thanks nester. i mean i need to suppress the variations of level data of variables. e.g. interest rate is in %, but housing price is an index number. i try to test bubble in housing market. Do you know how to select lag numbers in error correction models? kind regards

thanks nester. i found helpful. you mention i should use log-log in first answer, does it mean i should log twice of my data at level. e.g. log(log(housing price index))? in addition, is it ok i put interest (level, %) together with other variables at log to perform test e.g. (OLS, engle-granter cointegration test)? kind regards.

your variables should be consistent, you can not use log variables with index ones because each one has its own interpretations, I suggest to unify all your variables first, say by log, then as suggested by Clech, check for stationarity, and if you need to use first differences or not, followed by cointegration tests. And referring to your initial question, yes log technique squeeze data differentials and reduce outliers. Worth mentioning you should use Ln not Log. for the reasons, you can google it. you will find plenty of resources explaining the difference between them. 

If you think that a shock causes a variable to grow by a fraction then it is usual to use a log transformation of the variable in time series analysis. Consider a small country where a variable (think gdp) might have a value of 100 before a shock and 103 after the shock. A corresponding large variable might have GDP of 1000 before the shock and 1030 after the shock.  in levels in the small country is +3 and the large country +30.  If you do the calculations you will find that log(value after shock) - log(value before shock is approximately .0.0295588 in both cases. The use of logs stabilizes the effects of shocks as the variable increases.

Consider an asset price P_0 and returns r_1, r_2 r_3 in years then the ammount of the asset iafter three years is P_3 = P_0*(1+r_1)*(1+r_2)*(1+r_3). In log terms this is 

log(P_3) = log(P_0 * (1+r_1) * (1+r_2) * (1+r_3)) 

log(P_3) = log(P_0) + log(1+r_1) + log(1+r_2) + log(1+r_3) and if returns are small

log(P_3) = log(P_0) + r_1 + r_2 + r_3

Thus if the returns are stationary P_t is I(1).

This kind of logic applies to many economic variables as used in time series. prices volumes and some flows.

If r is a continuously compounded interest rate and P_1 is the value in year one then the value in year  is P_2 = P_1 * exp(r). Taking logs we get

log(P_2) - Log(P_1) = r

Thus a continuously compounded interest rate is the effect of a log difference like the growth rates above.

As a council of perfection I would recommend that one use convert % changes to continuous growth rates In the example above the 3% growth rate became a continuous growth rate of   0.0295588 and the difference is not significant. If the interest rates are large it can make a difference. Log differences are additive like most models percentage changes are not. A 50% fall reduces a value from 100 to 50.  A subsequent  50% rise only brings you back to 75.  If your variable changes a lot or goes up and down over the sample period you should use continuously compounded rates. Your explanations to management may have to be converted to percentage changes after your analysis.