Since econometric analyses can be misleading if the data generating process is different on various time scales, we test whether the significance can be confirmed on every time scale.

Econometric results are questionable if aggregated over time scales with different data generating processes. In financial markets, market participants have varying objectives with different corresponding investment horizons.

We need to define the competing models, and the divergence type statistic to measure the departure of each proposed parametric model from the data generating process.

Although our proposed model selection procedure does not require that the data generating process belong to either of the competing models, we consider the two limiting cases p = 0.00 and p = 1.00 for they correspond to the correctly specified cases.

In Table 3, the data generating process is chosen such that the log-normal model and the exponential model are approximatively equally close to it.

However, it is possible that the Data Generating Process of real output is characterized by an exogenous change in the level of the series or an exogenous change in the rate of growth instead of a break in both the trend and the level.

In the presence of nonlinearities in the data generating process, where the speed of adjustment towards the equilibrium is asymmetric, the traditional linear unit root tests, because of their low power, often fail to reject the null hypothesis of unit root behavior.

In model (2) under the null hypothesis of the presence of a unit root, the speed of mean reversion parameter is zero ([theta]= 0) and it is positive ([theta] > 0) under the alternative hypothesis of a nonlinear but globally stationary data generating process [see, for further mathematical details, Kapetanios et al.

Dcterministic terms include both the constant and time trend As discussed above, ignoring the presence of structural breaks in the data generating process would result in size distortion and lower the power of the tests.