Abstract
Testing for cointegration in the presence of nonlinear adjustments or structural breaks is important for examining the equilibrium relationship among economic variables. It is known that standard cointegration tests perform poorly when a cointegration relationship has nonlinear adjustments or structural breaks. However, it is not clear how some cointegration tests allowing for nonlinearity perform under other classes of nonlinear cointegration models. This paper investigates which cointegration tests help detect a cointegration relationship with nonlinear adjustments or structural breaks. Our Monte Carlo simulation results demonstrate that the cointegration test with threshold adjustment generally has better power performance under most cointegration relationships with nonlinearity. We also provide empirical applications to the money demand and term structure of the U.S. interest rates. The empirical results show that the test allowing for threshold adjustment provides strong evidence of the cointegration relationships of money demand and the term structure of interest rates.
Similar content being viewed by others
References
Balke NS, Fomby T (1997) Threshold cointegration. Int Econ Rev 38: 627–643
Bec F, Rahbek A, Shephard N (2008) The ACR Model: a multivariate dynamic mixture autoregression. Oxf Bull Econ Stat 70: 583–618
Cheung YW, Lai KS (1993) A fractional cointegration analysis of purchasing power parity. J Bus Econ Stat 11: 103–112
Choi CY, Moh YK (2007) How useful are tests for unit-root in distinguishing unit-root processes from stationary but nonlinear processes. Econom J 10: 82–112
Choi I, Saikkonen P (2004) Testing linearity in cointegrating smooth transition regressions. Econom J 7: 341–365
Clements MP, Galvãro AB (2003) Testing the expectations theory of the term structure of interest rates in threshold models. Macroecon Dyn 7: 567–585
Diebold FX, Inoue A (2001) Long memory and regime switching. J Econom 105: 131–159
Dittmann I (2000) Residual-based tests for fractional cointegration: a Monte Carlo study. J Time Ser Anal 21: 615–647
Enders W, Siklos PL (2001) Cointegration and threshold adjustment. J Bus Econ Stat 19: 166–176
Engle RR, Granger CWJ (1987) Cointegration and error correction: representation, estimation and testing. Econometrica 55: 251–276
Gabriel VJ, Psaradakis Z, Sola M (2002) A simple method of testing for cointegration subject to multiple regime changes. Econ Lett 76: 213–221
Gil-Alana LA (2003) Testing of fractional cointegration in macroeconomic time series. Oxf Bull Econ Stat 65: 517–529
Gregory AW, Hansen BE (1996) Residual-based tests for cointegration in models with regime shifts. J Econom 70: 99–126
Gregory AW, Nason JM, Watt DG (1996) Testing for structural breaks in cointegration relationships. J Econom 71: 321–341
Hall SP, Psaradakis Z, Sola M (1997) Cointegration and changes in regime: the Japanese consumption function. J Appl Econom 12: 151–168
Hansen PR (2003) Structural changes in the cointegrated vector autoregressive model. J Econom 114: 261–295
Hatemi-J A (2008) Tests for cointegration with two unknown regime shifts with an application to financial market integration. Empir Econ 35: 497–505
Hristova D (2005) Maximum likelihood estimation of a unit root bilinear model with an application to prices. Stud Nonlinear Dyn Econom 9(1): 56–68
Hualde J, Robinson PM (2003) Cointegration in fractional systems with unknown integration orders. Econometrica 71: 1727–1766
Inoue A (1999) Tests of cointegrating rank with a trend break. J Econom 90: 215–237
Johansen S (2008) A representation theory for a class of vector autoregressive models for fractional processes. Econom Theory 24: 651–676
Johansen S (2010) An extension of cointegration to fractional autoregressive processes. Discussion paper 10-28. University of Copenhagen, Department of Economics
Kapetanios G, Shin Y, Snell A (2006) Testing for cointegration in nonlinear smooth transition error correction models. Econom Theory 22: 279–303
Kiliç R (2011) Testing for co-integration and nonlinear adjustment in a smooth transition error correction model. J Time Ser Anal 32: 647–660
Kristensena D, Rahbekb A (2011) Likelihood-based inference for cointegration with nonlinear error-correction. J Econom 158: 78–94
Lardic S, Mignon V (2004) Fractional cointegration and the term structure. Empir Econ 29: 723–736
Lee CC, Chen PF, Chang CP (2007) Testing linearity in a cointegrating STR model for the money demand function: international evidence from G-7 countries. Math Comput Simul 76: 293–302
Lo MC, Zivot E (2001) Threshold cointegration and nonlinear adjustment to the low of one price. Macroecon Dyn 5: 533–576
Lütkepohl H, Saikkonen P, Trenkler C (2004) Testing for the cointegrating rank of a VAR processes with level shift at unknown time. Econometrica 72: 647–662
Maki D (2006) Nonlinear adjustment in the term structure of interest rates: a cointegration analysis in the nonlinear STAR framework. Appl Financ Econ 16: 1301–1307
Maki D (2010) An alternative procedure to test for cointegration in STAR models. Math Comput Simul 80: 999–1006
Maki D, Kitasaka S (2006) The equilibrium relationship among money, income, prices, and interest rates: evidence from a threshold cointegration test. Appl Econ 38: 1585–1592
Mcmillan DG (2009) Non-linear interest rate dynamics and forecasting: evidence for US and Australian interest rates. Int J Econ Finance 14: 139–155
Peel D, Davidson J (1998) A non-linear error correction mechanism based on the bilinear model. Econ Lett 58: 165–170
Psaradakis Z, Sola M, Spagnolo F (2004) On Markov error-correction models, with an application to stock prices and dividends. J Appl Econom 19: 69–88
Robinson PM, Marinucci D (2003) Semiparametric frequency domain analysis of fractional cointegration. In: Robinson PM (eds) Time series with long memory. Oxford University Press, Oxford, pp 334–373
Robinson PM, Yajima Y (2002) Determination of cointegration rank in fractional systems. J Econom 106: 217–241
Saikkonen P, Lütkepohl H (2000) Testing for the cointegrating rank of a VAR process with structural shifts. J Bus Econ Stat 18: 451–464
Sarno L (1999) Adjustment costs and nonlinear dynamics in the demand for money: Italy, 1861–1991. Int J Econ Finance 4: 155–177
Sarno L, Taylor MP, Peel DA (2003) Nonlinear equilibrium correction in U.S. real money balances, 1869–1997. J Money Credit Bank 35: 787–797
Seo B (1998) Tests for structural change in cointegrated systems regressions. Econom Theory 14: 222–259
Seo M (2006) Bootstrap testing for the null of no cointegration in a threshold vector error correction model. J Econom 134: 129–150
Seo B, Hansen B (2002) Testing for two-regime threshold cointegration in vector error correction models. J Econom 110: 293–318
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Maki, D. Detecting cointegration relationships under nonlinear models: Monte Carlo analysis and some applications. Empir Econ 45, 605–625 (2013). https://doi.org/10.1007/s00181-012-0605-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00181-012-0605-1