First difference or log first difference? I am evaluating the effect of covariances between series on returns. That is I run the following regression: $$ r_t = \beta_0 + \beta_1\text{Cov}(Y_t,r_t) + ...$$ 
I have conducted my analysis with both first difference and log(first difference) on the series. That is I can take either $r_t = P_{t+1}- P_{t}$ or  $\ln(P_{t+1}/P_{t})$. (and similarly for $Y_t$)
However, the level of significance of my coefficients is considerably reduced (sometimes they are just not significant anymore) when I use the log rather than the simple first difference to compute the covariance. 
Is there something incorrect in using only the first difference to compute the covariances rather than a log(first difference)?
What am I missing here?
 A: For some time series, like equity prices exchange rates and GDP growth, log returns are approximately invariant, meaning that it is stable over time. One way to see this would be to plot the histogram of the first and second half of the available data, which should be roughly similar, and check a scatter plot of the returns versus their lags, which should show no relationship. 
For these series, changes in prices are a function of the lag of the price. As the price increases, the change increases. This means that the mean and variance changes over time. So if you try to perform a regression of the changes of two series without incorporating this heteroskedasticity, then your standard errors will be wrong. 
The proper procedure (for these types of time series) is to use the log returns for estimation. If you want to forecast the original series, you have to first project the log returns to the future and then convert back to prices. 
A: eviews can forecast the original series and save the time of having to reconvert back to prices. just use brackets when entering the  dependent variable in the equation to be estimated as follows: for example d(log(GBP))
