GARCH Models under Power Transformed Returns: Empirical Evidence from International Stock Indices

Authors

  • Didit Budi Nugroho Universitas Kristen Satya Wacana
  • Tundjung Mahatma Universitas Kristen Satya Wacana
  • Yulius Pratomo Universitas Kristen Satya Wacana

DOI:

https://doi.org/10.17713/ajs.v50i4.1075

Abstract

This study evaluates the empirical performance of four power transformation families: extended Tukey, Modulus, Exponential, and Yeo--Johnson, in modeling the return in the context of GARCH(1,1) models with two error distributions: Gaussian (normal) and Student-t. We employ an Adaptive Random Walk Metropolis method in Markov Chain Monte Carlo scheme to draw parameters. Using 19 international stock indices from the Oxford-Man Institute and basing on the log likelihood, Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion, the use of power transformation families to the return series clearly improves the fit of the normal GARCH(1,1) model. In particular, the Modulus transformation family provides the best fit. Under Student's t-error distribution assumption, the GARCH(1,1) models under power transformed returns perform better in few cases.

Author Biographies

Didit Budi Nugroho, Universitas Kristen Satya Wacana

Department of Mathematics

Tundjung Mahatma, Universitas Kristen Satya Wacana

Department of Mathematics

Yulius Pratomo, Universitas Kristen Satya Wacana

Department of Economics

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Published

2021-07-15

How to Cite

Nugroho, D. B., Mahatma, T., & Pratomo, Y. (2021). GARCH Models under Power Transformed Returns: Empirical Evidence from International Stock Indices. Austrian Journal of Statistics, 50(4), 1–18. https://doi.org/10.17713/ajs.v50i4.1075