A minimum distance lack-of-fit test in a Markovian multiplicative error model

This paper proposes a lack-of-fit test for a parametric specification of the conditional mean function in a Markovian multiplicative error time series model. The proposed test is based on a minimized distance obtained using an integral of the square of a certain marked residual process. The asymptotic null distribution of the proposed test is model dependent and is not free from the underlying nuisance parameters. We propose a bootstrap method to implement the test and establish that the proposed bootstrap method is asymptotically valid. A finite sample simulation study that evaluates the empirical level and power is included. It compares the finite sample performance of the proposed test with several competing tests from the literature.