Arıma ve gri tahmin modellerinde Fourier serisi modifikasyonu: Türkiye enflasyonu uygulaması

Günümüzde birçok merkez bankası enflasyonu kontrol altında tutarak fiyat istikrarını sağlayan istikrarlı bir ekonomik yapı kurmaya çalışmaktadır. Özellikle gelişmekte olan ülkeler diğer makroekonomik dengeleri de olumsuz etkilediği için yüksek enflasyon üzerine yoğunlaşmaktadırlar. Bu yönüyle fiyat istikrarının sürdürülmesi birçok ülkenin politika yapıcılarının ana hedefi haline gelmiştir. Özellikle enflasyon verilerinin tahmini, çok geniş kitleleri etkilemesi bakımından daha da önemli hale gelebilmektedir. Enflasyon verileri de, önemi göz önünde bulundurularak çalışmamızda kullanılmıştır. Bu anlamda tahmin etmek kadar, yapılan tahminin doğruluğunun da hayati olduğu düşünülmüştür. Bu çalışmada öncelikle, literatürde sıkça kullanılan iki farklı tahmin tekniği olan ARIMA modeli ve GM(1,1) modeli ile Türkiye’de enflasyon oranı tahmin edilerek hata terimleri hesaplanmıştır. Elde edilen bu hata terimleri, Fourier serileri yardımıyla modifiye edilerek yeni tahmin değerleri elde edilmiş ve doğruluk oranları arttırılmıştır. Orijinal modeller ile yapılan tahminlemelerde ARIMA modelinin GM(1,1) modelinden daha başarılı olduğu görülmüştür. Sonrasında, Fourier modifikasyonu uygulanmış ve bu modellerin modellerin orijinal modellerden çok daha başarılı sonuçlar ürettiği, en başarılı sonucun da Fourier modifikasyonlu GM(1,1) modeline ait olduğu görülmüştür. Gelecek dönem tahminlerinde de benzer durum söz konusu olmuştur. Türkiye açısından bakıldığında enflasyonun ciddi bir düşüş eğilimi göstermeyeceği ve bu konu üzerine yoğunlaşılması gerektiği söylenebilir.

Anahtar Kelimeler:

Tahmin modelleri, ARIMA Model, Gri Tahmin Modeli, Fourier Hata Düzeltmesi, Enflasyon Tahmini

Fourier series modification in Arima and grey prediction models: A case of Turkey's inflation

Many central banks are trying to establish a stable economic structure that ensures price stability by keeping inflation under control. Especially developing countries concentrate on high inflation since it affects other macroeconomic balances negatively. In this respect, maintaining price stability has become the main goal of many countries' policy makers. In particular, the estimation of inflation data can become even more important as it affects a wide audience. Inflation data was also used in our study, considering its importance. In this sense, it is known that the accuracy of the prediction is as vital as the forecast. In this study, two different estimation techniques commonly used in the literature that ARIMA model and GM (1,1) model estimated the Turkey’s inflation rate and the error terms are calculated. These error terms were modified with the Fourier series and new prediction values were obtained and their accuracy rates were increased. It has been observed that the ARIMA model is more successful than the GM (1,1) model on the models installed with the original models. Then, it has been observed that the models with Fourier modification produced much more successful results than the original models, and the most successful result belonged to the Fourier modified GM(1,1) model. A similar situation occurred in the future projections. From the perspective of Turkey, where inflation will not showing a downward trend seriously and said that it should focus on this issue.

Keywords:

Forecasting Models, ARIMA Model, Grey Prediction Model, Fourier Residual Modification, Forecasting Inflation,

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