Complex Systems in Finance and Econometrics

2011 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Econometrics: Non-linear Cointegration

  • Juan-Carlos Escanciano
  • Alvaro Escribano
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-7701-4_11

Article Outline

Glossary

Definition of the Subject

Introduction

Linear Measures of Memory and Linear Error Correction Models

Nonlinear Error Correction (NEC) Models

Nonlinear Cointegration

Future Directions

Bibliography

Keywords

Ordinary Little Square Cointegration Test Money Demand Error Correction Model Error Correction Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Bibliography

Primary Literature

  1. 1.
    Aparicio F, Escribano A (1999) Information‐theoretic analysis of serial correlation and cointegration. Stud Nonlinear Dyn Econ 3:119–140CrossRefGoogle Scholar
  2. 2.
    Aparicio F, Escribano A, Sipols AE (2006) Range unit root (RUR) tests: Robust against nonlinearities, error distributions, structural breaks and outliers. J Time Ser Anal 27:545–576CrossRefGoogle Scholar
  3. 3.
    Bae Y, de Jong RM (2005) Money demand function estimation by nonlinear cointegration. Working Paper, Department of Economics, Ohio State UniversityGoogle Scholar
  4. 4.
    Bandi FM (2004) On persistente and nonparametric estimation (with an application to stock return predictability). Unpublished manuscriptGoogle Scholar
  5. 5.
    Balke NS, Fomby TB (1997) Threshold cointegration. Int Econ Rev 38:627–645CrossRefGoogle Scholar
  6. 6.
    Bec F, Rahbek A (2004) Vector equilibrium correction models with nonlinear discontinuous adjustments. Econ J 7:628–651Google Scholar
  7. 7.
    Boswijk HP (1995) Efficient inference on cointegration parameters in structural error correction models. J Econ 69:113–158Google Scholar
  8. 8.
    Breitung J (2001) Rank tests for nonlinear cointegration. J Bus Econ Stat 19:331–340CrossRefGoogle Scholar
  9. 9.
    Breitung J, Goriéroux C (1997) Rank tests for unit roots. J Econ 81:7–27Google Scholar
  10. 10.
    Breitung J, Wulff C (2001) Nonlinear error correction and the efficient market hypothesis: The case of german dual-class shares. Ger Econ Rev 2:419–434CrossRefGoogle Scholar
  11. 11.
    Burgess SM (1992) Nonlinear dynamics in a structural model of employment. J Appl Econ 7:101–118CrossRefGoogle Scholar
  12. 12.
    Chang Y, Park JY (2003) Index models with integrated time series. J Econ 114:73–16Google Scholar
  13. 13.
    Chang Y, Park JY, Phillips PCB (2001) Nonlinear econometric models with cointegrated and deterministically trending regressors. Econ J 4:1–36Google Scholar
  14. 14.
    Choi I, Saikkonen P (2004) Testing linearity in cointegrating smooth transition regressions. Econ J 7:341–365Google Scholar
  15. 15.
    Choi I, Saikkonen P (2005) Tests for nonlinear cointegration. Unpublished manuscriptGoogle Scholar
  16. 16.
    Davidson J (1994) Stochastic limit theory. Oxford U. P., New YorkGoogle Scholar
  17. 17.
    de Jong RM (2001) Nonlinear estimation using estimated cointegrating relations. J Econ 101:109–122Google Scholar
  18. 18.
    de Jong RM (2002) Nonlinear minimization estimators in the presence of cointegrating relations. J Econ 110:241–259Google Scholar
  19. 19.
    Dufrénot G, Mignon V (2002) Recent developments in nonlinear cointegration with applications to macroeconomics and finance. Kluwer, BostonGoogle Scholar
  20. 20.
    Engle RF, Granger CWJ (1987) Co‐integration and error correction: Representation, estimation, and testing. Econetrica 55:251–276CrossRefGoogle Scholar
  21. 21.
    Engle RF, Granger CWJ, Rice J, Weiss A (1986) Semiparametric estimates of the relationship between weather and electricity sales. J Am Stat Assoc 81:310–320CrossRefGoogle Scholar
  22. 22.
    Ericsson NR, Hendry DF, Prestwich KM (1998) The demand for broad money in the United Kingdom, 1878–1993. Scand J Econ 100:289–324CrossRefGoogle Scholar
  23. 23.
    Escanciano JC, Hualde J (2005) Persistence and long memory in nonlinear time series. Unpublished manuscriptGoogle Scholar
  24. 24.
    Escanciano JC, Velasco C (2006) Testing the martingale difference hypothesis using integrated regression functions. Comput Stat Data Anal 51:2278–2294CrossRefGoogle Scholar
  25. 25.
    Escribano A (1986) Non‐Linear error‐correction: The case of money demand in the UK (1878–1970), ch IV. Ph.D. Dissertation, University of California, San DiegoGoogle Scholar
  26. 26.
    Escribano A (1987) Error‐Correction systems: Nonlinear adjustment to linear long-run relationships. Core Discussion Paper 8730, C.O.R.EGoogle Scholar
  27. 27.
    Escribano A (2004) Nonlinear error correction: The case of money demand in the UK (1878–2000). Macroecon Dyn 8:76–116Google Scholar
  28. 28.
    Escribano A, Aparicio F (1999) Cointegration: Linearity, nonlinearity, outliers and structural breaks. In: Dahiya SB (ed) The current state of economic science. Spellbound Publications, pp 383–408Google Scholar
  29. 29.
    Escribano A, Granger CWJ (1998) Investigating the relationship between gold and silver prices. J Forecast 17:81–107CrossRefGoogle Scholar
  30. 30.
    Escribano A, Mira S (1997) Nonlinear error correction models. Working Paper 97-26. Universidad Carlos III de MadridGoogle Scholar
  31. 31.
    Escribano A, Mira S (2002) Nonlinear error correction models. J Time Ser Anal 23:509–522CrossRefGoogle Scholar
  32. 32.
    Escribano A, Mira S (2007) Specification of nonlinear error correction models: a simulation study. Mimeo, Universidad Carlos III de MadridGoogle Scholar
  33. 33.
    Escribano A, Pfann GA (1998) Non‐linear error correction, asymmetric adjustment and cointegration. Econ Model 15:197–216CrossRefGoogle Scholar
  34. 34.
    Escribano A, Sipols AE, Aparicio F (2006) Nonlinear cointegration and nonlinear error correction: Applications of tests based on first differences of ranges. Commun Stat Simul Comput 35:939–956CrossRefGoogle Scholar
  35. 35.
    Escribano A, Santos MT, Sipols AE (2008) Testing for cointegration using induced order statistics. Comput Stat 23:131–151Google Scholar
  36. 36.
    Fotopoulos SB J, Ahn SK (2001) Rank based Dickey‐Fuller tests statistics. J Time Ser Anal 24:647–662CrossRefGoogle Scholar
  37. 37.
    Friedman M, Schwartz A (1982) Monetary trends in the united sates and the United Kingdom: Their relation to income, prices, and interest rates, 1867–1975. University of Chicago Press, ChicagoGoogle Scholar
  38. 38.
    Gonzalo J (1994) Five alternative methods of estimating long run equilibrium relationships. J Econ 60:1–31Google Scholar
  39. 39.
    Gonzalo J, Pitarakis J-Y (2006) Threshold cointegrating relationships. Oxford Bull Econ Stat 68:813–833CrossRefGoogle Scholar
  40. 40.
    Gouriéroux C, Jasiak J (1999) Nonlinear persistence and copersistence. Unpublished manuscriptGoogle Scholar
  41. 41.
    Gouriéroux C, Jasiak J (2002) Nonlinear autocorrelograms: An application to inter-trade durations. J Time Ser Anal 23:127–154Google Scholar
  42. 42.
    Granger CWJ (1981) Some properties of time series data and their use in econometric model specification. J Econ 16:121–130Google Scholar
  43. 43.
    Granger CWJ (1986) Developments in the study of cointegrated variables. Oxford Bull Econ Stat 48:213–228CrossRefGoogle Scholar
  44. 44.
    Granger CWJ (1995) Modelling nonlinear relationships between extended‐memory variables. Econetrica 63:265–279CrossRefGoogle Scholar
  45. 45.
    Granger CWJ (2002) Long memory, volatility, risk and distribution. Unpublished manuscriptGoogle Scholar
  46. 46.
    Granger CWJ, Hallman J (1991) Long memory series with attractors. Oxford Bull Econ Stat 53:11–26CrossRefGoogle Scholar
  47. 47.
    Granger CWJ, Hallman J (1991) Nonlinear transformations of integrated time series. J Time Ser Anal 12:207–224CrossRefGoogle Scholar
  48. 48.
    Granger CWJ, Lee TH (1989) Investigation of production, sales and inventory relationships using multicointegration and non‐symmetric error correction models. J Appl Econ 4:145–159Google Scholar
  49. 49.
    Granger CWJ, Swanson N (1996) Further developments in the study of cointegrated variables. Oxford Bull Econ Stat 58:537–553CrossRefGoogle Scholar
  50. 50.
    Granger CWJ, Teräsvirta T (1993) Modelling nonlinear economic relationships. Oxford University Press, New YorkGoogle Scholar
  51. 51.
    Granger CWJ, Maasoumi E, Racine J (2004) A dependence metric for possibly nonlinear processes. J Time Ser Anal 25:649–669CrossRefGoogle Scholar
  52. 52.
    Hamilton JD (1994) Time series analysis. Princeton University Press, PrincetonGoogle Scholar
  53. 53.
    Hansen B, Phillips PCB (1990) Estimation and inference in models of cointegration: A simulation study. Adv Econ 8:225–248Google Scholar
  54. 54.
    Hansen B, Seo B (2002) Testing for two‐regime threshold cointegration in vector error correction models. J Econ 110:293–318Google Scholar
  55. 55.
    Härdle W (1990) Applied nonparametric regression. Econetric Society Monographs, vol 19. Cambridge University Press, CambridgeGoogle Scholar
  56. 56.
    Hargreaves CP (1994) Nonstationary time series analysis and cointegration. Oxford University Press, OxfordGoogle Scholar
  57. 57.
    Hargreaves CP (1994) A review of methods of estimating cointegrating relationships. In: Hargreaves CP (ed) Nonstationary time series analysis and cointegration. Oxford University Press, OxfordGoogle Scholar
  58. 58.
    Haug AA (2002) Testing linear restrictions on cointegrating vectors: Sizes and powers of wald and likelihood ratio tests in finite samples. Econ Theory 18:505–524CrossRefGoogle Scholar
  59. 59.
    Hendry DF (1995) Dynamic econometrics. Oxford University Press, OxfordCrossRefGoogle Scholar
  60. 60.
    Hendry DF, Ericsson N (1983) Assertion without empirical basis: An econometric appraisal of ‘monetary trends in the … the United Kingdom’ by Friedman M, Schwartz AJ. In: Monetary trends in the United Kingdom. Bank of England Panel of Academic Consultants, Paper 22, 45–101Google Scholar
  61. 61.
    Hendry DF, Ericsson NR (1991) An econometric analysis of the uk money demand in ‘monetary trends in the united states and the United Kingdom’ by Friedman M, Schwartz AJ. Am Econ Rev 81:8–38Google Scholar
  62. 62.
    Hendry DF, Massmann M (2007) Co‐breaking: Recent advances and a synopsis of the literature. J Bus Econ Stat 25:33–51Google Scholar
  63. 63.
    Inder B (1993) Estimating long-run relationships in economics: A comparison of different approaches. J Econ 57:53–68Google Scholar
  64. 64.
    Johansen S (1988) Statistical analysis of cointegration vectors. J Econ Dyn Control 12:231–54CrossRefGoogle Scholar
  65. 65.
    Johansen S (1991) Estimation and hypothesis testing of cointegration vectors, in gaussian vector autoregressive models. Econetrica 59:1551–1580CrossRefGoogle Scholar
  66. 66.
    Johansen S (1992) Cointegration in partial systems and the efficiency of single‐equation analysis. J Econ 52:389–402Google Scholar
  67. 67.
    Juselius K (2006) The cointegrated VAR model: Methodology and applications. Oxford University Press, OxfordGoogle Scholar
  68. 68.
    Jusmah A, Kunst RM (2008) Modelling macroeconomic sub‐aggregates: An application of non‐linear cointegration. Economics Series, Institute for Advanced Studies. Macroecon Dyn 12:151–171Google Scholar
  69. 69.
    Karlsen HA, Tjøstheim D (2001) Nonparametric estimation in null recurrent time series. Ann Stat 29:372–416Google Scholar
  70. 70.
    Karlsen HA, Myklebust T, Tjøstheim D (2007) Nonparametric estimation in a nonlinear cointegration type model. Ann Stat 35(1):252–299Google Scholar
  71. 71.
    Kitamura Y, Phillips PCB (1995) Efficient IV estimation in nonstationary regression: An overview and simulation study. Econ Theory 11:1095–1130CrossRefGoogle Scholar
  72. 72.
    Kunst RM (1992) Threshold cointegration in interest rates. Working Paper, Institute for Advanced Studies, ViennaGoogle Scholar
  73. 73.
    Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationarity against the alternative of a unit root. J Econ 54:159–178Google Scholar
  74. 74.
    Lo AW (1991) Long-term memory in stock market prices. Econometrica 59:1279–1313CrossRefGoogle Scholar
  75. 75.
    Lo M, Zivot E (2001) Threshold cointegration and nonlinear adjustment to the law of one price. Macroecon Dyn 5:533–576Google Scholar
  76. 76.
    Longbottom A, Holly S (1985) Econometric methodology and monetarism: Professor Friedman and Professor Hendry on the demand for money, Discussion Paper No. 131. London Business SchoolGoogle Scholar
  77. 77.
    Lütkephol H (2005) New introduction to multiple time series analysis. SpringerGoogle Scholar
  78. 78.
    Marmol F, Escribano A, Aparicio FM (2002) Instrumental variable interpretation of cointegration with inference results for fractional cointegration. Econ Theory 18:646–672CrossRefGoogle Scholar
  79. 79.
    Park JY (1992) Canonical cointegrating regressions. Econometrica 60:119–143CrossRefGoogle Scholar
  80. 80.
    Park JY, Phillips PCB (1988) Statistical inference in regressions with integrated process: Part 1. Econ Theory 4:468–498CrossRefGoogle Scholar
  81. 81.
    Park JY, Phillips PCB (1989) Statistical inference in regressions with integrated process: Part 2. Econ Theory 4:95–132CrossRefGoogle Scholar
  82. 82.
    Park JY, Phillips PCB (1989) Asymptotics for nonlinear transformations of integrated time series. Econ Theory 15:269–298Google Scholar
  83. 83.
    Park JY, Phillips PCB (2000) Nonstationary binary choice. Econometrica 68:1249–1280CrossRefGoogle Scholar
  84. 84.
    Park JY, Phillips PCB (2001) Nonlinear regressions with integrated time series. Econometrica 69:117–161CrossRefGoogle Scholar
  85. 85.
    Phillips PCB (1991) Optimal inference in cointegrated systems. Econometrica 59:283–306CrossRefGoogle Scholar
  86. 86.
    Phillips PCB, Hansen BE (1990) Statistical inference in instrumental variable regression with I(1) processes. Rev Econ Stud 57:99–125CrossRefGoogle Scholar
  87. 87.
    Phillips PCB, Loretan M (1991) Estimating long-run economic equilibria. Rev Econ Stud 59:407–436Google Scholar
  88. 88.
    Phillips PCB, Park JY (1998) Nonstationary density estimation and kernel autoregression. Unpublished manuscriptGoogle Scholar
  89. 89.
    Robinson PM, Gerolimetto M (2006) Instrumental variables estimation of stationary and nonstationary cointegrating regressions. Econ J 9:291–306Google Scholar
  90. 90.
    Rothman P, van Dijk D, Franses PH (2001) A multivariate star analysis of the relationship between money and output. Macroecon Dyn 5:506–532Google Scholar
  91. 91.
    Saikkonen P (1991) Asymptotically efficient estimation of cointegration regressions. Econ Theory 7:1–21CrossRefGoogle Scholar
  92. 92.
    Saikkonen P (2005) Stability results for nonlinear error correction models. J Econ 127:69–81Google Scholar
  93. 93.
    Saikkonen P, Choi I (2004) Cointegrating smooth transition regressions. Econ Theory 20:301–340CrossRefGoogle Scholar
  94. 94.
    Seo MH (2006) Bootstrap testing for the null of no cointegration in a threshold vector error correction model. J Econ 134:129–150Google Scholar
  95. 95.
    Seo MH (2007) Estimation of nonlinear error correction models. Unpublished manuscriptGoogle Scholar
  96. 96.
    Silverman BW (1985) Some aspects of the spline smoothing approach to nonparametric regression curve fitting. J Roy Stat Soc Ser B 47:1–52Google Scholar
  97. 97.
    Sims CA (1972) Money, income, and causality. Am Econ Rev 62:540–552Google Scholar
  98. 98.
    Stock JH (1987) Asymptotic properties of least squares estimation of cointegrating vectors. Econometrica 55:1035–1056CrossRefGoogle Scholar
  99. 99.
    Stock JH (1994) Deciding between I(1) and I(0). J Econ 63:105–131Google Scholar
  100. 100.
    Stock JH, Watson MW (1993) A simple estimator of cointegration vectors in higher order integrated systems. Econometrica 61:783–820CrossRefGoogle Scholar
  101. 101.
    Teräsvirta T (1998) Modelling economic relationships with smooth transition regressions. In: Ullah A, Giles DEA (eds) Handbook of applied economic statistics. Marcel Dekker, New York, pp 507–552Google Scholar
  102. 102.
    Teräsvirta T, Eliasson AC (2001) Non‐linear error correction and the uk demand for broad money, 1878–1993. J Appl Econ 16:277–288Google Scholar
  103. 103.
    Velasco C (2006) Semiparametric estimation of long‐memory models. In: Patterson K, Mills TC (eds) Palgrave handbook of econometrics, vol 1. Econometric Theory. MacMillan, Palgrave, pp 353–395Google Scholar
  104. 104.
    Wahba G (1975) Smoothing noisy data with spline functions. Num Math 24:309-63–75CrossRefGoogle Scholar
  105. 105.
    Watson M (1994) Large sample estimation and hypothesis testing, vector autoregression and cointegration. In: Engle RF, McFadden DL (eds) Handbook of econometrics, vol IV. Elsevier Science, AmsterdamGoogle Scholar

Books and Reviews

  1. 106.
    Franses PH, Terasvirta T (eds)(2001) Special issue on nonlinear modeling of multivariate macroeconomic relations. Macroecon Dyn 5(4)Google Scholar
  2. 107.
    Banerjee A, Dolado JJ, Galbraith JW, Hendry DF (1993) Co‐integration, error correction and the econometric analysis of non‐stationary data. Oxford University Press, OxfordCrossRefGoogle Scholar
  3. 108.
    Bierens HJ (1981) Robust methods and asymptotic theory in nonlinear econometrics. Lecture Notes in Economics and Mathematical Systems, vol 192. Springer, BerlinGoogle Scholar
  4. 109.
    Clements MP, Hendry DF (1999) Forecasting non‐stationary economic time series. MIT Press, CambridgeGoogle Scholar
  5. 110.
    Dhrymes P (1998) Time series, unit roots, and cointegration. Academic Press, San DiegoGoogle Scholar
  6. 111.
    Enders W (1995) Applied econometric time series. WileyGoogle Scholar
  7. 112.
    Engle RF, Granger CWJ (eds) (1991) Long-run economic relationships: Readings in cointegration. Oxford University Press, OxfordGoogle Scholar
  8. 113.
    Franses PH, van Dijk D (2000) Nonlinear time series models in empirical finance. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  9. 114.
    Gonzalo J, Dolado JJ, Marmol F (2001) A primer in cointegration. In: Baltagui BH (ed) A companion to theoretical econometrics. Blackwell, New York, ch 30Google Scholar
  10. 115.
    Granger CWJ (2001) Overview of nonlinear macroeconometric empirical models. Macroecon Dyn 5:466–481Google Scholar
  11. 116.
    Granger CWJ (2007) Some thoughts on the past and future of cointegration. MimeoGoogle Scholar
  12. 117.
    Hatanaka M (1996) Time series‐based econometrics. Oxford University Press, OxfordCrossRefGoogle Scholar
  13. 118.
    Maddala GS, Kim I-M (1998) Unit roots, cointegration and structural change. Cambridge University Press, CambridgeGoogle Scholar
  14. 119.
    Phillips PCB (1986) Understanding spurious regressions in econometrics. J Econ 33:311–340Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Juan-Carlos Escanciano
    • 1
  • Alvaro Escribano
    • 2
  1. 1.Department of EconomicsIndiana UniversityBloomingtonUSA
  2. 2.Department of EconomicsUniversidad Carlos III de MadridMadridSpain