Öngörü tekniklerinin doğruluk kıyaslaması: basit ekonometrik, arma ve armax teknikleri
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Date
2003
Authors
Akal, Mustafa
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Publisher
Uludağ Üniversitesi
Abstract
Bu çalışmada Basit Regresyon (X), Otoregresif Hareketli Ortalamalar Ekonometrik Sebep-Sonuç (ARMAX) ve Otoregresif Hareketli Ortalamalar (ARMA) tipi tekniklerin öngörü doğruluk dereceleri Ortalama Mutlak Yüzde Hata (MAPE) ve model seçimi istatistik kriterleri (RMSE, AIC, SBC) açısından karşılaştırılmıştır. Ayrıca bu kriterlerin teknikler arası uyumlulukları araştırılmıştır. Basit econometrik modellerden ARMAX modellerine geçişlerde RMSE, AIC ve SBC değerleri karşılaştırılan model çiftlerinde % 88’in üzerinde, MAPE’ de ise dönemler itibariyle % 63-%79 arasında azalmıştır. ARMA’dan ARMAX’a geçişlerde AIC, SBC ve RMSE’da görülen % 71’lik azalışlar MAPE’de dönemler itibariyle % 24-% 35 arasındadır. Bunlar modellerin genelinde sırasıyle % 86, % 86, % 81 olup MAPE’de dönemler itibariyle sırasıyle % 50, % 50, % 60, % 55’dir. Basit ekonometrik (X) ve ARMA modellerinden komplike ARMAX tipi modellere geçişlerde, RMSE, AIC ve SBC arasında % 95’lere varan bir uyumluluk gözlenirken, bu kriterlerin MAPE ile olan uyumlulukları % 52-62 arasında düşük bulunmuştur. Bu sonuç özetleyici istatistiklerle MAPE arasındaki tutarsızlığı işaret eder. Bu uyumsuzluk RMSE, AIC ve SBC kriterlerine göre ARMAX’ın ARMA’ya % 71 olasılıkla tercih edilmesine karşın MAPE kriterine göre ARMA tekniğinin ARMAX’a ilk dönem tahmininde % 60, iki dönem tahmininde % 70, üç dönem tah- mininde % 60 ve dört dönem tahmininde % 65 olasılıkla tercih edilmesi çelişkisini sonuçlandırmıştır. Fakat, MAPE kriterine göre ARMAX tekniği basit ekonometrik sebep-sonuç tekniğine bir dönemlik tahmininde % 64, iki dönemlik tahminde % 73, üç dönemlik tahminde % 82 ve dört dönemlik tahminde % 77’lik bir üstünlük sağlamıştır. Tahmin edilen modeller Dickey-Fuller ko-entegrasyon testine göre uzun dönem ilişki göstermiştir.
In this study, each one of Autoregressive Moving Average Cause-Effect (ARMAX), Simple Regression (X) and autoregressive moving average (ARMA) techniques is compared with each other in terms of MAPE and in terms of another three summary statistics of model selection criterions (RMSE, AIC, SBC). And the consistency of these criterions is examined among these techniques. In passing from simple econometric models to ARMAX models more than eighty-eight percent of compared couples indicated reductions in values of RMSE, AIC and SBC statistics. However, the reductions in MAPE values range between sixty-three and seventy-nine percent along prediction periods. In passing from ARMA model to ARMAX model, the reduction in summary statistics is about seventy-one percent but the reductions in MAPE range along twenty-four and thirtyfive percent. In overall comparisons, RMSE declined eight-six percent, AIC declined eighty-nine percent, and SBC declined eighty-one percent in entirely sample predictions. On the other hand, the reduction in MAPE is about fifty percent in one and two periods advance predictions, sixty percent in three periods advance and fifty-five percent in four periods advance sample predictions. In passing from a simple econometric (X) and ARMA model to the complicated ARMAX models, a ninety-five percent consistency is observed among RMSE, AIC and SBC criterions in values, however; their consistency with MAPE ranges between fifty-two and sixty-two percent along the sample prediction period. This result implies inconsistency between summary statistics and MAPE criterion. As a result, ARMA technique outperformed ARMAX technique about seventy-one percent in terms of summary statistics; in contrast, ARMAX technique outperformed ARA technique about sixty percent in one and three periods advanced predictions, seventy percent in two periods advanced and sixty-five percent in four periods advanced the sample predictions in terms of MAPE criterion. However, according to MAPE criterion the ARMAX technique outperformed the simple regression around sixty-four percent in one period, seventy-three percent in two periods, eighty-two percent in three periods and seventy-seven percent in four periods advanced sample predictions. And the estimated models exhibited long run relationships based on the Dickey-Fuller test.
In this study, each one of Autoregressive Moving Average Cause-Effect (ARMAX), Simple Regression (X) and autoregressive moving average (ARMA) techniques is compared with each other in terms of MAPE and in terms of another three summary statistics of model selection criterions (RMSE, AIC, SBC). And the consistency of these criterions is examined among these techniques. In passing from simple econometric models to ARMAX models more than eighty-eight percent of compared couples indicated reductions in values of RMSE, AIC and SBC statistics. However, the reductions in MAPE values range between sixty-three and seventy-nine percent along prediction periods. In passing from ARMA model to ARMAX model, the reduction in summary statistics is about seventy-one percent but the reductions in MAPE range along twenty-four and thirtyfive percent. In overall comparisons, RMSE declined eight-six percent, AIC declined eighty-nine percent, and SBC declined eighty-one percent in entirely sample predictions. On the other hand, the reduction in MAPE is about fifty percent in one and two periods advance predictions, sixty percent in three periods advance and fifty-five percent in four periods advance sample predictions. In passing from a simple econometric (X) and ARMA model to the complicated ARMAX models, a ninety-five percent consistency is observed among RMSE, AIC and SBC criterions in values, however; their consistency with MAPE ranges between fifty-two and sixty-two percent along the sample prediction period. This result implies inconsistency between summary statistics and MAPE criterion. As a result, ARMA technique outperformed ARMAX technique about seventy-one percent in terms of summary statistics; in contrast, ARMAX technique outperformed ARA technique about sixty percent in one and three periods advanced predictions, seventy percent in two periods advanced and sixty-five percent in four periods advanced the sample predictions in terms of MAPE criterion. However, according to MAPE criterion the ARMAX technique outperformed the simple regression around sixty-four percent in one period, seventy-three percent in two periods, eighty-two percent in three periods and seventy-seven percent in four periods advanced sample predictions. And the estimated models exhibited long run relationships based on the Dickey-Fuller test.
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Keywords
Öngörü teknikleri, Forecasting techniques, İstatistiksel kriterler, Doğruluk karşılaştırması, Doğruluk karşılaştırması, Statistical criterions, Accuracy comparisons
Citation
Akal, M. (2003). "Öngörü tekniklerinin doğruluk kıyaslaması: basit ekonometrik, arma ve armax teknikleri" Uludağ Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 22(1), 233-269.