Time Series Analysis of Global Energy Indices: Logarithmic and Normalized Techniques for Developmental Studies

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.

GRB 210121A: A Typical Fireball Burst Detected by Two Small Missions

The Chinese CubeSat Mission, Gamma Ray Integrated Detectors (GRID), recently detected its first gamma-ray burst, GRB 210121A, which was jointly observed by the Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM). This burst is confirmed by several other missions, including Fermi and Insight-HXMT. We combined multimission observational data and performed a comprehensive analysis of the burst’s temporal and spectral properties. Our results show that the burst is relatively special in its high peak energy, thermal-like low-energy indices, and large fluence. By putting it to the E p –E γ,iso relation diagram with assumed distance, we found that this burst can be constrained at the redshift range of [0.3, 3.0]. The thermal spectral component is also confirmed by the direct fit of the physical models to the observed spectra. Interestingly, the physical photosphere model also constrained a redshift of z ∼ 0.3 for this burst, which helps us to identify a host galaxy candidate at such a distance within the location error box. Assuming that the host galaxy is real, we found that the burst can be best explained by the photosphere emission of a typical fireball with an initial radius of r 0 ∼ 3.2 × 107 cm.