Modeling of Returns Volatility using GARCH(1,1) Model under Tukey Transformations


  • Didit Budi Nugroho Department of Mathematics, Satya Wacana Christian University, Indonesia
  • Bambang Susanto Department of Mathematics, Satya Wacana Christian University, Indonesia
  • Kezia Natalia Putri Prasetia Department of Mathematics, Satya Wacana Christian University, Indonesia
  • Rebecca Rorimpandey Department of Mathematics, Satya Wacana Christian University, Indonesia



Tukey transformation, Excel Solver, GARCH, Matlab, volatility


This study proposed two new classes of GARCH(1,1) model by applying the Tukeytransformations to the returns and to the lagged variance. The behavior of return volatility was investigated on the basis of models with normal and Student-t distributions for return error. The competing models were estimated by using the Excel Solver and Matlab tools. The empirical analysis is based on simulated data, daily exchange rates of the IDR/USD, and daily stock indices of FTSE100 and TOPIX. This study recommends the use of Excel Solver for finance academics and practitioners working on volatility using GARCH(1,1) models. Our empirical findings conclude that GARCH(1,1) models under Tukey transformations should be considered in risk management decisions since the models are more appropriate than standard for describing returns and volatility of financial time series and its stylized facts including fat tails and mean reverting. The Tukey transformed returns imply a shorter volatility half-life, and thus this study suggests that investors should invest the observed assets in a shorter time period to obtain higher returns.


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