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Threshold Error Correction Model: A Methodological Overview

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Economic Miracles in the European Economies

Abstract

In this chapter, the methodology related to threshold error correction models is discussed. The aim of the chapter is to summarize several approaches to time series modelling using both a univariate case and a multivariate case. The concept of stationarity is crucial when a model specification is projected. When time series are stationary, then threshold autoregression models or threshold distributed lag models can be estimated. These models represent a framework for flexibly and describe associations showing potentially non-linear and delayed effects in time series data. On the other hand, however, when data exhibit non-stationarity, the non-linear cointegration approach is applied. In this case, the threshold effects around the long run path present in the Threshold Error Correction Model (TECM) are discussed. A modified method for testing for a threshold in TECM based on the Enders and Siklos approach is proposed. Furthermore, methods of statistical inference in the case of a threshold in both stationary and cointegrating spaces are discussed.

Financial support from research project no. 2015/17/B/HS4/01000 supported by the National Science Centre in Poland is gratefully acknowledged.

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References

  • Andrews DWK (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61(4):821

    Article  Google Scholar 

  • Balke NS, Fomby TB (1997) Threshold cointegration. Int Econ Rev 38:627–645

    Article  Google Scholar 

  • Boehlke J, Fałdziński M, Gałecki M, Osińska M (2017) Dynamics of economic growth in Ireland in 1980–2014. St. Petersburg State Polytechnical University Journal. Economics 10(2):7–20

    Google Scholar 

  • Bruzda J (2007) Procesy nieliniowe i zależności długookresowe w ekonomii. Analiza kointegracji nieliniowej. Wydawnictwo UMK, Toruń

    Google Scholar 

  • Chan KS (1993) Consistency and limiting distribution of the least squares estimation of a threshold autoregressive model. Ann Stat 21:520–533

    Article  Google Scholar 

  • Chan KS, Petruccelli JD, Tong H, Woolford SW (1985) A multiple-threshold AR(1) model. J Appl Probab 22(2):267–279

    Article  Google Scholar 

  • Enders W, Siklos PL (2001) Cointegration and threshold adjustment. J Bus Econ Stat 19(2):166–176

    Article  Google Scholar 

  • Engle RF, Granger CWJ (1987) Cointegration and error correction: representation, estimation, and testing. Econometrica 55(2):51–276

    Google Scholar 

  • Engle RF, Yoo S (1987) Forecasting and testing in a cointegrated system. J Econ 35:143–159

    Article  Google Scholar 

  • Frey G, Manera M (2007) Econometric models of asymmetric price transmission. J Econ Surv 21(2):349–415

    Article  Google Scholar 

  • Gasparrini A (2011) Distributed lag linear and non-linear models in R: the package DLNM. J Stat Softw 43(8):1–20

    Article  Google Scholar 

  • Ghassan HB, Banerjee PK (2013) A threshold cointegration analysis of asymmetric adjustment of OPEC and non-OPEC monthly crude oil prices. Empir Econ 49:305–323

    Article  Google Scholar 

  • Gonzalo J, Pitarakis J-Y (2002) Estimation and model selection based inference in single and multiple threshold models. J Econ 110(2):319–352

    Article  Google Scholar 

  • Gosińska E (2015) Testowanie zmiany strukturalnej w modelu VEC. Bank i Kredyt 46(6):579–600

    Google Scholar 

  • Granger CWJ, Lee TH (1989) Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models. J Appl Econ 4:145–159

    Article  Google Scholar 

  • Hansen H, Johansen S (1999) Some tests for parameter constancy in cointegrated VAR-models. Econometrics J 2(2):306–333

    Article  Google Scholar 

  • Hansen BE, Seo B (2002) Testing for two-regime threshold cointegration in vector error-correction models. J Econ 110:293–318

    Article  Google Scholar 

  • Hassouneh I, Serra T, Bojnec S, Gil JM (2017) Modelling price transmission and volatility spillover in the Slovenian wheat market. Appl Econ 49(41):4116–4126

    Article  Google Scholar 

  • Johansen S (1988) Statistical analysis of cointegration vectors. J Econ Dynam Control 12(2–3):231–254

    Article  Google Scholar 

  • Johansen S (1995) Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, Oxford

    Book  Google Scholar 

  • Kapetanios G, Shin Y, Snall A (2006) Testing for cointegration in nonlinear smooth transition error correction models. Economet Theor 22(6):279–303

    Google Scholar 

  • Leszkiewicz-Kędzior K, Welfe A (2014) Asymmetric price adjustments in the fuel market. Central European J Econ Modelling Economet (CEJEME) 6(2):105–127

    Google Scholar 

  • Lütkepohl H (2005) New introduction to multiple time series analysis. Springer Verlag, Berlin

    Book  Google Scholar 

  • Maddala G (1983) Limited-dependent and qualitative variables in econometric. Econometric Society Monographs No. 3. Cambridge University Press, New York

    Google Scholar 

  • Majsterek M (2008) Wielowymiarowa analiza kointegracyjna w ekonomii. Wydawnictwo Uniwersytetu Łódzkiego, Łódź

    Google Scholar 

  • Martens M, Kofman P, Vorst TCF (1998) A threshold error-correction model for intraday futures and index returns. J Appl Econ 13(3):245–263

    Article  Google Scholar 

  • Niglio M, Giordano F, Vitale CD (2012) On the stationarity of the threshold autoregressive process: the two regimes case. In: Giommi A (ed) 46th Scientific Meeting of the Italian Statistical Society

    Google Scholar 

  • Petruccelli JD, Woolford SW (1984) A threshold AR(1) model. J Appl Probab 21(2):270–286

    Article  Google Scholar 

  • Piłatowska M, Włodarczyk A (2017) The environmental Kuznets curve in the CEE countries-the threshold cointegration approach. Argumenta Oeconomica 39(2):307–340

    Article  Google Scholar 

  • Seo B (1998) Tests for structural change in cointegrated systems. Economet Theor 14:222–259

    Article  Google Scholar 

  • Seo M (2011) Estimation of nonlinear error correction models. Economet Theor 27(2):201–234

    Article  Google Scholar 

  • Stigler M (2010) Threshold cointegration: overview and implementation in: R. Revision 5: April 2013. https://cran.r-project.org/web/packages/tsDyn/vignettes/ThCointOverview.pdf.

  • Tong H (1983) Threshold models in non-linear time series analysis. Lecture notes in statistics Vol. 21. Springer-Verlag, New York

    Book  Google Scholar 

  • Tong H (1990) Non-linear time series: a dynamical system approach. Oxford University Press, Oxford

    Google Scholar 

  • Tsay RS (1998) Testing and modeling multivariate threshold models. J Am Stat Assoc 93(443):1188–1202

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Econometrics and Statistics, The Faculty of Economic Sciences and Management, Nicolaus Copernicus University, Toruń, Poland

    Maciej Gałecki & Magdalena Osińska

Authors
  1. Maciej Gałecki
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  2. Magdalena Osińska
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Correspondence to Magdalena Osińska .

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Editors and Affiliations

  1. Department of Econometrics and Statistics, The Faculty of Economic Sciences and Management, Nicolaus Copernicus University, Toruń, Poland

    Magdalena Osińska

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Gałecki, M., Osińska, M. (2019). Threshold Error Correction Model: A Methodological Overview. In: Osińska, M. (eds) Economic Miracles in the European Economies. Springer, Cham. https://doi.org/10.1007/978-3-030-05606-3_8

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