Diagnostic checking of the vector multiplicative error model

In many situations, we may encounter time series that are non-negative. Examples include trading duration, volume transaction and price volatility in finance, waiting time in a queue in social sciences, and daily/hourly rainfall in natural sciences. The vector multiplicative error model (VMEM) is a natural choice for modeling such time series in a multivariate framework. Despite the popularity and extensive use of the model, very little work has been done on the area of diagnostic checking which however provides useful information about the adequacy of model fitting. In this paper, the asymptotic distribution of residual autocorrelations is derived and used to devise a new multivariate portmanteau test for diagnostic checking. Simulation studies are performed to assess the performance of the asymptotic result in finite samples. An empirical example is also given to demonstrate that the commonly used goodness-of-fit test may lead to a misleading result in the case of the VMEM.