One-way anova for time series data with non-normal innovations: An application to unemployment rate data

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü, Türkiye

Tezin Onay Tarihi: 2017

Öğrenci: ÖZGECAN YILDIRIM

Danışman: CEYLAN YOZGATLIGİL

Özet:

ANOVA is a well-known approach when examining the equality of three or more than three groups’ means. However, like every parametric test, some assumptions are to be satisfied so that the appropriate and reliable conclusions are obtained. The major emphasis of this thesis is the non-validated model assumptions of the oneway ANOVA, where the independency and normality assumptions are considered as non-validated. Indeed, in real life applications, it is not realistic to validate all of those assumptions. That’s why, in the literature there exists a number of studies related to the non-validated assumptions. For this thesis, a test statistic for one-way ANOVA is introduced when the underlying distribution of the error terms is Student’s t and the each group, which are compared for the equality of their means, follows AR(1) process. In addition to one-way ANOVA test statistic, a test statistic for the linear contrasts is introduced as well. A comprahansive simulation study is done to investigate the performances of the corresponding test statistics. Finally, a real life data related to the unemployment rate are analysed in order to illustrate the application of the subjects stated under the scope of this thesis.