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.
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?