GARCH yöntemleri kullanarak döviz kuru volatilitelerinin modellenmesi

Abstract

Bu çalışmada, genelleştirilmiş otoregresif koşullu değişen varyans (GARCH) modelleri kullanılarak 2005-2019 döneminde ABD Doları (USD) ve Euro (EUR) döviz kurlarının Türk lirası (TRY) karşısında volatilitelerinin modellenmesi amaçlanmaktadır. Kaldıraç etkisi ve oynaklık kümelenmesi gibi döviz kuru getirileri ile ilgili faktörleri ölçmek için hem simetrik hem de asimetrik modeller uygulanmıştır. Simetrik model olan GARCH (1,1) ve asimetrik modeller olan EGARCH (1,1), GJR-GARCH (1,1) ve PGARCH (1,1) modelleri her bir para biriminin TRY karşısında volatilitesini öngörmek için uygulanmıştır. Çalışma sonuçlarına göre, USD/TRY döviz kurlarının oynaklığını tahmin etmek için en uygun yöntem simetrik GARCH (1,1) ve asimetrik GJR-GARCH (1,1) modeller olarak belirlenmiştir. USD/TRY modelinde olduğu gibi EUR/TRY'de PGARCH (1,1) modelinin yanı sıra GARCH (1,1) ve GJR-GARCH (1,1) modelleri en uygun modellerdir. Bununla birlikte EUR/TRY döviz kurlarının oynaklığını tahmin etmek için PGARCH (1,1) modeli de anlamlı bir sonuç sunmaktadır. Tahmin oynaklığı ile ilgili olarak, Kök Ortalama Kare Hata (RMSE), Ortalama Mutlak Hata (MAE) ve Ortalama Mutlak Yüzde Hata (MAPE) testleri kullanılmıştır. Sonuçlara göre, statik GJR-GARCH (1,1) modelinin, hem USD hem EUR için daha yüksek bir volatilite tahmininde bulunabileceği ortaya konulmuştur.

Keywords

• ARMA
• Döviz kuru volatilitesi
• Kaldıraç etkisi
• GARCH Modelleri
• Volatilite tahminleme

Modelling exchange rate volatility using GARCH models

Abstract

This paper aims to model the volatility of USD and EUR exchange rates against TRY for the period from January 2005 to December 2019 using the Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models. Both symmetric and asymmetric models have been applied to measure factors that are related to the exchange rate returns such as leverage effect and volatility clustering. The symmetric GARCH (1,1) model and the asymmetric EGARCH (1,1), GJR-GARCH (1,1), and PGARCH (1,1) have been applied to each currency against TRY. The results of this paper conclude that the most adequate model for estimating volatility of the USD/TRY exchange rates are the symmetric GARCH (1,1) and asymmetric GJR-GARCH (1,1) models. Moreover in USD/TRY returns, GARCH (1,1) and GJR-GARCH (1,1) models are the most appropriate models along with PGARCH (1,1) in EUR/TRY as well. Regarding forecasting volatility, Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) tests have been used. Based on the results, the static forecast of GJR-GARCH (1,1) is the best model in predicting the future pattern for both USD and EUR.

Keywords

• exchange rate volatility,
• leverage effect
• ARMA,
• GARCH models,
• forecasting volatility

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