A Unified Framework for Threshold Unit Root Testing with Asymmetric ESTAR Behavior

Abstract

In the context of the alternative hypothesis proposed by the exponential smooth transition autoregressive (ESTAR)nonlinear model, unit root tests serve similar objectives but differ in underlying assumptions across the literature. Various tests have been formulated to interpret the ESTAR framework under conditions of asymmetric and threshold effects. This study introduces a straightforward unit root test designed to assess the alternative hypothesis of asymmetric ESTAR nonlinearity with a threshold effect (〖AESTAR〗_C ). The asymptotic properties of the test statistics are established, followed by an evaluation of critical values, size, and power characteristics using Monte Carlo simulations. Based on the findings pertaining to size and power properties, the developed test demonstrates greater suitability than previous tests in scenarios involving asymmetric reversion and threshold effects. An empirical application of the proposed test is illustrated using methodologies described by Sollis (2009) and Kruse (2011).

Keywords

• ESTAR
• Nonlinear Time Series
• Unit Root Test

Asimetrik ESTAR Yapısını Temel Alan Eşikli Birim Kök Testi için Bütünleşik Bir Yaklaşım

Abstract

ESTAR (Exponential Smooth Transition Autoregressive) doğrusal olmayan model tarafından önerilen alternatif hipotez bağlamında, birim kök testleri benzer amaçlara hizmet etmekle birlikte, literatürdeki temel varsayımlar açısından farklılık göstermektedir. Literatürde, asimetrik ve eşik etkileri koşulları altında ESTAR çerçevesini yorumlamak üzere çeşitli testler geliştirilmiştir. Bu çalışma, asimetrik ESTAR doğrusal olmayanlığı ve eşik etkisini (〖AESTAR〗_C ) içeren alternatif hipotezi değerlendirmeye yönelik basit bir birim kök testi önermektedir. Önerilen testin istatistiklerine ilişkin asimptotik özellikler teorik olarak ortaya konulmuş, ardından Monte Carlo benzetimleri aracılığıyla kritik değerler, boyut ve güç özellikleri incelenmiştir. Elde edilen bulgular, geliştirilen testin özellikle asimetrik geri dönüş dinamiklerinin ve eşik etkilerinin var olduğu durumlarda, önceki testlere kıyasla daha uygun performans sergilediğini göstermektedir. Son olarak, önerilen testin ampirik bir uygulaması Sollis (2009) ve Kruse (2011) tarafından tanımlanan metodolojiler kullanılarak sunulmuştur.

Keywords

• ESTAR
• Doğrusaldışı zaman serileri
• Birim Kök Testleri

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