I have data on carbon emissions of a sector for the last 25 years. I want to know the best possible options available for forecasting future carbon emissions of the sector based upon yearly data.
It is important, unequivocally, to have observed values rather than relying on estimates to make Forecasting. Because, in fact, the forecast is not certain values but approximations to the real reality in the near or distant future.
There is, however, no effective technique of prediction, some are more efficient than others in a specific context. In other words, it is necessary to make a chronological analysis of the series: study of seasonality, stationarity, tendency, cyclic ... etc.
Then comes the stage of the preview approach for your series, commonly the Box and Jenkins method, the Engle method, the moving average method, the exponential smoothing method, the Hot-Winter method, the least square method. ..etc.
Among these methods and others that I have not mentioned, the Box-Jenkins approach is often solicitated in the predictive analyzes.
Each of these methods in principle require steps to be followed during the forecasting, some such as serial identification, serial estimation, validation and then finally the series prediction, associated with a confidence interval .
On the other hand, nothing prevents you to be able to consider several forecast techniques at once, and then compared them on their forecasting qualities namely: Sum Square Error, Mean Square Error, Root Mean Square Error and Mean Absolute Error and Mean Absolute Percentage Error and finally favor the best approach that seems to fit well to your series.
The econometric models that have proven more accuracy on prediction with minimun information and no restrictive assumption, are VAR models. However with 25 time observatios i would recommend a Bayesian VAR (BVAR), because the prior in this kind of model can help you deal with the small sample issue.
I can support you by applying Rough Set Theory. Please find below link:
www.redtoolkit.com
I would presume that these carbon emissions are related to the sector output, to some measure(s) of technology in the sector and possibly to some other variables. I would think that you would need to also produce some forecasts of these variables to provide an appropriate forecast.
An ARIMa process can be understood as producing a constant or trend forecast, estimating the current disequilibrium and then working out the path of the return to the produced constant or trend. It might be better to use an ARIMAX system which would take into account the the variables that determine emissions.
To evaluate your system take a sub-sample of say the first 15 to 20 0f your observations and use your favored methodology to forecast one step ahead (out of estimation sample). Then add one observation, re-estimate and forecast one step ahead. Continue the process until you reach the end of the sample. You now have a series of one step ahead out of sample forecasts errors. An analysis of these out of sample forecast errors can be very revealing. The analysis of these forecast errors is covered in many good books on forecasting. If you are using good forecasting software this should produce an analysis of these out of sample errors.
John C Frain You are right actually I am working with Input-output models.
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