I am analysing the effect of monetary policy on output and inflation during crisis and after. Monetary policy is represented by exchange rate, interest rate, money supply and indicator of systemic risk + dummy financial crisis.
I´ve chosen multiple regression analyses with time series to assess differences. The response variable, being a time series, has autocorrelation and heterogenity. I tried to change functional forms in different combination, I used logarithm and finally first differences for all responses. However, after performing these transformations, statistical tests still indicated that autocorrelation was present in these data.
My questions:
In model with the first differences, the Durbin-Watson test obtains the test statistic 2.6. I interpret this as do not reject the null hypothesis, these data are consistent with a lack of autocorrelation. Is this interpretation right? Please reference the image
. I worry that the correlogram residuals looks strange. I don´t understand what this means. Please check the second image. Do somebody know what does that mean?
If I use Breusch-Godfrey test or Ljung Box test of autocorrelation with 20 lags, results show, that there is not autocorrelation, but when I use only 5 lags, the Ljung Box p-value is under 0.05 and we reject the null hypothesis at the 0.05 level and conclude there is autocorrelation.
Are these results contradicting one another? How do I choose which set of results to report?