Climate Change Models

 I am just sharing here some climate change models.  The main objectives included: 

1) being able to fit the historical World temperature data; 

2) being able to forecast World temperature using true out-of-sample or Hold Out testing; and 

3) being able to demonstrate causality between CO2 temperature concentration and temperature level. 

The models disclosed within this following link:

Climate Change Models 

... were surprisingly successful in meeting objectives 1) and 2).  They did very well at fitting the historical temperature data and forecasting temperature (out-of-sample).  By just using CO2 concentration (in either nominal or log transformation) as the main independent variable, the models could reasonably accurately estimate or predict temperature level.  

The most surprising model was a Vector Autoregression (VAR) model using just one single lag (1-year lag given the yearly frequency of the data).  And, this same model using historical data up to 1981 was able to predict reasonably accurately yearly temperatures from 1982 to 2020!  In decades of modeling time series, I have never encountered a model that works so well (either developed by myself or anyone else).  The most surprising thing is that this same VAR model does not even use the known values of the independent variable (natural log of CO2 concentration) from 1982 to 2020.  Without feeding any information to the VAR model over the out-of-sample period, it still could predict temperature pretty well.  

Notice how the VAR forecast over the 1982 to 2020 period is typically much under + or - 0.2 degree Celsius off.  

Going back to the third objective of the climate change models regarding confirming statistical causality between CO2 concentration and temperature, the modeling results using Granger causality methodology were far more humble.  Establishing Granger causality was rather challenging.  This was probably due to the temperature level variable being so autocorrelated.  Notice that this was not a technical flaw within any of the developed OLS regressions or VAR models because the two variables were very much cointegrated (as tested using Cointegration regressions).