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A New Unit Root Test Against LSTAR Nonlinearity without Threshold

Yıl 2022, Cilt 17, Sayı 2, 311 - 326, 01.08.2022

Öz

In this paper, a simple unit root test was proposed against the alternative of stationary LSTAR nonlinearity without a threshold effect. The critical values, size and power properties were examined with Monte Carlo simulations. The power of the developed test was compared with linear Dickey and Fuller (DF) (1979) and nonlinear Kapetanios, Shin and Snell (KSS) (2003) unit root tests. The developed test (F_(LSTAR,c=0) ) assumed that no-threshold effect is more suitable than the comparable ones. The empirical application of the test was carried out for industrial production data from OECD countries and Europe 1961(i) - 1986(iv). The data used in the application part has been chosen, because it is suitable for the LSTAR model structure. The contribution of the study to the literature is to obtain an alternative test mechanism that explains the unit root structure of time series LSTAR model structure without a threshold. Empirical application results show that the use of the test is appropriate under the relevant model structure.

Kaynakça

  • Balke, N. S., & Fomby, T. B. (1997). Threshold cointegration. International economic review, 627-645.
  • Berben, R. P., & Dijk, D. J. C. (1999). Unit root tests and asymmetric adjustment: A reassessment. Econometric Institute.
  • Caner, M., & Hansen, B. E. (2001). Threshold autoregression with a unit root. Econometrica, 69(6), 1555-1596.
  • Chan, K. S., & Tong, H. (1986). On estimating thresholds in autoregressive models. Journal of time series analysis, 7(3), 179-190.
  • Chen, Y. T. (2003). Discriminating between competing STAR models. Economics Letters, 79(2), 161-167.
  • Chen, Y. T., & Kuan, C. M. (2002). The pseudo-true score encompassing test for non-nested hypotheses. Journal of Econometrics, 106(2), 271-295.
  • Davies, R. B. (1987). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 74(1), 33-43.
  • Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American statistical association, 74(366a), 427-431.
  • Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica: journal of the Econometric Society, 1057-1072.
  • Dijk, D. V., Teräsvirta, T., & Franses, P. H. (2002). Smooth transition autoregressive models—a survey of recent developments. Econometric reviews, 21(1), 1-47.
  • Eklund, B. (2003). Testing the unit root hypothesis against the logistic smooth transition autoregressive model (No. 546). SSE/EFI Working Paper Series in Economics and Finance.
  • Enders, W., & Granger, C. W. J. (1998). Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3), 304-311.
  • Escribano, A., & Jordá, O. (2001). Testing nonlinearity: Decision rules for selecting between logistic and exponential STAR models. Spanish Economic Review, 3(3), 193-209.
  • Granger, C., & Teräsvirta, T. (1993). Modelling Non-Linear Economic Relationships. Oxford University Press.
  • Gregoriou, A., & Kontonikas, A. (2009). Modeling the behaviour of inflation deviations from the target. Economic Modelling, 26(1), 90-95.
  • Guidolin, M., Hyde, S., McMillan, D., & Ono, S. (2009). Non-linear predictability in stock and bond returns: When and where is it exploitable?. International Journal of Forecasting, 25(2), 373-399.
  • Hall, A. D., Skalin, J., & Teräsvirta, T. (2001). A nonlinear time series model of El Nino. Environmental Modelling & Software, 16(2), 139-146.
  • Hamori, S., & Tokihisa, A. (1997). Testing for a unit root in the presence of a variance shift. Economics Letters, 57(3), 245-253.
  • Henry, O. T., & Shields, K. (2004). Is there a unit root in inflation?. Journal of Macroeconomics, 26(3), 481-500.
  • Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of econometrics, 112(2), 359-379.
  • Kruse, R. (2011). A new unit root test against ESTAR based on a class of modified statistics. Statistical Papers, 52(1), 71-85.
  • Leybourne, S. J., Mills, T. C., & Newbold, P. (1998). Spurious rejections by Dickey–Fuller tests in the presence of a break under the null. Journal of Econometrics, 87(1), 191-203.
  • Leybourne, S., Newbold, P., & Vougas, D. (1998). Unit roots and smooth transitions. Journal of time series analysis, 19(1), 83-97.
  • Lo, M. C., & Zivot, E. (2001). Threshold cointegration and nonlinear adjustment to the law of one price. Macroeconomic Dynamics, 5(4), 533.
  • Nelson, C. R., Piger, J., & Zivot, E. (2001). Markov regime switching and unit-root tests. Journal of Business & Economic Statistics, 19(4), 404-415.
  • Pavlidis, E., Yusupova, A., Paya, I., Peel, D. A., Martínez-García, E., Mack, A., & Grossman, V. (2013). Monitoring housing markets for episodes of exuberance: an application of the Phillips et al.(2012, 2013) GSADF test on the Dallas Fed International House Price Database. Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper, (165).
  • Pippenger, M. K., & Goering, G. E. (1993). A note on the empirical power of unit root tests under threshold processes. Oxford bulletin of economics and statistics, 55(4), 473-481.
  • Potter, S. (1999). Nonlinear time series modelling: An introduction. Journal of Economic Surveys, 13(5), 505-528.
  • Puspaningrum, H., Lin, Y. X., & Gulati, C. (2013). Unit root tests for ESTAR models. Journal of Statistical Theory and Practice, 7(3), 558-595.
  • Sarantis, N. (1999). Modeling non-linearities in real effective exchange rates. Journal of international money and finance, 18(1), 27-45.
  • Sollis, R. (2004). Asymmetric adjustment and smooth transitions: a combination of some unit root tests. Journal of time series analysis, 25(3), 409-417.
  • Sollis, R. (2009). A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries. Economic modelling, 26(1), 118-125.
  • Teräsvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the american Statistical association, 89(425), 208-218.
  • Teräsvirta, T., & Anderson, H. M. (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of applied econometrics, 7(S1), S119-S136.
  • Teräsvirta, T., & Anderson, H. M. (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of applied econometrics, 7(S1), S119-S136.
  • Ullah, A. (Ed.). (1998). Handbook of applied economic statistics. CRC Press.
  • Yoon, G. (2010). Does nonlinearity help resolve the Fisher effect puzzle?. Applied Economics Letters, 17(8), 823-828.
  • Zhang, L. (2013). Partial unit root and linear spurious regression: A monte carlo simulation study. Economics Letters, 118(1), 189-191.
  • Zhang, L. (2016). Performance of unit-root tests for non linear unit-root and partial unit-root processes. Communications in Statistics-Theory and Methods, 45(15), 4528-4536.

Eşiksiz LSTAR Doğrusal-dışılığına Karşı Yeni Bir Birim Kök Testi

Yıl 2022, Cilt 17, Sayı 2, 311 - 326, 01.08.2022

Öz

Öz Çalışmada, eşik içermeyen durağan LSTAR doğrusal-dışı yapısı alternatifine karşı basit bir birim kök testi önerilmiştir. Monte Carlo simülasyonları ile kritik değerler, boyut ve güç özellikleri incelenmiştir. Geliştirilen testin gücü, doğrusal Dickey ve Fuller (DF) (1979) ve doğrusal olmayan Kapetanios, Shin ve Snell (KSS) (2003) birim kök testleri ile karşılaştırılmıştır. Eşik etkisi olmadığı varsayılarak geliştirilen test (F_(LSTAR,c=0) ), karşılaştırılanlara göre daha uygundur. Testin ampirik uygulaması OECD ülkeleri ve Avrupa 1961(i)-1986(iv) endüstriyel üretim verileri için yapılmıştır. Uygulama kısmında kullanılan veriler, LSTAR model yapısına uygun olduğu için seçilmiştir. Çalışmanın literatüre katkısı, eşiksiz LSTAR model yapısına sahip zaman serilerinin birim kök yapısını açıklayan alternatif bir test mekanizması elde etmektir. Ampirik uygulama sonuçları göstermektedir ki, testin kullanımı ilgili model yapısı altında uygundur.

Kaynakça

  • Balke, N. S., & Fomby, T. B. (1997). Threshold cointegration. International economic review, 627-645.
  • Berben, R. P., & Dijk, D. J. C. (1999). Unit root tests and asymmetric adjustment: A reassessment. Econometric Institute.
  • Caner, M., & Hansen, B. E. (2001). Threshold autoregression with a unit root. Econometrica, 69(6), 1555-1596.
  • Chan, K. S., & Tong, H. (1986). On estimating thresholds in autoregressive models. Journal of time series analysis, 7(3), 179-190.
  • Chen, Y. T. (2003). Discriminating between competing STAR models. Economics Letters, 79(2), 161-167.
  • Chen, Y. T., & Kuan, C. M. (2002). The pseudo-true score encompassing test for non-nested hypotheses. Journal of Econometrics, 106(2), 271-295.
  • Davies, R. B. (1987). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 74(1), 33-43.
  • Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American statistical association, 74(366a), 427-431.
  • Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica: journal of the Econometric Society, 1057-1072.
  • Dijk, D. V., Teräsvirta, T., & Franses, P. H. (2002). Smooth transition autoregressive models—a survey of recent developments. Econometric reviews, 21(1), 1-47.
  • Eklund, B. (2003). Testing the unit root hypothesis against the logistic smooth transition autoregressive model (No. 546). SSE/EFI Working Paper Series in Economics and Finance.
  • Enders, W., & Granger, C. W. J. (1998). Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3), 304-311.
  • Escribano, A., & Jordá, O. (2001). Testing nonlinearity: Decision rules for selecting between logistic and exponential STAR models. Spanish Economic Review, 3(3), 193-209.
  • Granger, C., & Teräsvirta, T. (1993). Modelling Non-Linear Economic Relationships. Oxford University Press.
  • Gregoriou, A., & Kontonikas, A. (2009). Modeling the behaviour of inflation deviations from the target. Economic Modelling, 26(1), 90-95.
  • Guidolin, M., Hyde, S., McMillan, D., & Ono, S. (2009). Non-linear predictability in stock and bond returns: When and where is it exploitable?. International Journal of Forecasting, 25(2), 373-399.
  • Hall, A. D., Skalin, J., & Teräsvirta, T. (2001). A nonlinear time series model of El Nino. Environmental Modelling & Software, 16(2), 139-146.
  • Hamori, S., & Tokihisa, A. (1997). Testing for a unit root in the presence of a variance shift. Economics Letters, 57(3), 245-253.
  • Henry, O. T., & Shields, K. (2004). Is there a unit root in inflation?. Journal of Macroeconomics, 26(3), 481-500.
  • Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of econometrics, 112(2), 359-379.
  • Kruse, R. (2011). A new unit root test against ESTAR based on a class of modified statistics. Statistical Papers, 52(1), 71-85.
  • Leybourne, S. J., Mills, T. C., & Newbold, P. (1998). Spurious rejections by Dickey–Fuller tests in the presence of a break under the null. Journal of Econometrics, 87(1), 191-203.
  • Leybourne, S., Newbold, P., & Vougas, D. (1998). Unit roots and smooth transitions. Journal of time series analysis, 19(1), 83-97.
  • Lo, M. C., & Zivot, E. (2001). Threshold cointegration and nonlinear adjustment to the law of one price. Macroeconomic Dynamics, 5(4), 533.
  • Nelson, C. R., Piger, J., & Zivot, E. (2001). Markov regime switching and unit-root tests. Journal of Business & Economic Statistics, 19(4), 404-415.
  • Pavlidis, E., Yusupova, A., Paya, I., Peel, D. A., Martínez-García, E., Mack, A., & Grossman, V. (2013). Monitoring housing markets for episodes of exuberance: an application of the Phillips et al.(2012, 2013) GSADF test on the Dallas Fed International House Price Database. Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper, (165).
  • Pippenger, M. K., & Goering, G. E. (1993). A note on the empirical power of unit root tests under threshold processes. Oxford bulletin of economics and statistics, 55(4), 473-481.
  • Potter, S. (1999). Nonlinear time series modelling: An introduction. Journal of Economic Surveys, 13(5), 505-528.
  • Puspaningrum, H., Lin, Y. X., & Gulati, C. (2013). Unit root tests for ESTAR models. Journal of Statistical Theory and Practice, 7(3), 558-595.
  • Sarantis, N. (1999). Modeling non-linearities in real effective exchange rates. Journal of international money and finance, 18(1), 27-45.
  • Sollis, R. (2004). Asymmetric adjustment and smooth transitions: a combination of some unit root tests. Journal of time series analysis, 25(3), 409-417.
  • Sollis, R. (2009). A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries. Economic modelling, 26(1), 118-125.
  • Teräsvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the american Statistical association, 89(425), 208-218.
  • Teräsvirta, T., & Anderson, H. M. (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of applied econometrics, 7(S1), S119-S136.
  • Teräsvirta, T., & Anderson, H. M. (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of applied econometrics, 7(S1), S119-S136.
  • Ullah, A. (Ed.). (1998). Handbook of applied economic statistics. CRC Press.
  • Yoon, G. (2010). Does nonlinearity help resolve the Fisher effect puzzle?. Applied Economics Letters, 17(8), 823-828.
  • Zhang, L. (2013). Partial unit root and linear spurious regression: A monte carlo simulation study. Economics Letters, 118(1), 189-191.
  • Zhang, L. (2016). Performance of unit-root tests for non linear unit-root and partial unit-root processes. Communications in Statistics-Theory and Methods, 45(15), 4528-4536.

Ayrıntılar

Birincil Dil İngilizce
Konular Sosyal
Bölüm Makaleler
Yazarlar

Atilla HEPKORUCU> (Sorumlu Yazar)
KASTAMONU ÜNİVERSİTESİ
0000-0001-6060-3135
Türkiye

Yayımlanma Tarihi 1 Ağustos 2022
Başvuru Tarihi 1 Temmuz 2021
Kabul Tarihi 15 Ocak 2022
Yayınlandığı Sayı Yıl 2022, Cilt 17, Sayı 2

Kaynak Göster

APA Hepkorucu, A. (2022). A New Unit Root Test Against LSTAR Nonlinearity without Threshold . Eskişehir Osmangazi Üniversitesi İktisadi ve İdari Bilimler Dergisi , 17 (2) , 311-326 . Retrieved from https://dergipark.org.tr/tr/pub/oguiibf/issue/70614/960605