I have performed a number of tests to detect any presence of autocorrelation in my monthly return series. The test results confirm that the standard errors are not independent. A Durbin-Watson test result shows an upper bound violation with a d-statistics of 2.16, which implicates (first order) negative autocorrelation. A second, Breusch-Godfrey test, performed to examine higher order correlation points outs that for the first 12 lags the tests fails to reject the null of no serial correlation. Isn’t this strange since the test results are contradicting each other?
To get a better understanding of the correlation within the (dependent) variable I also implemented a corrgram. The Q-statistic results in this case shows a significantly autocorrelated data after the first lag (see image). The additional independent variable Q-statistic results show no presence autocorrelation.
What I came across so far while searching on the internet for solutions to solve the autocorrelation are a large number of solutions. In order to obtain meaningful results from my OLS-regression I thought it was best to include a lagged dependent variable in the regression and generate Newey-West standard errors. This is probably a relatively simple but accessible approach for inexperienced statisticians, like myself.
My question is; Is this a correct and sufficient approach of tackling this particular autocorrelation problem in my data, or should I think about more advanced models?
A link to the time series file;Time_Series_Data