Diverse opinions exist in the time series analysis of energy and related indices, difference in methodology, sample size, and time variation. This paper will make a conscious effort to converge the divergent outlooks. To accomplish this essential task, five energy indices consisting of energy consumption (EC), gross domestic product (GDP), carbon dioxide emission (CDE), the human development index (HDI), and oil price (OP) were selected. Two analytical methods were adopted, namely logarithmic and normalized techniques, which are designed to complement each other in drawing unfalsified statistical inference concerning the causality between the energy indices. The methods were subjected to four statistical tests and analyses: the augmented Dickey-Fuller, cointegration, pairwise Granger causality, and vector error correction model (VECM). Irrespective of prevailing challenges, both logarithmic and normalized techniques unanimously filtered out causalities. This consisted of neural flow between oil price and energy consumption, gross domestic product and carbon dioxide emission, and energy consumption and the human development index, unidirectional flow between energy consumption and the human development index, oil price and energy consumption, gross domestic product and carbon dioxide emission, and the human development index and oil price, whereas a normalized technique established bidirectional flow between gross domestic product and the human development index, and the human development index and oil price. Pertinently, the research suggests appropriate policies that will generate sustainable development in all the causal directions. Assiduously, the overwhelming agreement between both techniques at the 0.05 level is recommended for further validation with more modern econometric tests.