You're alluding to what is called "real-time data in economics", popularized by Diebold. The idea's that you use the data that was available at the time of decision making or analysis. Look at Section 3 to see the methodology they use to process the real-time data in this paper titled "Forecasting Output with the Composite Leading Index"
For instance, you conjecture that the demand for luxury goods depends on the previous month's GDP. Now the question is what is the mechanism of this cause-effect?
- Is it that luxury item buyers look at the published GDP number and proceed with buying decision?
- Or they don't really look at the GDP number but make a decision based on their finances and business outlook?
In the former case you definitely have to take into account the GDP data release schedule. So, for the demand in April, you can't use the final release of Q1 GDP because it will not be available in April yet.
For the second case you may argue that the final release numbers of GDP can be used, because they will best reflect the state of the economy that is the real driver of the demand.
Your case could be different than both of these cases: you are building an autocorrelation model. However, you may ask the same two questions about cause and effect, and depending on the answer make a call in terms of the treatment of the relases. Does the published number affect the next number? Or does the true value affect the next month?
This is also related to nowcasting in economtrics, see a brief note by Hansen here. The idea's to forecast the current quarter's numbers such as GDP. The final GDP number is published with a lag of few months, even the preliminary releases come with lags of weeks. So, nowcasting attempts to estimate the GDP number that will be published for this period based on real-time series such as TIPS yields or more frequent series such as unemployment and inflation.