Abstract: Median inferences are appealing for fitting an ARMA model with heteroscedastic errors to financial returns, because such returns are known to have heavy tails. To ensure that the model is still related to the conditional mean, we test for a zero mean of the errors by using a random weighted bootstrap method to quantify the estimation uncertainty. The proposed test is robust against heteroscedasticity and heavy tails, because we do not infer heteroscedasticity and need fewer finite moments. Simulations confirm that the proposed test exhibits good finite-sample performance in terms of size and power. Empirical applications show that we need to exercise caution when interpreting the model after using a median inference.

Key words and phrases: ARMA model, heteroscedasticity, weighted estimation, zero mean.