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Traditional grey models are integer order whitening differential models; these models are relatively effective for the prediction of regular raw data, but the prediction error of irregular series or shock series is large, and the prediction effect is not ideal.

The new model realizes the dynamic expansion and optimization of the grey Bernoulli model. Meanwhile, it also enhances the variability and self-adaptability of the model structure. And nonlinear parameters are computed by the particle swarm optimization (PSO) algorithm.

Establishing a prediction model based on the raw data from the last six years, it is verified that the prediction performance of the new model is far superior to other mainstream grey prediction models, especially for irregular sequences and oscillating sequences. Ultimately, forecasting models are constructed to calculate various energy consumption aspects in Chongqing. The findings of this study offer a valuable reference for the government in shaping energy consumption policies and optimizing the energy structure.

It is imperative to recognize its inherent limitations. Firstly, the fractional differential order of the model is restricted to 0 < a < 2, encompassing only a three-parameter model. Future investigations could delve into the development of a multi-parameter model applicable when a = 2. Secondly, this paper exclusively focuses on the model itself, neglecting the consideration of raw data preprocessing, such as smoothing operators, buffer operators and background values. Incorporating these factors could significantly enhance the model’s effectiveness, particularly in the context of medium-term or long-term predictions.

This contribution plays a constructive role in expanding the model repertoire of the grey prediction model. The utilization of the developed model for predicting total energy consumption, coal consumption, natural gas consumption, oil consumption and other energy sources from 2021 to 2022 validates the efficacy and feasibility of the innovative model.

These findings, in turn, provide valuable guidance and decision-making support for both the Chinese Government and the Chongqing Government in optimizing energy structure and formulating effective energy policies.

This research holds significant importance in enriching the theoretical framework of the grey prediction model.

The highlights of the paper are as follows:

1. A novel grey Bernoulli prediction model is proposed to improve the model’s structure.

2. Fractional derivative, fractional accumulating generation operator and Bernoulli equation are added to the new model.

3. The proposed model can achieve full compatibility with the traditional mainstream grey prediction models.

4. Energy consumption in Chongqing verifies that the performance of the new model is much better than that of the traditional grey models.

5. The research provides a reference basis for the government to formulate energy consumption policies and optimize energy structure.

A novel grey Bernoulli prediction model is proposed to improve the model’s structure.

Fractional derivative, fractional accumulating generation operator and Bernoulli equation are added to the new model.

The proposed model can achieve full compatibility with the traditional mainstream grey prediction models.

Energy consumption in Chongqing verifies that the performance of the new model is much better than that of the traditional grey models.

The research provides a reference basis for the government to formulate energy consumption policies and optimize energy structure.

The purpose of this paper is to analyse the relationship between foreign direct investment (FDI) inflows and economic growth with a special focus on the institutional environment at the state level. FDI-led economic growth and economic growth-led FDI have two dominant theoretical foundations, but empirical research supports contradictory findings. These perspectives largely ignore the institutional environment, assuming institutions to be background information.

To examine the causal relationship between FDI, the Granger causality method has been used. The impact of FDI inflows and other institutional factors on economic growth has been examined using the panel data regression method. The principal component analysis (PCA) method has also been used to develop indexes for some variables.

Results indicate a two-way Granger causality between FDI inflows and economic growth at the state level. Infrastructures, education expenses, labour availability and gross fixed-capital formation (GFCF) are positive and significant determinants, whilst corruption and FDI inflows are leaving negative impact on state-wise economic growth.

This study contributes to the body of the literature in four different ways: first, it empirically examines the trends and patterns of subnational FDI inflow and economic growth disparity in India; second, it examines the causality between FDI and economic growth. Third, with the institution-based paradigm in international business, it investigates how institutional variables affect the expansion of the economy. Fourth, it extends prior research by examining the link at the state level using a large panel data set made up of 29 states and 7 union territories (UTs) over the years 2000–2019.