Dear Reynaldo, Sure u can do it as you propose. 

Dear Casioni, lot of thanks for your quick answer. Then I can proceed following all alternatives that I considered right in my explanation, right?

This is a common issue when working with financial data and economic data.  Many of these time series have a unit root I(0) process inherent in their nature.  

Any time series with I(0) or close to I(0) process (integrated) should be differenced. Also, due the scaling effects, you should either use the first differences of the natural logs of the dependent variable (if the series is bounded away from zero and conforms at least partly to a long-normal distribution) or use the transformation you suggested to avoid heteroskedasticity in the transformed dependent variable.  

With regard the non significant variables in the short run, Should I remove them of the "short run" equation?

If i need to remove them, In case that the dependent variable in one of my equations only depends of itself lagged (the other variables were not significant), Should I "forget" about Granger causality, Impulse-Response and so on or they still are useful in the analysis? In this case consider that my interest is not to know if GDP depends of GDP(-1) or GDP (-2). Mi interest is more related to the relationship between GDP and investment rate, for example.

If my interest, is only to know the impact of one or two variables in another one, I just need to care about the first equation in the error correction mechanism (consider that i am working with Eviews) or do I need to analyze also the other equations involved in the system?

Yes, I meant I(1), unit root and possible cointegration.  First differencing and some form of normalizing (taking natural logs before first differences or using percentage change) is required for series such as GDP.  Be aware that with variables such as GDP, unlike many securities price models, you will likely still have significant AR processes (due to advanced commitments and timing); so either some lagged specification is required (assuming you can specify the process) or, at a minimum, you may need to correct the standard errors using the Newey-West or similar HAC method.

There will likely be structural changes and outliers in the data.  There is also likely to be a more complex feedback mechanism between GDP and investment in that increases in GDP may coincide with investment, may lead to investment (increased capacity utlilization with increase in GDP can lead to investment)  and investment may lead to increases in GDP at times.   I would caution against throwing out variables if statistically insignificant, especially if they have a logical theoretical relationship  or are part of the testing protocol in Granger-Sims types of causation tests.  

Senra, 

Every analysis you are carrying out are not far from what is happening around you. If my interest is on a variable(s), I should also be careful not to force the variable(s) to behave the way am expecting. If my data and model specification are right say my transformed variable(s) is ok, therefore, my aprior  expectation is of great important than my expectation.

well, do not remove the non significant variables in the short run from the "short run" equation but check the effect of the numbers of variables you included in equation by looking at the threshold of your Adjusted R2 if u subject the same variables to say OLS. Sometimes the beauty of a model may not allow us to consider the implications of some of our actions. Well take a close look at your transformed variable with in line with the variables you used.

Can I perform time series analysis with I(0) series (obtained by transformation of variables)? -  YES