What value of R-squared should you report to your boss or client? If you used
regression analysis, then to be perfectly candid you should of course include the Rsquared
for the regression model that was actually fitted--i.e., the fraction of the
variance of the dependent variable that was explained--along with the other details of
your regression analysis, somewhere in your report. However, if the original series is
nonstationary, and if the main goal is to predict the level (rather than the change or the
percent change) of the series, then it is perfectly appropriate to also report an
"effective" R-squared calculated relative to the variance of the original series (deflated
if appropriate), and this number may be the more important number for purposes of
characterizing the predictive power of your model. In such cases, it will often be the
case that most of the predictive power is derived from the history of the dependent
variable (through lags, differences, and/or seasonal adjustment) rather than from
exogenous variables. This is the reason why we spent some time studying the
properties of time series models before tackling regression models.