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I am doing a time-series data analysis. The idea is to produce a forecast from the regression output. I am regressing Air traffic passengers of country A with GDP/capita of country A.

I am getting very high R² (0,97) by regressing absolute values of Air traffic passengers of country A with GDP/capita of country A (p.value<0,05)

I am getting low R²(0,35) by regressing the same variables but that time, by taking the %growth of those variables. (p.value<0,05)

What is the most accurate in this case? regress absolute values or regress the %growth?

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  • $\begingroup$ You are right, absolute values is not precise enough and can have other meanings. When I said "absolute" I meant the real value of the gdp/capita and the real number of passengers (in units) $\endgroup$ – IlvarNourtan Jul 30 at 10:29
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Use the observed values as there may be lag structure needed for GDP (X) that may be different than the lag structure need for air traffic passenger data (Y) . You can always subsequently express the change in passenger forecast as a percentage of the previous value as it relates to the change in GDP as it relates to the previous value of GDP .

Finally to get correct/honest prediction limits for passenger data (Y) you may/will need to account for the uncertainty in GDP (X) predictions and possible re-occurring anomalies.

You might want to read https://autobox.com/pdfs/regvsbox-old.pdf which discusses some of the opportunities that are available when you have time series data and some of the pitfalls when you use simple OLS.

I surmise you ran a simple OLS of Y versus X and obtained .97 as the Rsq AND then you created two new series Y1 and X1 where Y1=[Y(t)-Y(t-1)]/Y(t-1) and X1=[X(t)-X(t-1)]/X(t-1) and obtained .35 when you regressed Y1 and X1 . This specification is probably suspect for a ton of reasons whereas a SARMAX https://autobox.com/pdfs/SARMAX.pdf is much more general approach. Your specification of the model (two ratios) is a possible model but not probable because it is based upon presumption.

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  • $\begingroup$ Many thanks for this IrishStat. though, I don't undersand why use absolute values and not %growth would allow a lag between passengers and GDP/capita? $\endgroup$ – IlvarNourtan Jul 30 at 10:08
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    $\begingroup$ It could BUT it is always IMHO much cleaner to use observed data rather than derived data (secondary data) due to possible obfuscation (KISS). $\endgroup$ – IrishStat Jul 30 at 10:14
  • $\begingroup$ Noted, never heard about the obfuscation. Thank you again for that. $\endgroup$ – IlvarNourtan Jul 30 at 10:21
  • $\begingroup$ If you are happy with my response please accept it to close the question $\endgroup$ – IrishStat Aug 15 at 8:18

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