recent developments on modelling macroeconomic variables with non-linear VARs. Specifically, the class of threshold VARs, including systems with threshold cointegration, is discussed. Techniques for specification, estimation, testing, computing impulse responses and forecasting are presented, including hints for practitioners. In addition, I analyze recent results on the evaluation of this class of models, providing guidance on the application of these models. Finally, a TVAR is applied to extract the information of the spread to predict recessions; and a TVECM is employed to test threshold cointegration in the context of the term structure of interest rates.

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37

Alizade, Arzu Rafik. "Johansen’s Cointegration Analysis of Some Factors of Economic Growth and Exports of Products from the Republic of Azerbaijan to Ukraine." PROBLEMS OF ECONOMY 2, no. 60 (2024): 5–20. http://dx.doi.org/10.32983/2222-0712-2024-2-5-20.

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In the present paper, a Johansen’s cointegration analysis is carried out considering the volume of exports from Azerbaijan to Ukraine, GDP per capita of Ukraine, the openness of the economy of Ukraine and the economically active population of Azerbaijan for the period 1996-2022, also a comparative analysis of the above indicators is carried out, the characteristics of joint short-term and long-term movements are determined. In the course of research the author used the methodology of modified gravitational modeling, the econometric methodology of time series analysis, including tests for checking stationarity, the extended Dickey-Fuller test, the Granger test for the detection of causality, determining the cointegration dependence using the Johansen’s test, a Vector Error Correction Model (VECM) has been built. First, a basic modified model of gravity has been built, and the statistical adequacy of this model has been checked. A comparative analysis of two regression models was carried out after the inclusion of the trend component in one of them. The dynamic structure of regression residuals was studied and the test for heteroscedasticity and autocorrelation was carried out. It is shown that the most suitable specification for cointegration is the quadratic trend in the initial levels with a linear trend in cointegration relationships, which has led to the emergence of two cointegration vectors. As a result of the completed analysis, two cointegration relationships are obtained. The results of the impulse response functions, decomposition of dispersions and the VECM model in the form of combinations of two cointegrating vectors with the expected signs of the adjustment integers showed that the economic indicators used in the analysis for the specified period maintain cointegration in the long term with the not stable equilibrium joint movements of the factors under study.

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38

Lupekesa, Chipasha Salome Bwalya, Johannes Tshepiso Tsoku, and Lebotsa Daniel Metsileng. "Econometric Modelling of Financial Time Series." International Journal of Management, Entrepreneurship, Social Science and Humanities 5, no. 2 (2022): 52–70. http://dx.doi.org/10.31098/ijmesh.v5i2.622.

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This paper examines the relationship between assets, capital, liabilities and liquidity in South Africa using the Johansen cointegration analysis and the GARCH model using times data for the period 02/2005 to 06/2018. The results obtained from the study suggests that the time series are integrated of order one, I(1). The findings from the Johansen cointegration test indicated that the variables have a long run cointegrating relationship. Furthermore, the results from the GARCH model revealed that the estimated model has statistically significant coefficients at 5% significance level. Additionally, results revealed that assets have a positive relationship with capital, liabilities and liquidity. This implies that a percentage increase in assets will result to a percentage increase in capital, liabilities and liquidity. The results also revealed that shocks decay quickly in the future and that the conditional variance is explosive. The diagnostic tests revealed that the estimated models show the characteristics of a well specified model. The recommendations for future studies were formulated. Keywords: ARCH model; Cointegration; Financial time series; GARCH model; VECM; Volatility

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39

Kębłowski, Piotr. "Monte Carlo comparison of LCCA- and ML-based cointegration tests for panel var process with cross-sectional cointegrating vectors." Przegląd Statystyczny 65, no. 2 (2019): 173–82. http://dx.doi.org/10.5604/01.3001.0014.0533.

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Small-sample properties of bootstrap cointegration rank tests for unrestricted panel VAR process are considered when long-run cross-sectional dependencies occur. It is shown that the bootstrap cointegration rank tests for the panel VAR model based on levels canonical correlation analysis are oversized, whereas the bootstrap cointegration rank tests based on maximum likelihood framework are undersized. Moreover, the former tests are in general outperformed by the latter in terms of performance. The results of the investigation indicate that the ML-based bootstrap cointegration rank tests perform well in small samples for small-sized panel VAR models with a few cross-sections.

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40

Barigozzi, Matteo, Marco Lippi, and Matteo Luciani. "Dynamic Factor Models, Cointegration, and Error Correction Mechanisms." Finance and Economics Discussion Series 2016, no. 018 (2016): 1–28. http://dx.doi.org/10.17016/feds.2016.018.

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41

Cai, Biqing, Jiti Gao, and Dag Tjøstheim. "A New Class of Bivariate Threshold Cointegration Models." Journal of Business & Economic Statistics 35, no. 2 (2017): 288–305. http://dx.doi.org/10.1080/07350015.2015.1062385.

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42

Larsson, Rolf, and Johan Lyhagen. "Inference in Panel Cointegration Models With Long Panels." Journal of Business & Economic Statistics 25, no. 4 (2007): 473–83. http://dx.doi.org/10.1198/073500106000000549.

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43

Caporale, Guglielmo Maria, and Luis A. Gil-Alana. "Fractional cointegration and tests of present value models." Review of Financial Economics 13, no. 3 (2004): 245–58. http://dx.doi.org/10.1016/j.rfe.2003.09.009.

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44

Seong, Byeongchan. "Extended complex error correction models for seasonal cointegration." Journal of the Korean Statistical Society 38, no. 2 (2009): 191–98. http://dx.doi.org/10.1016/j.jkss.2008.09.003.

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45

Yang, Minxian, and Ronald Bewley. "On cointegration tests for VAR models with drift." Economics Letters 51, no. 1 (1996): 45–50. http://dx.doi.org/10.1016/0165-1765(95)00783-0.

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46

Jarner, Søren F., and Snorre Jallbjørn. "Pitfalls and merits of cointegration-based mortality models." Insurance: Mathematics and Economics 90 (January 2020): 80–93. http://dx.doi.org/10.1016/j.insmatheco.2019.10.005.

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47

Durr, Robert H. "An Essay on Cointegration and Error Correction Models." Political Analysis 4 (1992): 185–228. http://dx.doi.org/10.1093/pan/4.1.185.

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Abstract:

For political scientists who engage in longitudinal analyses, the question of how best to deal with nonstationary time-series is anything but settled. While many believe that little is lost when the focus of empirical models shifts from the nonstationary levels to the stationary changes of a series, others argue that such an approach erases any evidence of a long-term relationship among the variables of interest. But the pitfalls of working directly with integrated series are well known, and post-hoc corrections for serially correlated errors often seem inadequate. Compounding (or perhaps alleviating, if one believes in the power of selective perception) the difficult question of whether to difference a time-series is the fact that analysts have been forced to rely on subjective diagnoses of the stationarity of their data. Thus, even if one felt strongly about the superiority of one modeling approach over another, the procedure for determining whether that approach is even applicable can be frustrating.

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Hunt, Gary L. "Population-Employment Models: Stationarity, Cointegration, and Dynamic Adjustment." Journal of Regional Science 46, no. 2 (2006): 205–44. http://dx.doi.org/10.1111/j.0022-4146.2006.00439.x.

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49

Lin, Yingqian, and Yundong Tu. "Functional coefficient cointegration models with Box–Cox transformation." Economics Letters 234 (January 2024): 111472. http://dx.doi.org/10.1016/j.econlet.2023.111472.

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de Boef, Suzanna, and Jim Granato. "Testing for Cointegrating Relationships with Near-Integrated Data." Political Analysis 8, no. 1 (1999): 99–117. http://dx.doi.org/10.1093/oxfordjournals.pan.a029807.

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Abstract:

Testing theories about political change requires analysts to make assumptions about the memory of their time series. Applied analyses are often based on inferences that time series are integrated and cointegrated. Typically analyses rest on Dickey—Fuller pretests for unit roots and a test for cointegration based on the Engle—Granger two-step method. We argue that this approach is not a good one and use Monte Carlo analysis to show that these tests can lead analysts to conclude falsely that the data are cointegrated (or nearly cointegrated) when the data are near-integrated and not cointegrating. Further, analysts are likely to conclude falsely that the relationship is not cointegrated when it is. We show how inferences are highly sensitive to sample size and the signal-to-noise ratio in the data. We suggest three things. First, analysts should use the single equation error correction test for cointegrating relationships; second, caution is in order in all cases where near-integration is a reasonable alternative to unit roots; and third, analysts should drop the language of cointegration in many cases and adopt single-equation error correction models when the theory of error correction is relevant.

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