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This study aims to use gray models to predict abnormal stock returns.

Data are collected from listed companies in the Tehran Stock Exchange during 2005-2015. The analyses portray three models, namely, the gray model, the nonlinear gray Bernoulli model and the Nash nonlinear gray Bernoulli model.

Results show that the Nash nonlinear gray Bernoulli model can predict abnormal stock returns that are defined by conditions other than gray models which predict increases, and then after checking regression models, the Bernoulli regression model is defined, which gives higher accuracy and fewer errors than the other two models.

The stock market is one of the most important markets, which is influenced by several factors. Thus, accurate and reliable techniques are necessary to help investors and consumers find detailed and exact ways to predict the stock market.

Although the Nash nonlinear grey Bernoulli model (NNGBM(1, 1)) is incomparable with respect to its flexibility over traditional grey models, errors are still inevitable in forecasting. The purpose of this paper is to propose a Fourier residual modified Nash nonlinear grey Bernoulli model (FNNGBM(1, 1)) and use it to forecast the nonlinear time series of the international trade of Chinese high-tech products.

A Fourier series is used to modify the forecasting residual of the NNGBM(1, 1) model, so as to improve its forecasting ability. The parameters optimization of FNNGBM(1, 1) is formulated as a combinatorial optimization problem and is solved collectively using the concept of Nash equilibrium.

The simulation and practical application to fluctuation data both prove that FNNGBM(1, 1) could offer a more precise forecast than NNGBM(1, 1) and the Fourier residual GM(1, 1) (FGM(1, 1)). The import/export data of Chinese high-tech products will maintain rapid growth, with corresponding trade balance enlargement; however, there will be a concomitant decrease in the trade specialization coefficient.

This study is deliberately general in its scope and outlook: its focus is mainly on the overall condition of Chinese high-tech products trade. Future research is recommended to analyze specific industrial trade sectors and extraneous influencing factors.

An effective method is proposed to enhance the accuracy of NNGBM(1, 1) model in forecasting a small sample, nonlinear time series.

The widespread application of traditional grey model (GM) in different academic fields such as electrical engineering, education, mechanical engineering and agriculture provided the authors with an incentive to conduct the present empirical research in an accounting field, in particular, auditing practice. In this regard, the purpose of this paper is to employ the nonlinear type of the original GM to forecast the drastically changed data on audit reports, primarily due to the fact that the linear nature of GM is unable to forecast nonlinear data precisely. In essence, this paper adds value to the strand of audit report literature by examining the impact of different financial ratios on auditors’ opinion and then forecasting audit reports by employing GMs.

The grey forecasting model is known as a system containing uncertain information presented by grey numbers, equations and matrices. The grey forecasting model is employed by using a differential equation in an uncertain system with limited data set which is suitable for smoothing discrete data. In addition, the analyses are conducted by applying a sample of top 50 listed companies on the Tehran Stock Exchange during 2011-2016.

The findings suggest that audit reports are most influenced by the current ratio and conversely, least influenced by the ratio of working capital turnover. Moreover, the authors argue that the Nash nonlinear grey Bernoulli model is more precise than the nonlinear grey Bernoulli model and GM in forecasting audit reports.

The current study may give more strength to stakeholders in order to analyse and forecast audit report.

The purpose of this paper is to propose a new method based on nonlinear least squares (NLS) for solving the parameters of nonlinear grey Bernoulli model (NGBM(1,1)) and to verify the proposed model using the case of employee demand prediction of high-tech enterprises in China.

First of all, minimising the square sum of fitting error of grey differential equation of NGBM(1,1) is taken as the optimisation target and the parameters of classic grey model (GM(1,1)) are set as the initial value of parameter vector. Afterwards, the structural parameters and power exponents are solved by using the Gauss-Newton iteration algorithm so as to calculate the parameters of NGBM(1,1) under given rules for ceasing the algorithm. Finally, by taking the employee demand of high-tech enterprises in the state-level high-tech industrial development zone in China as examples, the validity of the new method is verified.

The results show that the parameter estimation algorithm based on the NLS method can effectively identify the power exponents of NGBM(1,1) and therefore can favourably adapt to the nonlinear fluctuations of sequences. In addition, the algorithm is superior to the GM(1,1) model, grey Verhulst model, and Quadratic-Exponential smoothing algorithm in terms of the simulation and prediction accuracy.

Under the framework of solving parameters based on NLS, various aspects of NGBM(1,1) remain to be further investigated including background value, initial condition and variable structural modelling methods.

The parameter estimation algorithm based on NLS can effectively identify the power exponent of NGBM(1,1) and therefore it can favourably adapt to the nonlinear fluctuation of sequences.

According to the basic principle of NLS, a new method for solving the parameters of NGBM(1,1) is proposed by using the Gauss-Newton iteration algorithm. Moreover, by conducting the modelling case about employees demand in high-tech enterprises in China, the effectiveness and superiority of the new method are verified.

A new method for forecasting wind turbine capacity of China is proposed through grey modelling technique.

First of all, the concepts of discrete grey model are introduced into the NGBM(1,1) model to reduce the discretization error from the differential equation to its discrete forms. Then incorporating the conformable fractional accumulation into the discrete NGBM(1,1) model is carried out to further improve the predictive performance. Finally, in order to effectively seek the emerging coefficients, namely, fractional order and nonlinear coefficient, the whale optimization algorithm (WOA) is employed to determine the emerging coefficients.

The empirical results show that the newly proposed model has a better prediction performance compared to benchmark models; the wind turbine capacity from 2019 to 2021 is expected to reach 275954.42 Megawatts in 2021. According to the forecasts, policy suggestions are provided for policy-makers.

By combing the fractional accumulation and the concepts of discrete grey model, a new method to improve the prediction performance of the NGBM(1,1) model is proposed. The newly proposed model is firstly applied to predict wind turbine capacity of China.

The purpose of this paper is to find out which algorithm, among Genetic Algorithm (GA), Particle Swarm Optimizer (PSO), the novel Grey Wolf Optimizer (GWO) and the novel Ant Lion Optimizer (ALO), is the best to obtain the optimal value of the nonlinear parameter γ of nonlinear grey Bernoulli model (NGBM(1,1)) under different situations.

The optimization of γ has been attributed to a nonlinear programming problem at first. The convergence, convergence rate, time consuming and stability of GA, PSO, GWO and ALO are compared in the numerical experiments, and in each subcase the criteria are set to be the same. Over 10,000 iterations have been run on the same environment in order to guarantee the reliability of the results.

All the selected algorithms can converge to the same optimal value with sufficient iterations. But the best algorithm should be chose under different situations.

The optimal value of γ seems to exist uniquely due to the empirical results. And there does not exist a best algorithm for all the cases. The researchers and commercial software developers should choose a proper algorithm due to different cases.

The performance of GA, PSO, GWO and ALO to compute the optimal γ of NGBM(1,1) has been compared for the first time. And it is the original work which uses the GWO and ALO to optimize the NGBM(1,1).

Because of the high volatility with unstable data patterns in the real world, the ability of forecasting price indices is notoriously embarrassing and represents a major challenge with traditional time series mechanisms; especially, most of the traditional approaches are weak to forecast future predictions in the high volatile and unbalanced frameworks under the global and local financial depressions. The purpose of this paper is to propose a new statistical approach for portfolio selection and stock market forecasting to assist investors as well as stock brokers to predict the future behaviors.

This study mainly takes an attempt to understand the trends, behavioral patterns and predict the future estimations under the new proposed frame for the Colombo Stock Exchange (CSE), Sri Lanka. The methodology of this study is carried out under the two main phases. In the first phase, constructed a new portfolio mechanism based on k-means clustering. In the second stage, proposed a nonlinear forecasting methodology based on grey mechanism for forecasting stock market indices under the high-volatile fluctuations. The autoregressive integrated moving average (ARIMA) predictions are used as comparison mode.

Initially, the k-mean clustering was applied to pick out the profitable sectors running under the CSE and results indicated that BFI is more significant than other 20 sectors. Second, the MAE, MAPE and MAD model comparison results clearly suggested that, the newly proposed nonlinear grey Bernoulli model (NGBM) is more appropriate than traditional ARIMA methods to forecast stock price indices under the non-stationary market conditions.

Because of the flexible nonlinear modeling capability, proposed novel concepts are more suitable for applying in various areas in the field of financial, economic, military, geological and agricultural systems for pattern recognition, classification, time series forecasting, etc.

For the large sample of data forecasting under the normality assumptions, the traditional time series methodologies are more suitable than grey methodologies. However, the NGBM is better both in model building and ex post testing stagers under the s-distributed data patterns with limited data forecastings.

The time series forecasting is an essential methodology which can be used for analysing time series data in order to extract meaningful statistics based on the information obtained from past and present. These modelling approaches are particularly complicated when the available resources are limited as well as anomalous. The purpose of this paper is to propose a new hybrid forecasting approach based on unbiased GM(1,1) and artificial neural network (UBGM_BPNN) to forecast time series patterns to predict future behaviours. The empirical investigation was conducted by using daily share prices in Colombo Stock Exchange, Sri Lanka.

The methodology of this study is running under three main phases as follows. In the first phase, traditional grey operational mechanisms, namely, GM(1,1), unbiased GM(1,1) and nonlinear grey Bernoulli model, are used. In the second phase, the new proposed hybrid approach, namely, UBGM_BPNN was implemented successfully for forecasting short-term predictions under high volatility. In the last stage, to pick out the most suitable model for forecasting with a limited number of observations, three model-accuracy standards were employed. They are mean absolute deviation, mean absolute percentage error and root-mean-square error.

The empirical results disclosed that the UNBG_BPNN model gives the minimum error accuracies in both training and testing stages. Furthermore, results indicated that UNBG_BPNN affords the best simulation result than other selected models.

The authors strongly believe that this study will provide significant contributions to domestic and international policy makers as well as government to open up a new direction to develop investments in the future.

The new proposed UBGM_BPNN hybrid forecasting methodology is better to handle incomplete, noisy, and uncertain data in both model building and ex post testing stages.

The purpose of this paper is to analyze the mechanism and filter efficacy of accumulation generation operator (AGO)/inverse accumulation generation operator (IAGO) in the frequency domain.

The AGO/IAGO in time domain will be transferred to the frequency domain by the Fourier transform. Based on the consistency of the mathematical expressions of the AGO/IAGO in the gray system and the digital filter in digital signal processing, the equivalent filter model of the AGO/IAGO is established. The unique methods in digital signal processing systems “spectrum analysis” of AGO/IAGO are carried out in the frequency domain.

Through the theoretical study and practical example, benefit of spectrum analysis is explained, and the mechanism and filter efficacy of AGO/IAGO are quantitatively analyzed. The study indicated that the AGO is particularly suitable to act on the system's behavior time series in which the long period parts is the main factor. The acted sequence has good effect of noise immunity.

The AGO/IAGO has a wonderful effect on the processing of some statistical data, e.g. most of the statistical data related to economic growth, crop production, climate and atmospheric changes are mainly affected by long period factors (i.e. low-frequency data), and most of the disturbances are short-period factors (high-frequency data). After processing by the 1-AGO, its high frequency content is suppressed, and its low frequency content is amplified. In terms of information theory, this two-way effect improves the signal-to-noise ratio greatly and reduces the proportion of noise/interference in the new sequence. Based on 1-AGO acting, the information mining and extrapolation prediction will have a good effect.

The authors find that 1-AGO has a wonderful effect on the processing of data sequence. When the 1-AGO acts on a data sequence X, its low-pass filtering effect will benefit the information fluctuations removing and high-frequency noise/interference reduction, so the data shows a clear exponential change trends. However, it is not suitable for excessive use because its equivalent filter has poles at the non-periodic content. But, because of pol effect at zero frequency, the 1-AGO will greatly amplify the low-frequency information parts and suppress the high-frequency parts in the information at the same time.