Zaman serileri analizi için optimize ARIMA-YSA melez modeli

Öz

Zaman serileri analizi alanında son yıllarda birden çok modelin bir arada kullanıldığı melez modeller ortaya konulmaktadır. Literatürde yer alan en önemli melez model sınıflarından biri ARIMA-Yapay Sinir Ağları (YSA) melez model sınıfıdır. Gerçek hayatta karşılaşılan zaman serilerinin genellikle doğrusal ve doğrusal olmayan özellikleri bir arada taşıması, ARIMA-YSA melez modellerin tahmin performanslarının yüksek olmasını sağlamaktadır. Bu çalışmada optimizasyon tabanlı özgün bir ARIMA-YSA melez model ortaya konulmaktadır. İleri sürülen melez model, zaman serisini doğrusal ve doğrusal olmayan iki serinin toplamı olarak kabul etmektedir. İki aşamalı modelin ilk aşamasında, doğrusal ve doğrusal olmayan bileşenlerin elde edilmesi amacıyla ARIMA ve YSA modelleri ile gerçek seri bir en küçük kareler optimizasyonu sürecinden geçmektedir. İkinci aşamada ise doğrusal bileşenin hataları doğrusal olmayan bileşene aktarılarak doğrusal olmayan bileşen revize edilmekte ve YSA ile tekrar modellenmektedir. Tahmin performansının tespiti için Optimize ARIMA-YSA (OptAA) melez modeli, ARIMA, YSA, literatürdeki başlıca melez ARIMA-YSA modelleri ve rassal yürüyüş modeli ile karşılaştırılmaktadır. Uygulama aşaması için literatürde sıklıkla kullanılan üç farklı zaman serisi seçilmiştir. Elde edilen sonuçlar OptAA melez modelin özellikle görece kısa dönem tahmin performansının diğer modellere göre oldukça yüksek olduğunu ve zaman serisi analizi alanında oldukça güçlü bir yöntem olduğunu göstermektedir.

Anahtar Kelimeler

• Zaman Serisi Analizi
• ARIMA
• Yapay Sinir Ağları
• Optimize ARIMA-YSA Melez Model
• En Küçük Kareler Optimizasyonu

Optimized ARIMA-ANN hybrid model for time series analysis

Öz

In recent years, hybrid models, using more than one models together, are presented in the field of time series analysis. One of the most important hybrid model classes is ARIMA-Artificial Neural Networks (ANN) hybrids. Time series encountered in real life usually carry linear and nonlinear characteristics together, which causes high forecasting performance of ARIMA-ANN hybrid models. In this study, a novel optimization based ARIMA-ANN hybrid model is presented. Proposed hybrid model assumes time series is the sum of linear and nonlinear two series. In the first stage of the two staged model, ARIMA and ANN models with real time series pass through a least squares optimization process to obtain linear and nonlinear components. In the second stage, error values of the linear component are transferred to nonlinear component, nonlinear component is revised and remodeled with ANN. Optimized ARIMA-ANN (OptAA) hybrid model is compared with ARIMA, ANN, main ARIMA-ANN hybrid models in literature and random walk model to determine the forecasting performance. Three different time series used often in the literature are chosen for the application purposes. Obtained results show that OptAA hybrid model has higher performance than other models especially in relatively short term forecasting and is a very powerful methodology in time series analysis field.

Anahtar Kelimeler

• Time Series Analysis
• ARIMA
• Artificial Neural Networks
• Optimized ARIMA-ANN Hybrid Model
• Least Squares Optimization

Kaynakça

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