AIC , BIC values for linear regression are found to be better than for linear regression with ARMA errors. Why? I have 48 observations and I am fitting a linear regression model with 3 explanatory variables but  on residual analysis the residuals are found to be correlated. So I  fitted a linear regression model with ARMA errors and after that again conducted the residual analysis and they are now uncorrelated but on calculating the AIC,BIC, log likelihood values for both the models, the linear regression model is found to have better values than the linear regression with ARMA errors. What are the possible reasons for this phenomenon ?
 A: One possibility is that the AIC/BIC are computed differently in the two cases. The definition of AIC varies a little between software --- sometimes the constant is omitted, sometimes the value is divided by some scaling factor, sometimes the variance is counted as a parameter, etc.
A: What is you describe is perfectly plausible as the AR/MA model might actually estimate many more parameters. That on it's own might mean that any improvement in the model fit is offset by the penalty AIC/BIC acquires by using extra parameters for the AR/MA terms.
A: Rob Hyndman and user 11852 provide excellent answers.  Just to add to it a bit, one of the main purposes of AIC and BIC is to detect a model overfitting.  And, an ARMA model could be vulnerable to overfitting by adding many more variables compared to a more parsimonious regression structure. 
In the end, AIC and BIC tests on a stand alone basis may not give you all the information you need to make your model selection.  A more straightforward way of detecting model overfitting and differentiating between models is to conduct cross validation, Hold Out, or out-of-Sample testing.  All those methods are very similar.  They consist in testing the models on new data (real or created from the existing time series).  
In view of the above, the definition of an overfit model is a model that fits the history very well, but does not forecast as well.  And, ARMA models given their structure are highly vulnerable to that.  That is not only because they use additional variables.  It is because they use the majority of their information from endogenous variables, or from the time series itself.  Once, you forecast future periods beyond the lags or the lag in the error correcting mechanism in the model, these models forecast accuracy collapse.  That's not something that AIC and BIC capture.  That is what you uncover when you test with new data as mentioned above.  And, that is probably the better way to truly test and compare the accuracy of forecasts between your ARMA model and your simpler regression.  By definition, your regression will not fit the history as well.  And, as you indicated its residuals will often have some degree of autocorrelation and heteroskedasticity that is not as problematic as people think (just make adjustments with Robust Standard Error methodology to ensure that your selected variables are still statistically significant... and you are good).  ARMA models by contrast have typically far cleaner residual behaviors than simple regression, but at what price... The minute you conduct some sort of medium term to long term forecast, in the out periods very often the simpler regression model prevails. 
