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Economic data often get revised after first release, usually 1-3 months. Obviously we cannot use the revised value in the month it's first released. How do we use the revised values in time series analysis like arima?

Suppose we want to regress X vs it's lagged values, and all values are revised 1 month after first release and no further revises. Is the following correct way to do the regression? Is there any packages to do so?

X_May ~ X_Apr_first_release + X_Mar_revised + X_Feb_revised + ... 

Edit:

@GeoMatt22 the above equation is not by year, the clearer version is:

X(t) ~ X_first_release(t-1) + X_revised(t-2) + X_revised(t-3) + ...
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  • $\begingroup$ It's not quite clear what kind of answer you're seeking $\endgroup$ – Glen_b -Reinstate Monica Apr 27 '17 at 1:24
  • $\begingroup$ @Glen_b It's unclear because there are multiple questions or I didn't explain what's economic data revision? $\endgroup$ – user3226167 Apr 27 '17 at 1:36
  • $\begingroup$ 1. When you say "how do we use the revised values?" it's not at all clear what sort of thing you're asking for. Normally wouldn't you simply fit your model using the newest available data? Given that's both so short and so obvious that it would be strange to ask, I presume you intend to ask something else than what it looks like, or there's some complication that's not obvious to a naive reader (which you should explain). 2. When you're asking "is the following correct what to do the regression" it's not clear what the alternative is; it's certainly a regression model, ... ctd $\endgroup$ – Glen_b -Reinstate Monica Apr 27 '17 at 1:44
  • $\begingroup$ ctd... but there are various reasons that might not be suitable, depending on the characteristics of the time series. 3. When you ask for packages, it's not at all clear what those packages are intended to do that a regression package doesn't already do. ... broadly, across the post you seem to be assuming we comprehend something about the situation, but I am not sure what it is I'm even missing (and I assume many other readers will not quite see what the issue is either). ... .One thing that was fairly clear was what you mean by "data revision" -- that's not the issue. $\endgroup$ – Glen_b -Reinstate Monica Apr 27 '17 at 1:44
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    $\begingroup$ This is a very common problem in econometrics. You can certainly use the latest version of each data point, ignoring the fact that they will be revised later. Any package that does the time series models you want will work. You can also study the revision dynamics themselves (across vintages) if you have access to real-time datasets. This will allow you to answer slightly different questions (e.g. "what is the best forecast of the final, revised figure, given the preliminary figure and past figures?") $\endgroup$ – Chris Haug Apr 27 '17 at 2:21
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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?

UPDATE

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.

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