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Atmospheric visibility is an important indicator that reflects the transparency of the atmosphere and characterizes the air quality, so it is of great significance to study the long-term change in visibility. This paper is based on the global surface summary of day data (GSOD) site dataset and other relevant data, using the Mann–Kendall (MK) mutation point test, wavelet transform, and seasonal autoregressive integrated moving average (SARIMA) model forecasting. The time-frequency domain variation characteristics and related influencing factors of regional visibility in China were studied in detail, and the visibility was predicted; the results of the study showed the following: (1) the overall interannual variation of regional visibility in China has a decreasing trend, and the four-season variation has a decreasing trend, except for the rising trend in summer, with abrupt change points in both the overall interannual variation and the four-season variation. (2) There are main cycles of visibility in the Chinese region with time scales of 180 months and 18 months. Under the time scale of 180 months for the main cycle, the variation period of visibility is about 123 months, experiencing two high to low variations; under the time scale of 18 months for the main cycle, the variation period of visibility is 12 months, experiencing 21 high to low variations. (3) The development of the economy indirectly affects changes in visibility. Cities with high economies are densely populated, with concentrations of various particulate emissions and high concentrations of particulate matter, which can directly reduce visibility. (4) Two prediction models, SARIMA and long and the short-term memory (LSTM) neural network, were used to predict the visibility in China, both of which achieved good evaluation indexes, and the visibility in China may show an increasing trend in the future. [ABSTRACT FROM AUTHOR]

• A grey seasonal trend support vector machine for energy forecasting is proposed. • The model can efficiently identify the seasonal fluctuations in energy data. • The model is powerful to predict China's energy production. • The predictive performance of the new model is much superior to the benchmarks. This paper proposed a hybrid ensemble forecasting technique that incorporates the merits of the accumulation generation operation (AGO), least-square support vector regression (LSSVR), dummy variable, and time trend item to forecast the seasonal time series characterized by nonlinearity and uncertainty. This proposed framework, a grey seasonal trend least squares support vector machine (GSTLSSVR), can make it easy to add arbitrary seasonality to any feature, which improves model realism significantly. Furthermore, the grid search method and the last block validation are developed to identify the optimal hyperparameter, making it possible for the developed method to capture seasonal and nonlinear patterns of the original data. For illustration and verification, the quarterly petroleum coke production and monthly crude oil production in China are employed to construct diverse competing models, including the seasonal fluctuation grey model (SGM(1,1)), seasonal autoregressive integrated moving average (SARIMA), Holt-Winters (HW), backpropagation neural network (BPNN), a grey seasonal least squares support vector machine (GSLSSVR), long short term memory (LSTM) and LSSVR. The forecasting values of quarterly petroleum coke production are 668.74, 682.68, 679.99, 704.35 for 2019 and 717.59, 734.99, 727.16, 741.53 for 2020, with the lowest MAPEP value (3.7566%). Moreover, the monthly predicted crude oil production for 2019 are 3113.9, 1645, 1562.2, 1625.4, 1599.3, 1619.1, 1627, 1576.9, 1629.6, 1583.6, and 1615.6, while those counterparts for 2020 are 3093.2, 1625, 1547.5, 1621.5, 1610.6, 1644.9, 1662.9, 1615.4, 1667.4, 1615, 1667.4, 1615, and 1640.2, with the lowest MAPEP value (1.0034%). Generally, the empirical results show that the proposed model obtains superior overall performance to other benchmarks in both case studies. Therefore, this proposed model exhibits promising prospects for identifying seasonal patterns in energy production sequences. [ABSTRACT FROM AUTHOR]