Is there an absolute goodness of fit measure for ARIMA models? I'm currently trying to make my first ARIMA model.  In my limited experience with linear regressions I find that R-squared gives me a pretty good absolute idea of how the model performs.  I haven't found anything similar to that with ARIMA models.  I know that there is AIC and SBC, but from my understanding they don't mean much by themselves and are used to compare the goodness of fit to other models.  Am I correct in my understanding of AIC and SBC?  Is there a metric that is similar to R-squared for ARIMA models in that it is a standalone measure of goodness of fit?
 A: The Box-Ljung residuals can be used to assess the fit of the time series model. Of course, there are no absolutes and all measures have drawbacks. I am not sure how one would interpret $R^2$ in the context of a time series. Also, ARIMA models are not linear models; they are more general.
Besides the many threads on this site covering these types of models, you can find out a lot about them in the most current edition of Box and Jenkins book titled Time Series Analysis: Forecasting and Control. This book is now in its 5th Edition published in June 2015 by Wiley. Additional co-authors include Gregory C. Reinsel and Greta M. Ljung. In addition, the bootstrap approach to time series analysis is covered in a number of books including my book An Introduction to Bootstrap Methods with Applications to R which I coauthored with Robert A. LaBudde and was also published by Wiley in 2011.
A: $R^2$ is as valid for ARIMA models as it is for linear regression models. In both cases it measures the proportion of the total variance that is explained by the model. It also has the same drawbacks for ARIMA as for linear regression models. 
I do not see why goodness of fit should be measured in different ways for ARIMA vs. linear regression, so your question reduces to a more general question of measuring goodness of fit in linear models. That has been discussed in other threads under the tag goodness-of-fit.
A: There are typically no "absolutes" when assessing model performance. For a simple and realistic alternative to in-sample measures like BIC, R-squared, etc, try what I call "percent of variation explained," which I define as $1-\frac {\|\epsilon\|}{\|y-m\|}$ where $\epsilon$ are your forecast errors, $y$ is your observed out of sample time series, $\|\cdot\|$ is an appropriately-chosen norm, and $m$ is a measure of center for $y$ according to your choice of norm. This metric will be equal to 1 only if your model perfectly fits $y$.
That means to first split your data into two sets, build your model on the first set, check this metric on the second. Or, you can also try what's known as time series cross validation.
Googling this topics will complete the picture if it sounds at all vague.
