Doğrusal Olmayan Gri Bernoulli Model için Parametre ve Model Yapısı Optimizasyonu

Anlaşılması ve tahmin edilmesi kolay geleneksel gri modeller yaygın olarak kullanılmaktadırlar. Ancak, bu modeller mevcut kestirim ve öngörü hassasiyeti arttırılmak istenildiği zaman ihtiyaç duyulan uyarlamalar için gereken esneklikten yoksundurlar. Diğer taraftan, oldukça esnek olan doğrusal olmayan gri Bernoulli model tek parametresi ayarlanarak, birikim üretim operatörü uygulanmış zaman serisine uyan eğriyi etkin bir şekilde uydurulabilmektedir. Yine de, bu modelinin parametreleri ve yapısı çerçevesinde yapılabilecek iyileştirmeler mevcuttur. Bu yüzden, bu çalışmada doğrusal olmayan gri Bernoulli model için önerilen başlangıç koşulunu optimizasyonu, gri modellerin öngörü performanslarını yükseltmek adına önerilen kayan pencere yöntemi ve sezgisel algoritmalar ile model parametrelerinin optimizasyonu yaklaşımları bir arada kullanılmıştır. Doğrusal olmayan gri Bernoulli model kayan pencere yöntemine dayalı olarak tahmin edilmiştir. Diferansiyel denklemin çözümünde başlangıç koşulu olarak birinci dereceden birikim üretim operatörü uygulanmış serinin düzeltilmiş son elemanı kullanılmıştır. Geçmiş değer ve kuvvet katsayısının en iyi değerleri ise salp sürüsü optimizasyon algoritması kullanılarak bulunmuştur. Dolayısıyla, model yapısının ve parametrelerinin birlikte değerlendirildiği yeni bir optimize edilmiş doğrusal olmayan gri Bernoulli model önerilmiştir. Çalışmada, parametre tahmin yöntemi ve/veya model yapısı açısından birbirinden farklı sekiz gri model değerlendirilmiştir. Ulaşılan sonuçlar önerilen modelin diğer gri modellere göre daha başarılı olduğunu göstermektedir. Sonuç olarak, Türkiye’nin gayrisafi yurt içi hasıla hacim endeksi önerilen gri model ile daha iyi modellenmiştir.

Anahtar Kelimeler:

Doğrusal olmayan gri Bernoulli model, Salp sürüsü algoritması, GSYH öngörüsü

Parameter and Model Structure Optimization for the Nonlinear Grey Bernoulli Model

Traditional grey models, easy to understand and estimate, are widely used. However, these models lack the flexibility with regard to the adaptations required to increase the current prediction and forecast accuracy. However, the highly flexible non-linear grey Bernoulli model can effectively fit the curve for the accumulated generating operation series by adjusting its single parameter. Nevertheless, there are still improvements that can be made within the framework of the structure and parameters of this model. Therefore, in this study, initial condition optimization proposed for the non-linear grey Bernoulli model, the rolling window method proposed to improve the forecasting performance of the grey models and, optimization of the model parameters with heuristic algorithm combined. The non-linear grey Bernoulli model was estimated by using the rolling window method. The corrected last element of the accumulated generating operation series was used as the initial condition in the solution of the differential equation. The optimal values of the background value and power index were determined by using the salp swarm optimization algorithm. Therefore, a new optimized non-linear grey Bernoulli model is proposed by considering the structure and parameters of the model together. In the study, eight different grey models were evaluated in terms of parameter estimation method and/or model structure. The results showed that the proposed model outperformed the other grey models. Consequently, gross domestic product volume index of Turkey was better modeled with the proposed grey model.

Keywords:

Non-linear grey Bernoulli model, Salp swarm algorithm, GDP forecast,

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