How to predict future data by running AR Regressions

[Hammad Farooqui]

Hello everyone, I have time-series data from the year 2007 to 2019 looking into Rail & Inland Waterways Transportation. I have carried out the first difference of the two variables 'Rail Freight' and InlandFreightTonneKm' to create the variables 'RailFreightFirstDifference' and 'INWFreightFirstDifference'. Based on these two variables created, I carried out the ADF test separately and the time-series were stationary. Similarly, I carried the Akaike Information Criterion (AIC) and found the optimal lags in both cases were two.

Thus, my regression equations are the following:

ΔRoad_t = β₀ + β₁ΔRoad_t-1 + β₂ΔRoad_t-2 + ɛ_t
ΔRail_t = β₀ + β₁ΔRail_t-1 + β₂ΔRail_t-2 + ɛ_t


I am facing the following problem: I cannot understand how should I run the regression so that from the regression results, I could calculate predictions in the changes in Rail and Inland Transportation from 2020 to 2030.

I have also attached the example of the variables in the data set using dataex.

* Example generated by -dataex-. To install: ssc install dataex
clear
input int year double(RailFreight InlandFreightTonneKilometers) float(RailFreightFirstDifference INWFreightFirstDifference)
2007 5215857.5    28064         .        .
2008   5517042    29483  301184.5     1419
2009 6001460.5    37085  484418.5     7602
2010 6258546.5    40259    257086     3174
2011 6676754.5    38098    418208    -2161
2012 6492099.5    30629   -184655    -7469
2013   6656881    24183  164781.5    -6446
2014   6812517    28468    155636     4285
2015 6542969.5    34597 -269547.5     6129
2016 6205501.5    38308   -337468     3711
2017   6934109 41297.89  728607.5  2989.89
2018   7389954 47421.54    455845  6123.65
2019 7081282.5 44412.36 -308671.5 -3009.18
end