Quantification of GARCH (1, 1) Model Misspecification with Three Known Assumed Error Term Distributions

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.