Is the R-square valid in a Regression model with Lag values of the Dependent Variables I was working on some Time dependent data. Due to Client requirements I am forced to use LInear REgression for the modelling instead of Time series regression techniques like ARIMA.
In order to not offend the Gods of data analysis, and also the Client, I was trying to cast a ARIMA model into a LInear Regression kind of framework. For that, I ended up including lagged values of the dependent variables (To imitate AR terms). End goal is to add terms so that the error terms are white noise.
Since what we have is not a text-book Linear Regression model, I had some concerns if Rsquare would be valid in such a situation. Could somebody please shed some light on the appropriateness of Rsquare in this situation of a Linear REgression with lagged dependent variable?
 A: Yes, the $R^2$ is valid. 
Autoregressive models (with or without exogenous regressors) can be estimated using OLS as they satisfy the standard regression assumptions (where the requirement of independent regressors is replaced by a requirement for predetermined regressors). As far as I know, AR(X) and VAR(X) models are often estimated by OLS, and $R^2$ is used without problems. 
I agree with @ssdecontrol that If it only has autoregressive components, it already is linear regression.
A: I think you have two options to consider if you do not want to go with Time Series like ARIMA.
The first one is Generalized Linear Models, which is basically a linear regression that allows you to characterize the residuals with other distributions other than Normal. This includes lots of methods such as Ridge Regression, LASSO, and Automatic Relevance Determination Regression.
The second is Exponential smoothing where you average out the smooth out the previous set of data. This includes Holt winters (for trends), Brown model, and there is also a dampened model for things like growth and decay.
Not sure if this helps but you can also put prediction bands on data or use something like GARCH to have a range for your predictions.
