Open AccessGARCH Models under Power Transformed Returns: Empirical Evidence from International Stock Indices
Author(s) -
Didit Budi Nugroho,
Tundjung Mahatma,
Yulius Pratomo
Publication year - 2021
Publication title -
österreichische zeitschrift für statistik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.342
H-Index - 9
ISSN - 1026-597X
DOI - 10.17713/ajs.v50i4.1075
Subject(s) - deviance information criterion , autoregressive conditional heteroskedasticity , econometrics , mathematics , bayesian information criterion , akaike information criterion , markov chain , statistics , exponential function , bayesian probability , markov chain monte carlo , volatility (finance) , mathematical analysis
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.