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

Öz

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.

Anahtar Kelimeler

• Birim Kök Testleri
• AESTAR
• Çoklu Yapısal Kırılma

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

Öz

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.

Anahtar Kelimeler

• Unit Root
• AESTAR
• Multi-Structural Breaks

Kaynakça

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