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<p>The objective of this study is to propose extensions of the GARCHX model in two ways, namely allowing for jumps in the return process and applying the power transformation family to dependent (return) and exogenous X (RV) variables. The Jump GARCHX (JGARCHX) model is constructed by using an analytical framework that endogenously decomposes return into normal and jump-related components. The extended GARCHX and JGARCHX models are then developed by converting dependent and/or exogenous variables using the same power transformation family. On the basis of empirical comparisons using real data on the Nikkei 225 stock index and USD/IDR exchange rate, we found that: (1) dynamic jumps in the asset price is important for volatility modeling and multi-step-ahead Value-at-Risk forecasting by comparing the GARCHX and JGARCHX frameworks, and (2) the extended models with modulus or Tukey transformation families are favoured models according to AIC, BIC, log-score, and loss analysis.</p>

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Power Transformations in Jump GARCHX: Applications to Stock Index and Exchange Rate Modeling

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Didit Budi Nugroho,
  • Obed Christian Dimitrio,
  • Faldy Tita,
  • Bambang Susanto

摘要

The objective of this study is to propose extensions of the GARCHX model in two ways, namely allowing for jumps in the return process and applying the power transformation family to dependent (return) and exogenous X (RV) variables. The Jump GARCHX (JGARCHX) model is constructed by using an analytical framework that endogenously decomposes return into normal and jump-related components. The extended GARCHX and JGARCHX models are then developed by converting dependent and/or exogenous variables using the same power transformation family. On the basis of empirical comparisons using real data on the Nikkei 225 stock index and USD/IDR exchange rate, we found that: (1) dynamic jumps in the asset price is important for volatility modeling and multi-step-ahead Value-at-Risk forecasting by comparing the GARCHX and JGARCHX frameworks, and (2) the extended models with modulus or Tukey transformation families are favoured models according to AIC, BIC, log-score, and loss analysis.