Kırılgan Beşli Ülkelerinin Menkul Kıymet Borsalarının Kaotik Yapısının İncelenmesi

Kaotik veri analizi, 1980’lerden itibaren finansal piyasaların davranışlarının açıklanmasında ve modellenmesinde faydalı bir araç olarak kullanılmaktadır. Bu çalışmada Yükselen ekonomiler sınıfında yer alan ve Morgan Stanley tarafından Kırılgan Beşli Ülkeleri olarak adlandırılan Brezilya, Endonezya, Hindistan, Türkiye ve Güney Afrika (BIITS)’nın menkul kıymet borsalarının kaotik yapısının incelenmesi amaçlanmıştır. Bu amaçla Kırılgan Beşli ülkelerinin önde gelen borsa endekslerinin 2001-2015 dönemini kapsayan günlük kapanış değerlerini içeren veri seti ile çalışılmıştır. Ülkelerin menkul kıymet borsalarının kaotik yapısının incelenmesinde, kaotik davranışın en önemli göstergelerinden olan ve Grassberger ve Procaccia (1983) tarafından önerilen Korelasyon Boyutu ile Kantz (1994)’ın en büyük Lyapunov üsteli algoritması kullanılmıştır. Korelasyon boyutu analizine göre incelenen ülkelerin menkul kıymet borsalarının aynı fraktal boyuta, diğer bir ifade ile aynı karmaşıklık düzeyine sahip oldukları belirlenmiştir. En büyük Lyapunov üsteli değerlerine göre ise tüm ülkelerin genel olarak zayıf kaotik yapıya sahip oldukları belirlenmiştir. Kaotik analizler sonucu elde edilen bulgular, Kırılgan Beşli ülkelerinin menkul kıymet borsalarının benzer kaotik davranış sergilemeleri nedeniyle aynı grupta yer almasını destekleyici niteliktedir.

Anahtar Kelimeler:

Kaotik zaman serileri, Korelasyon boyutu, En büyük Lyapunov üsteli, Menkul kıymet borsası, Kırılgan Beşli

Investigation of the Chaotic Structure of Stock Exchanges of Fragile Five Countries

Chaotic data analysis has been used since the 1980s as a useful tool in describing and modeling the behavior of financial markets. In this study, it was aimed to examine the chaotic structure of the stock exchanges of Brazil, Indonesia, India, Turkey, and South Africa (BIITS), categorized as the emerging economies and called the Fragile Five by Morgan Stanley. For this purpose, the leading indexes of the Fragile Five countries were studied with the data set containing daily closing values for the period 2001-2015. The chaotic structure of the stock exchanges of the countries was determined using the correlation dimension proposed by Grassberger and Procaccia (1983), which is an important indicator of chaotic behavior, and the largest Lyapunov exponents calculated using the Kantz (1994) algorithm. According to the correlation dimension analysis, it was found that the stock exchanges of the Fragile Five have the same fractal dimension and according to the largest Lyapunov exponent values, all the countries were found to have a weak chaotic structure in general. The findings obtained as a result of the chaotic analysis support the fact that the studied countries are in the same group.

Keywords:

Chaotic time series, Correlation dimension, Largest Lyapunov exponent, Stock exchange, Fragile Five,

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