# White noise for level, log and log differences data sets

I am using eviews 7 and I have 3 data sets for DAX stock market index: level (dax), log (ldax), and log differences (dldax). I need to check whether the error terms of these data sets are white noise or not.

Attempt: I am estimating an equation $y_t=c+\beta y_{t-1} +v_t$ for each data set. Then, I perform the residuals diagnostics on each. For level data set (dax) looking at the graph of the residuals is enough to see that the error term is not white noise: the variance is not constant. However, I am having difficulties with determining whether the error terms of log (ldax) and log differences (dldax) data sets are white noise or not. The log (ldax) data set is not stationary and the auto correlation is very high while log differences (dldax) data set is stationary and has no auto correlation. I also checked the stationarity of these sets by Augmented Dickey Fuller test. So when I estimate the equation I listed above and check the residuals it looks like the error terms of both data sets are white noise. Here are the graphs for the log:
and for the log difference:

Also the correlogram of the residuals shows no auto correlation for both. So the error terms of both log and log differences are white noise, but this does not make sense because log data set is not stationary. Am I missing something?

Thank you for your help. If something is confusing or you need more info let me know. I will make necessary edits.

• @gung thanks. I could not add graphs myself due to low reputation. – Koba Nov 19 '12 at 20:57
• No problem, @Dostre, welcome to the site. – gung Nov 19 '12 at 21:07