Fourier-Sollis Birim Kök Testi’nin simetrik ve asimetrik yönelimleri için özelliklerinin belirlenmesi

Year 2021, , 171 - 181, 01.12.2021

Mehmet Çınar , Atilla Hepkorucu

https://doi.org/10.33707/akuiibfd.793591

Abstract

Ranjbar ve diğerleri (2018) tarafından önerilen birim kök testi, yapısal kırılmalar altında asimetrik yönelime izin veren üssel yumuşak geçişli otoregresif (AESTAR) model yapılarının durağanlıklarının incelenmesine izin vermektedir. Bu çalışmada eksiklik olarak göze çarpan deterministik terim yapısını içermeyen model yapısı dikkate alınmıştır. Çünkü zamana bağlı değişen deterministik terimler, yapısal kırılmayı tanımlamak adına zaman serisinden uzaklaştırılmaktadır. Fark denkleminin yeniden tanımlanması sırasında da dönüşümden dolayı herhangi bir deterministik terimin oluşmaması, elde edilen yapının sıfır ortalamaya sahip model yapısında değerlendirilmesi gerektiğine işaret etmektedir. Bu durum için, sonlu örneklem altında kritik değerler hesaplanmış ve boyut/güç özellikleri değerlendirilmiştir. Alternatif olarak geliştirilen bu test yöntemi Sollis (2009) modelinin Fourier serileri altında yorumlanması halindedir ve Fourier-Sollis olarak adlandırılmıştır. Fourier-Sollis ve Fourier-KSS testlerinin güç özellikleri simetrik/asimetrik yönelimleri altında karşılaştırılmıştır. Elde edilen sonuçlara göre, Fourier-Sollis testi asimetrik varsayım altında daha güçlü bulunmuştur. Ancak simetrik varsayım altında bu testler birlikte kullanılabilir.

Keywords

Birim Kök Testleri, AESTAR, Çoklu Yapısal Kırılma

Testing the power properties of Fourier-Sollis Unit Root Test under symmetric and asymmetric reversions

Abstract

The unit root test proposed by Ranjbar et al. (2018) was examined for an alternative of stationary asymmetric exponential smooth transition autoregressive (AESTAR) under structural breaks. The situation that stands out as a deficiency in the mentioned study was that the model that does not includes the zero-mean structure not taken into account. On the contrary, the features of the zero-mean model should also had been explained. Because time-varying deterministic terms were removed from the time series for describing the structural breaks. The fact that no deterministic terms were formed due to the transformation during the redefinition of the difference equation indicates that the obtained structure should be evaluated in the model structure with zero-mean. This test methodology developed as an alternative is the interpretation of Sollis (2009) model under Fourier series that can be called Fourier-Sollis test for zero-mean model condition. The critical values in terms of finite samples were calculated and the size and power properties were evaluated. The power properties of the Fourier-Sollis and Fourier-KSS tests were compared under the assumption of symmetric/asymmetric reversions. Under the asymmetric reversions, Fourier-Sollis test was found to be more successful. However, under the symmetric assumption, these tests can be used together.

Keywords

Unit Root, AESTAR, Multi-Structural Breaks

References

• Becker R., Walter E. & Junsoo L. (2006). A stationarity test in the presence of an unknown number of smooth breaks, Journal of Time Series Analysis, 27(3). p. 381-409. https://doi:10.1111/j.1467-9892.2006.00478.x
• Becker R., Walter E. & Stan H. (2004). A general test for time dependence in parameters, Journal of Applied Econometrics, 19(7). p. 899-906.
• Christopoulos, D. K., & León-Ledesma, M. A. (2010). Smooth breaks and non-linear mean reversion: Post-Bretton Woods real exchange rates. Journal of International Money and Finance, 29(6), p. 1076-1093. https://doi:10.1016/j.jimonfin.2010.02.003
• Enders W., & Junsoo L. (2004). Testing for a unit root with a nonlinear Fourier function, Econometric Society, 2004 Far Eastern Meetings, Vol:457, p. 1-47.
• Escribano, A., & Jordá, O. (2001). Testing nonlinearity: Decision rules for selecting between logistic and exponential STAR models. Spanish Economic Review, 3(3), p. 193-209.
• Granger, C. W., & Lee, T. H. (1989). Investigation of production, sales and inventory relationships using multicointegration and non‐symmetric error correction models. Journal of Applied Econometrics, 4(1), p. 145-159.
• Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of econometrics, 112(2), p. 359-379. https://doi.org/10.1016/S0304-4076(02)00202-6
• Kruse, R. (2011). A new unit root test against ESTAR based on a class of modified statistics. Statistical Papers, 52(1), p. 71-85. https://doi.org/10.1007/s00362-009-0204-1
• Ludlow, J., & Enders, W. (2000). Estimating non-linear ARMA models using Fourier coefficients. International Journal of Forecasting, 16(3), p. 333-347.
• Neftci, S. N. (1984). Are economic time series asymmetric over the business cycle?. Journal of Political Economy, 92(2), p. 307-328.
• Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica: Journal of the Econometric Society, p.1361-1401.
• Ranjbar, O., Chang, T., Elmi, Z. M., & Lee, C. C. (2018). A new unit root test against asymmetric ESTAR nonlinearity with Smooth Breaks. Iranian Economic Review, 22(1), p. 51-62. https://doi.org/10.22059/IER.2018.65349
• Sarantis, N. (1999). Modeling non-linearities in real effective exchange rates. Journal of International Money and Finance, 18(1), p. 27-45.
• 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), p. 118-125. https://doi.org/10.1016/j.econmod.2008.06.002
• Sollis, R., Leybourne, S., & Newbold, P. (2002). Tests for symmetric and asymmetric nonlinear mean reversion in real exchange rates. Journal of Money, Credit and Banking, p. 686-700.
• Terasvirta, T., & Anderson, H. M. (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of Applied Econometrics, 7(1), p. 119-136.