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İSTANBUL MENKUL KIYMETLER BORSASI 100 ENDEKSİNİN DOĞRUSALLIK TESTİ

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Abstract (2. Language): 
The aim of the study is nonlinearity test of ISE – 100 returns. The most usedly nonlinearity test of BDS test is applied. Data is obtained from the Central Bank of Turkey. Return data is calculated by the difference of natural logarthim of daily closing value. The data has 4352 observations, between the data of 02.01.1989 and 04.07.2006. BDS test is done on the four different error term. Before the ARMA process to make the BDS test days are used as a dummies and error term is obtained by regression. Second data set is ARMA process is done and error term is obtained and then BDS test is applied. Third data set is logarithm of the squared standardized residuals of GARCH (1,1) process. Fourth data set is logarithm of the squared standardized residuals of AR (1) - GARCH (1,1) process. First, second and fourth data sets reject the null hypothesis that means there exist a nonlinear relation. Third data set fail to reject the null hypothesis of iid, for some embedding dimension, that means GARCH (1,1) process removes most of the nonlinearity.
Abstract (Original Language): 
Bu çalışmanın amacı İMKB-100 endeksi getirisinin doğrusal bir yapıya sahip olup olmadığını göstermektir. Çalışmada doğrusallık testlerinden en fazla kullanılan BDS testinden faydalanılacaktır. Kullanılan veri seti Merkez Bankasından elde edilmiştir. Getiri serisi endeksin günlük kapanış değerlerinin logaritmik farkı alınarak hesaplanmıştır. Çalışmada kullanılan veri seti 02.01.1989 – 04.07.2006 yılları arasında olup 4352 gözlemden oluşmaktadır. Çalışmada veri seti dört şekilde değerlendirilmiştir: ilk değerlendirme veri setine günler kukla değişken olarak kullanıldıktan sonra ARMA süreci uygulanmıştır hata terimlerine BDS testi uygulanmıştır. İkinci veri seti ise getiri serisine ARMA süreci uygulanarak hata terimleri elde edildikten sonra BDS testi uygulanmıştır. Üçüncü veri setinde GARCH(1,1) süreci ve dördüncü veri setinde ise AR(1) – GARCH(1,1) ile standartlaştırılmış hata karelerinin logaritmalarına BDS testi uygulanmıştır. Birinci, ikinci ve dördüncü veri setinde BDS testi sonuçlarına göre getirilerin doğrusal olmayan bir yapıya sahip olduğu bulunmuştur. Üçüncü veri seti incelendiğinde ise BDS testi bazı boyutlarda hata terimlerinin bağımsız benzer dağılıma sahip olduğunu göstermiştir.
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