Methodology for selecting assessment periods of Logarithmic Mean Divisia Index decomposition techniques

Logarithmic Mean Divisia Index Decomposition Analysis (IDA-LMDI) is a widely used statistical technique in the engineering, economics, energy, and environmental sciences. The main application of the IDA-LMDI method is to identify the drivers that explain the change in carbon dioxide emissions of a country or region over a given time span. Therefore, proper selection of each time period is fundamental to ensure that its implemented accurately and meaningful results are obtained. In the literature, decomposition periods have been defined based on a single-, n-, or one-year period. However, in all these cases, the duration of each period was fixed and depended on arbitrary criteria. The adoption of fixed periods did not capture specific changing trends in the time series under analysis. Therefore, this study presents a new methodology for defining the number of periods and their extent to obtain unbiased drivers using the IDA-LMDI technique. The period selection was defined according to the mean square error of all feasible combinations. We illustrated the application of this method in two cases. First, an illustrative example was successfully validated using multivariate linear regression. Second, we obtained the Kaya factors of the Organisation for Economic Co-operation and Development countries of Europe. The results were compared with the decomposition results provided by the International Energy Agency on 10-7 year fixed periods. The results showed that the application of fixed periods in IDA-LMDI dismissed critical drivers that could only be captured with the proper selection of each period under analysis. Therefore, the proposed methodology will aid in accurate information analysis and decision making in energy policy and other applications. The proposed method has a broad application and could be applied to any decomposition method in the Divisia family.