The Consumer Price Index (CPI) is a vital gauge of economic performance, reflecting fluctuations in the costs of goods, services, and other commodities essential to consumers. It is a cornerstone measure used to evaluate inflationary trends within an economy. In Saudi Arabia, forecasting the Consumer Price Index (CPI) relies on analyzing CPI data from 2013 to 2020, structured as an annual time series. Through rigorous analysis, the SARMA (0,1,0) (12,0,12) model emerges as the most suitable approach for estimating this dataset. Notably, this model stands out for its ability to accurately capture seasonal variations and autocorrelation patterns inherent in the CPI data. An advantageous feature of the chosen SARMA model is its self-sufficiency, eliminating the need for supplementary models to address outliers or disruptions in the data. Moreover, the residuals produced by the model adhere closely to the fundamental assumptions of least squares principles, underscoring the precision of the estimation process. The fitted SARMA model demonstrates stability, exhibiting minimal deviations from expected trends. This stability enhances its utility in estimating the average prices of goods and services, thus providing valuable insights for policymakers and stakeholders. Utilizing the SARMA (0,1,0) (12,0,12) model enables the projection of future values of the Consumer Price Index (CPI) in Saudi Arabia for the period from June 2020 to June 2021. The model forecasts a consistent upward trajectory in monthly CPI values, reflecting ongoing economic inflationary pressures. In summary, the findings underscore the efficacy of the SARMA model in predicting CPI trends in Saudi Arabia. This model is a valuable tool for policymakers, enabling informed decision-making in response to evolving economic dynamics and facilitating effective policies to address inflationary challenges.

High-quality development in China requires higher vocational education, scientific and technological innovation, and sustainable economic development. The spatial distribution patterns of these factors show higher levels in the east and coastal areas compared to the west and inland regions, emphasizing the need for coupling coordination with the social economy. This study examines the impact of sustainable economic development on the coupling coordination degree using the spatial Durbin model. The results show a positive promotion and spillover effect, with regional variations. The main factors affecting the difference in coupling coordination are the amount of technology market contracts, fiscal expenditure on science and technology, patent application authorizations, tertiary industry output value, and the number of R&D institutions. According to the grey prediction model, the coupling coordination degree is expected to increase from 2022 to 2025, but achieving primary coordination may still be challenging in some areas. Therefore, strategies that utilize regional characteristics for coordinated development should be developed to improve the level of coupling coordination and create a mutually beneficial environment.