A note regarding ARCH and threshold processes: results from a Monte Carlo study

Abstract

Many economic relationships are non-linear. Hence, when analysing economic data it is important to identify any non-linearity. The primary type of non-linearity examined by economists is the ARCH-class model. However, other types of non-linear processes may be expected in economic and financial data. One of these is the threshold-class autoregressive process. This paper finds that the power of standard ARCH pre-test procedures for detecting threshold type non-linearity is very poor under certain parameter specifications; and that ARCH may be ‘detected’ in a significant number of cases even though the true process is of the threshold class. Thus care should be taken when interpreting ARCH pre-tests in economic series that are likely to contain threshold boundaries.