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

Yıl 2018, Cilt: 20 Sayı: 1, 173 - 188, 24.04.2018

Ayşe İşi Sedat Yenice Fatih Çemrek

Öz

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.

Anahtar Kelimeler

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

Kırılgan Beşli Ülkelerinin Menkul Kıymet Borsalarının Kaotik Yapısının İncelenmesi

Öz

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

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