TITLE:
Quantification of GARCH (1, 1) Model Misspecification with Three Known Assumed Error Term Distributions
AUTHORS:
Zonia Chandre Stiglingh, Modisane Bennett Seitshiro
KEYWORDS:
Bond Market, Heavy Tailed Distribution, GARCH Model, Model Misspecification
JOURNAL NAME:
Journal of Financial Risk Management,
Vol.11 No.3,
August
11,
2022
ABSTRACT: Generalized autoregressive conditional heteroscedastic (GARCH) models
have become significant tools in the assessment of time series data, largely
the traditional normal distribution of GARCH models because of their ease of use in practice.
However, it is proven that high frequency financial data have heavy tails
leading to the resulting estimates being inefficient. The Student-t and General
error (GED) distributions are more capable of representing these financial
series. In this paper, we conduct a series of simulations for the GARCH (1, 1)
model assuming the error terms follow a Normal distribution. We fit the
simulated returns to the GARCH (1, 1) with Normal, Student-t and GED
innovations and varying sample sizes. The return series of Samsung electronics
daily stock prices, Bitcoin-USD daily cryptocurrency and Moody’s seasoned AAA
corporate bond yield (BAAA) are fitted to the GARCH (1, 1) with Normal,
Student-t and GED innovations. We investigate if these models are subject to
model misspecification if the error terms do not assume similar distributions
as the simulated data and real data innovations. Model misspecification was identified
in the GARCH model building process of the simulated and real datasets.