Autocorrelated Regression Model Used in Seasonal Fractionally Integrated Processes

Abstract

In the literature, there are a few studies for seasonal fractionally integrated processes in recent years. Semi-parametric methods based on logarithmic periodogram were proposed to estimate seasonal fractionally differencing parameter. The methods based on logarithmic periodogram can be used as a spectral density function of seasonal fractionally integrated processes. Also autocorrelation function instead of spectral density function can be used to seasonal fractionally integrated processes. In this study, a new parameter estimation method based on autocorrelation function is proposed for seasonal fractionally integrated process. This new method is compared classical methods in the literature by a simulation studies.

Keywords

• Seasonality
• Seasonal Fractionally Integrated Processes
• Seasonal Fractionally Differencing Parameter
• Autocorrelation Regression

Mevsimsel Kesirli Bütünleşik Akgürültü Sürecinde Otokorelasyonlu Regresyon Yöntemi

Abstract

Mevsimsel kesirli bütünleşik zaman serileri için son yıllarda az sayıda çalışma literatürde yer almaktadır. Mevsimsel kesirli bütünleşik zaman serilerinde fark parametresinin tahmini için logaritmik periodograma dayalı bazı yarı parametrik tahmin yöntemleri önerilmiştir. Logaritmik periodograma dayalı yöntemler, genellikle mevsimsel kesirli bütünleşik serilerin spektral yoğunluk fonksiyonunun özelliklerinden esinlenmektedir. Spektral yoğunluk fonksiyonu yerine, bu fonksiyonla aynı bilgiyi taşıyan otokorelasyon fonksiyonundan yararlanmak da mümkündür. Bu çalışmada mevsimsel kesirli bütünleşik akgürültü sürecinde örneklem otokorelasyon katsayılarına dayalı yeni bir tahmin yöntemi önerilmiştir. Önerilen yöntem bir benzetim çalışması yardımıyla daha önceki yöntemler ile karşılaştırılarak, üstün yönleri belirlenmiştir.

Keywords

• Mevsimsellik
• Mevsimsel Kesirli Bütünleşik Zaman Serileri
• Mevsimsel Kesirli Fark Parametresi
• Otokorelasyon Regresyonu

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