Initial tests and optimum model: A problem of misleading results in real exchange rate behaviour

Two common statistical tests and statistical models are applied to the real exchange rate of several Southern European countries. Initial tests show that real exchange rate of the considered countries mostly behaves as linear process, particularly long memory. However, the result of model checking is not always consistent with this, meaning that the initial tests do not always guide to the optimum model. Estimation and model checking become important and crucial for the case in which there are misleading properties between the competing processes.