How does the sample size affect GARCH model?

Abstract

GARCH model has a long history and permeates the modern financial theory. Most researchers use several thousands of financial data and maximum likelihood to estimate the coefficients of model. Statistically, more samples imply better estimation but are hard to obtain. How many samples are sufficient for estimation? What is the impact of the limited samples on the estimation? In this paper, we examined these questions using GARCH, MEM-GARCH models and NASDAQ composite index. The problems, raised from the limited samples, were discussed. Correlation of the conditional variances of the estimated models between the limited samples and the large samples were calculated. The effectiveness of model estimation for the limited samples was evaluated by the correlation.