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I am currently conducting a study regarding lifelong learning in EU member states. As part of this research, I analyze several indicators for the following time series: 2007, 2011 and 2013.

I have hit a roadblock with one of my indicators - Internet use activities (Individuals who used Internet, in the last 3 months, for training and education). The issue is that data is only available on Eurostat for the years 2011 and 2013, data for 2007 is missing for all EU member countries.

My question is if there is any way to estimate the missing data from 2007 based on the data available in 2011 and 2013, which has no missing values (my dilemma comes from the fact that I need to estimate past values, not predict future missing values).

For clarification, this is the data:

| GEO/TIME                                         | 2007 | 2011 | 2013 |
|--------------------------------------------------|------|------|------|
| Austria                                          | -    | 3    | 3    |
| Belgium                                          | -    | 3    | 5    |
| Bulgaria                                         | -    | 2    | 2    |
| Cyprus                                           | -    | 2    | 3    |
| Czech Republic                                   | -    | 3    | 2    |
| Germany (until 1990 former territory of the FRG) | -    | 5    | 5    |
| Denmark                                          | -    | 7    | 7    |
| Estonia                                          | -    | 5    | 5    |
| Greece                                           | -    | 4    | 4    |
| Spain                                            | -    | 10   | 10   |
| Finland                                          | -    | 12   | 13   |
| France                                           | -    | 4    | 5    |
| Croatia                                          | -    | 2    | 5    |
| Hungary                                          | -    | 5    | 4    |
| Ireland                                          | -    | 5    | 5    |
| Italy                                            | -    | 4    | 5    |
| Lithuania                                        | -    | 7    | 8    |
| Luxembourg                                       | -    | 6    | 9    |
| Latvia                                           | -    | 4    | 3    |
| Malta                                            | -    | 6    | 5    |
| Netherlands                                      | -    | 5    | 7    |
| Norway                                           | -    | 6    | 10   |
| Poland                                           | -    | 2    | 2    |
| Portugal                                         | -    | 3    | 2    |
| Romania                                          | -    | 4    | 3    |
| Sweden                                           | -    | 5    | 8    |
| Slovenia                                         | -    | 5    | 3    |
| Slovakia                                         | -    | 2    | 4    |
| United Kingdom                                   | -    | 6    | 9    |
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Take the data from 2011 to 2013 and reorder it so that the first value is the true value for 12/2013 , the second value is 11/2013 and the 36th value is 1/2011 . Now forecast/model this series for 48 periods . Your first forecast will be an estimate for 12/2010 and your 48th forecast will be an estimate for 1/2007.

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  • $\begingroup$ The issue is that data is also missing for 2012, 2009 and 2008 (these statistics are collected every 3 years), so I don't know if this approach would give the desired results. $\endgroup$
    – alexius
    Commented Dec 15, 2015 at 19:50
  • $\begingroup$ This seems to assume monthly data. The OP has now clarified that there are just two annual values. $\endgroup$
    – Nick Cox
    Commented Dec 15, 2015 at 19:52
  • $\begingroup$ Oops my bad ...But if I had three annual numbers , I could fit a trend line and reverse forecast the prior 4 years just as I described for monthly data. $\endgroup$
    – IrishStat
    Commented Dec 15, 2015 at 20:48
  • $\begingroup$ Or if I had two I would also fit a trend line and reverse forecast 2009 and 2007 and then linearly interpolate to get 2008, 2010 and 2012 $\endgroup$
    – IrishStat
    Commented Dec 15, 2015 at 21:13
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    $\begingroup$ Croatia $2$ and $5$. Linear fit implies $-4$ in 2007. As the data are evidently rounded to the nearest percent as well, "can't be done reasonably" is another answer. $\endgroup$
    – Nick Cox
    Commented Dec 16, 2015 at 14:50

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