Multiscale Integrated Forecasting of Growth and International Trade Impacts in China's Pet Industry: A Unified Modeling Framework based on SARIMAX, ARIMA, and Regression

Abstract

Driven by evolving consumption structures and increasing export potential, China’s pet industry has experienced robust growth in recent years. This study proposes an integrated multiscale modeling framework that combines SARIMAX, ARIMA, and multivariate regression techniques to forecast pet population dynamics, pet food production, and export trends. The framework aims to provide quantitative insights for industry regulation and international strategic planning. On the domestic front, ten key socio-economic variables-including urbanization rate, per capita expenditure, and aging ratio-are used to construct future input features via multivariate quadratic regression. These features serve as inputs to SARIMAX models for forecasting the populations of pet cats and dogs from 2024 to 2026. Results indicate that the cat population will increase steadily from 69.8 million in 2023 to 87.53 million by 2026, while the dog population is expected to stabilize at around 51.68 million. To assess global demand, ARIMA models are applied to  size of pet market from the United States, France, and Germany, with forecasts showing a declining trend in the U.S. market and steady growth in European countries. Subsequently, a linear regression model is developed to quantify the impact of domestic pet numbers and international sales on China’s pet food industry. The projections suggest that by 2026, the total production value will reach USD 578.62 billion, and exports will amount to USD 46.45 billion. The proposed multiscale modeling strategy balances forecasting accuracy with interpretability, and is extensible to other complex industry systems driven by heterogeneous factors, offering strong potential for cross-domain transfer and policy-oriented modeling applications.