2024 APMCM summary sheet

summary

With the high-quality development of China's economy, people's living standards are rising, the demand for pets is increasing, and the pet industry is developing rapidly. However, the trend of market economy and a variety of foreign policies will have an impact on the development of the pet industry, this paper aims to conduct a simulation analysis and discussion of the development of China's pet industry in a variety of ways, and to reason and integrate the data in recent years, so as to provide new methods and opportunities for the development of the industry in the future.

Contents

catalogue

1. Introduction3

1.1 background

1.2 Problem Restatement

2. assumptions and justification

3. symbol

4. Factors affecting thedevelopment of pet industryin China

4.1 data declaration

4.1.1 Data collection and preprocessing

4.2 The development model of the pet industry

4.2.1 Influencing factors and indicator setting

4.2.2 Multiple linear regression model

4.2.3 Results

5. Development of Pet Industry in China in the Next Three Years

5.1 data

5.1.1 Data collection and preprocessing

5.2 Prediction Model of Pet Industry Development in China

5.2.1 influence factor

5.2.2 ARIMA time series prediction

5.2.3 Results

6. Global demand for pet food in the next three years

6.1 data declaration

6.1.1 Data collection

6.1.2 Data preprocessing

6.2 Impact Analysis Model: Global Pet Development by Pet Type

6.2.1 Optimal Species Competition Model in Mathematical Modeling

6.2.2 结果

7.未来三年（无论经济政策如何变化）其宠物食品生产和出口情况。

7.1 数据说明

7.1.1 Data collection

7.1.2 Data preprocessing

7.2 Impact Analysis Model: Global Pet Development by Pet Type

7.2.1 Optimal Species Competition Model in Mathematical Modeling

7.2.2 Results

8. Economic Policy Impact on China Pet Industry

8.1 index settings

8.2 double difference model

8.3 result

9. Sensitivity analysis and error analysis

10. Model evaluation and further discussion

10.1 model evaluation

10.1.1 the advantages of

10.1.2 Weaknesses of the model

10.2 generalization of the model

11. reference data

12. appendix

(At the beginning of this text)

introduction

1.1 background

With the rapid development of China's economy and social progress, the living standard of residents continues to improve,people's consumption concept continues to change, more and more people choose tokeep petsforcompanionship and comfort, sothe pet industry rises accordingly. Pets are regarded as part of the family, and pet consumption has gradually become a fashion and trend. With the continuous development of pet industry,the industrial chain of pet industry is gradually improved, including pet food, supplies, medical treatment, beauty and other links. Professional services such as pet nutritionists, designers, playmates and other occupations reflect the trend of specialization and segmentation in the pet industry.

1.2 Question reformulation takes into account background information and certain constraints

In problem reformulation, we need to solve the following problems:

Question 1:

Based on the data in Attachment 1 and additional data collected by the team, analyze the development of pet industry in China in the past five years by pet type. And analyze the factors of China pet industry development, thus make a suitable mathematical model to predict the development of China pet industry in the next three years.

Question 2:

Overseas pet industries, such as European countries and the United States, have also grown rapidly in recent years. Please analyze the development of the global pet industry by pet type based on the data in Attachment 2 and other data collected by your team. And develop a mathematical model to predict global demand for pet food over the next three years.

Question 3:

According to China's pet food production and export volume in Annex 3, please analyze the development of China's pet food industry according to the global pet food market demand trend and the development of China, and predict its pet food production and export situation in the next three years (regardless of changes in economic policies).

Question 4:

China's pet food industry will inevitably be affected by the new foreign economic policies (such as tariff policies) of European and American countries. To quantitatively analyze this effect, please develop a suitable mathematical model, taking into account the data in the attachment, the additional data you collected, and the calculations in the above questions. Based on your calculations, please formulate feasible strategies for sustainable development of pet food industry in China.

assumptions and justification

Hypothesis 1: Assume that the data obtained from search has a certain degree of credibility and rationality.

Hypothesis 2: Suppose that in the optimal species competition differential equation model, when the pet industry exists independently, they follow...

Hypothesis 3:

Hypothesis 4:

Hypothesis 5:

symbol

4. Development of pet industry in China

4. 1Description of data

data collection

图 1 Market size of pet-related businesses in China

Figure 1 from www.statista.com

Figure2Changes in the market size of China pet industry in recent years

Figure3Comparison of Chinese and American pet industry market size

Pet type market preferences (food vs. medical). Data Unit: Average annual cost of pet owners (yuan/pet).

Economic consumption scale of pets. Data unit: RMB 100 million yuan.

Relationship between urbanization rate and pet population

As shown above, we collected data on four main areas:

Petpopulation data:extract trends and characteristicsfrom Attachment 1:

The cat population continues to grow, possibly influenced by changes in pet culture and lifestyle.

The number of dogs is relatively stable and fluctuates slightly,showing a slight downward trend overall,which may be related to policy, urbanization impact and changes in pet demand structure.

·Market size data:

The market size of China's pet industry increased by 25.2% year-on-year in 2022 to RMB 81.14 billion yuan and is expected to reach RMB 267 billion yuan in 2025.

From 2015 to 2022, the market size increased from 72.5 billion yuan to 396 billion yuan, indicating a strong development trend.

·Consumer behavior data:

47% of pet owners were born after 1990, indicating that young consumers are the main driver of industry growth.

Pet product purchase frequency is mainly concentrated in 1-2 times per month, mainly through e-commerce and offline pet stores to obtain products and information.

·Social and economic drivers:

Single economy and aging society promote rapid development of pet industry. Singles and older adults are more likely to keep pets as emotional sustenance.

During the COVID-19 pandemic, the accelerated popularity of online consumption further boosted the growth of the pet industry.

Summary of data sources

1. National Bureau of Statistics of China: "China's Urbanization Rate Data from 2019 to 2023".

2. iiMedia Consulting: "2023 Research Report on the Market Size and Trend of China's Pet Industry".

3. JD Pet Consumption Report (2019-2023).

4. Tmall Global: White Paper on the Development of China's Pet Consumption.

China Pet Industry Association: "Analysis of the Development Status of China's Pet Industry in 2023".

4.1.2 Data preprocessing:

·Missing data handling:

Verify that pet count data is complete for all years.

Supplements annual data trends for market size for subsequent analysis.

·Data standardization:

Unified data unit (market size expressed in RMB billion, pet number expressed in million).

Historical data adjusted for inflation.

·Data visualization:

According to Annex I,plot the growth of cat and dog populations.

Figure4Discounted growth of cats and dogs

Create a histogram of market size versus growth rate.

Figure5Bar chart and broken line chart of pet market size and growth rate in China from 2019 to 2023:

Blue bar chart: indicates the market size of each year (unit: 100 million yuan).

Orange line chart: indicates the growth rate (in percentage) for each year.

4.1.3 Analyze the development of pet industry in China in the past five years

4.1.3.1Cat Market Performance: Core Drivers of Significant Growth

Number growth: from 44.12 million in 2019 to 69.8 million in 2023, with an average annual growth rate of about 12.2%.

Economic contribution: Cat economy increased from 109.2 billion yuan in 2019 to 195 billion yuan in 2023, accounting for 64.8% of the total pet economy from 53.9%.

Consumption habits:

Cat food consumption is increasing year by year, with a five-year compound growth rate of approximately 9.2%.

Health care spending has increased significantly, suggesting cat owners are more concerned about pet health.

4.1.3.2Dog Market Performance: Growth Slows But Stable

Number change: The number of dogs dropped from 55.03 million in 2019 to 51.75 million in 2023, an overall decrease of 5.96%, and the growth rate slowed down.

Economic contribution: Although the economic scale of dogs has increased slightly (from 93.2 billion yuan in 2019 to 105.8 billion yuan in 2023), its proportion in the total scale has decreased from 46.1% to 35.2%.

Consumption habits:

Dog food consumption grew steadily, while medical consumption grew slightly slower than cats.

The dog market is more dependent on high-end food and medical consumption.

4.1.3.3Driving Factor Analysis

Urbanization is closely related to cat growth: for every 1 percentage point increase in urbanization, the average annual growth rate of cat population increases by about 2.5%.

Changes in family structure: The rise of the singles economy has made cats the pet of choice because of their more manageable characteristics.

Consumption upgrade: The increase in residents 'income has a more significant impact on the cat market, especially in high-end food and services.

4.1.3.4 conclusion

Over the past five years, China's pet industry has grown rapidly with cats as the main driver, while the dog market has gradually stabilized. The analysis shows thatthe core factors for the growth of cat economyinclude urbanization, single economy and upgrading of household consumption, whiledog economy relies on high-end consumption. This trend provides basic data support for the establishment of market forecasting models in the next three years.

4.2 Establish a model toanalyzethe factors affecting the development of pet industry in China.

4.2.1According to the available data and background information, the main factors for the development of pet industry in China can be divided into the following categories:

1. macroeconomic factors

Household disposable income: income level directly affects pet consumption ability.

Urbanization rate: increased urbanization drives pet population growth.

2. sociocultural factor

Demographic changes: solitary, aging trends increase pet demand.

Pet culture: pet status changed from "animal" to "family member".

3. consuming behavior

Online channel: e-commerce development boosts the growth of pet food and services.

Mid-to-high-end consumer trends: Consumers tend to provide better products and services for pets.

4. industry factors

Product innovation: New pet food, medical services and other innovations boost industry development.

Policy support: policy support for industry standardization and healthy development.

4.2.2 Determination of Core Driving Factors

When analyzing the development of pet industry in China, identifying key drivers is the basis for establishing prediction models. Core drivers should satisfy the following conditions:

High correlation with industry scale: factors need to be able to directly affect the market scale of pet industry, such as the number of pets directly determines market demand, and residents 'income affects consumption ability.

Data availability: Factors need to have clear historical data and good predictability.

Theoretical support: The choice of factors requires theoretical support in the framework of economics or industry analysis.

The selection of core drivers will provide assurance of model accuracy and interpretability through the above criteria.

4.2.2.1 normalization processing

Normalizethe data related to the above factors, so that each variable can be compared horizontally. Theformula is:

4.2.2.2 correlation analysis

Pearson correlation coefficient is used to measure the correlation between each factor and market size. The formula is:

The following correlation coefficients were calculated:

4.2.2.3Analyze and comparedifferent influencing factors

Highly correlated factors

Number of pets(r=0.91):

Pet numbers are a direct source of market demand and are clearly highly correlated with market size.

For example, from 2019 to 2023, the increase in the number of pets is highly consistent with the growth trend of market size.

Household income(r=0.85):

The increase in residents 'income directly affects their consumption capacity, especially the demand for high-end pet food and services by middle-and high-income groups.

medium correlation factor

Proportion of pet medical expenditure(r=0.68) andproportion of pet food consumption(r=0.71):

These factors reflect the segmented demand of pet consumption structure, but their changes are relatively stable, and the growth rate is slightly lower than that of the market scale.

For example, while total expenditure on health care and food is growing, its share fluctuates relatively little and has limited explanatory power for market size.

Urbanization rate(r=0.62):

Urbanization rate affects the popularity of pet breeding, but its rate of change is slow and has little impact on the fluctuation of market size in the short term.

factors with lower correlation

Proportion of population ageing(r=0.55):

The aging trend does have potential implications for the pet industry, but from the current data, it is changing slowly and has not yet become a dominant factor.

4.2.2.4Conclusion

By correlation analysis,pet number(r=0.91) anddisposable income per capita(r=0.85) are the core driving factors affecting the market size of pet industry in China. These two factors are both highly correlated and have clear theoretical support:

Pet numbersdirectly determine the size of the market and are the most direct source of demand.

Residents 'incomedetermines their ability to pay and is an important driving force for consumption upgrading.

In contrast, other factors such as the proportion of medical expenditure and urbanization rate, although relevant, are less explanatory of market size than pet number and household income. Therefore, we selectpet populationandhousehold incomeas the core drivers of our prediction model.

4.2.3Selection and construction of mathematical models

To predict the market size growth trend over the next three years, we usedmultiple linear regression models. The model can combine multiple variables(pet numbers, disposable income per capita)to predict the target variable (market size).

4.2.3.1Model Formula

4.2.3.2 Simplify and summarize collected data

The following data should be utilized:

Market size data(some historical data have been provided for the title).

Number of pets(sum of the number of cats and dogs in the title).

Data on disposable income per capita(available from publicly available statistical yearbooks).

The data collected were tabulated as follows:

4.2.3.3Model Training

Using Python to fit the regression model, the code is implemented as follows:

import numpy as np

import pandas as pd

from sklearn.linear_model import LinearRegression

from sklearn.metrics import mean_squared_error

#Data loading

data = {

"Year": [2019, 2020, 2021, 2022, 2023],

"Market_Size": [725, 1160, 1800, 2252, 3960], #Unit: billion yuan

"Pet_Count": [9915, 10084, 11235, 11655, 12155], #Unit: ten thousand

"Income": [30733, 32189, 35150, 37839, 41200] #Unit: Yuan

}

df = pd.DataFrame(data)

#Features and target variables

X = df[["Pet_Count", "Income"]]

y = df["Market_Size"]

#Model training

model = LinearRegression()

model.fit(X, y)

Predicting the next three years

future_data = pd.DataFrame({

"Pet_Count": [12600, 13000, 13400], #Assuming future pet population growth trends

"Income": [43000, 45000, 47000] #Assuming per capita income increases by 2000 yuan per year

})

predictions = model.predict(future_data)

#Print results

print("Predicted market size for the next three years (billion yuan):", predictions)

4.2.3.4Model Prediction Results

According to the model forecast, the market size in the next three years may be:

2024: about 480 billion yuan

2025: about 550 billion yuan

2026: about 630 billion yuan

5.The development of the global pet industry

5.1 Data description

5.1.1 Data Collection

In order to analyze the development of the global pet industry and predict the future demand for pet food, we have developed the following data collection strategy to ensure comprehensiveness and accuracy.

We divide the data into the following categories:

Pet number data：

Source

Data on the number of pets (cats and dogs) in the United States, France and Germany provided in Annex 2.

 The Statista database expands the number of pets in Japan, South Korea, India, and other countries.

 The World Small Animal Veterinary Association (WSAVA) annual report on the global pet population.

Supplementary data content:

Asian markets: such as Japan (cats: 9.6 million, dogs: 8.9 million, 2023), South Korea (cats: 8 million, dogs: 7.5 million).

Latin American markets: such as Brazil (cats: 12 million, dogs: 30 million).

Assumption: The future pet population growth rate is 3%.

(2)Pet food consumption habits

Figure6Pet food consumption data

Source of data:

IBISWorld provides data on the proportion of pet food market consumption.

NielsenIQ Global Retail Report annual average consumption.

Pet food consumption breakdown in public sector reports.

Supplementary data content:

Average annual food consumption per cat and dog (country-differentiated data). For example, dogs in the United States average $250 a year and cats $150 a year; European countries are slightly lower, and French dogs average $200 a year.

(3)Economic and environmental data

Source of data:

GDP per capita, consumer spending, World Bank.

OECD urbanization rate data and impact analysis.

(4)Industry drivers

Source of data:

Industry Report: American Pet Products Association (APPA) Report.

Policy data: animal protection and import policies of various countries.

Sociocultural trends: academic papers on the impact of aging, solitary populations on the pet industry.

Example of summarized data table structure

5.1.2Data preprocessing

Data standardization:

 Unify the units of different data, for example, the number of pets is in the unit of "10,000", and the market size is in the unit of "100 million US dollars".

 Convert currency units, such as euros to dollars, using the average exchange rate for 2023.

Data cleaning:

 Delete or complete missing data, for example, when some market data is missing in some years, fill in according to the linear interpolation method.

 Removal of outliers, such as certain extreme growth rates.

Build derived variables:

 Pet Market Growth Rate: The growth rate is calculated based on the annual market size.

 Pet Penetration Rate: Number of pets/number of households, used to measure the popularity of pet ownership.

 Pet per capita expenditure: total market size / total number of pets, reflecting the level of consumer investment.·

分类型聚合：
Type aggregation:

按“猫”和“狗”分别分析，计算全球和主要国家的市场规模趋势、年增长率。
Analyze by "cat" and "dog" respectively, calculate global and major country market size trend, annual growth rate.

5.1.3数据分析
5.1.3 data analysis

5.1.3.1宠物数量的全球趋势分析
5.1.3.1Global trend analysis of pet populations

根据附件2及额外收集的数据，我们对过去五年全球猫和狗的数量变化趋势进行分析：
Based on Annex 2 and additional data collected, we analyze trends in global cat and dog populations over the past five years:

（1）猫的数量趋势
(1)Trends in cat numbers

美国：
United States:

猫的数量在2019年和2021年出现波动，分别为9,420万只，而2020年降至6,500万只后缓慢回升。2023年恢复到7,380万只。
The cat population fluctuated in 2019 and 2021, at 94.2 million, and slowly recovered after falling to 65 million in 2020. By 2023, it had recovered to 73.8 million.

变化分析：疫情可能导致部分家庭减少宠物饲养，但随着经济恢复，养宠热潮重新兴起。
Change analysis: The epidemic may cause some families to reduce pet ownership, but as the economy recovers, the pet craze re-emerges.

法国：
France:

猫的数量从2019年的1,300万只稳步增长至2023年的1,660万只，年均增长率约为6.3%。
The number of cats has grown steadily from 13 million in 2019 to 16.6 million in 2023, an average annual growth rate of about 6.3%.

变化分析：法国养宠家庭以猫为主，养猫成本低、空间需求小，契合法国高比例城市居民的生活方式。
Change analysis: French pet families are dominated by cats, with low cost and small space demand, which is in line with the lifestyle of a high proportion of urban residents in France.

德国：
Germany:

猫的数量也呈增长态势，从2019年的1,470万只增长至2023年的1,570万只，增长幅度较小，年均增长率约为1.7%。
The number of cats has also increased, from 14.7 million in 2019 to 15.7 million in 2023, a smaller increase, with an average annual growth rate of about 1.7%.

变化分析：德国家庭多关注宠物健康和福利，猫作为更易养护的宠物受到欢迎。
Change analysis: German families pay more attention to pet health and welfare, and cats are welcomed as pets that are easier to care for.

（2）狗的数量趋势
(2)Trends in dog numbers

美国：
United States:

狗的数量相对稳定，从2019年的8,970万只下降到2020年的8,500万只，随后回升至2023年的8,010万只。
The number of dogs has remained relatively stable, dropping from 89.7 million in 2019 to 85 million in 2020, before recovering to 80.1 million in 2023.

变化分析：虽然养狗总体趋势平稳，但饲养成本高及城市化可能抑制其增长。
Change analysis: Although the overall trend of dog ownership is stable, the high cost of raising dogs and urbanization may inhibit its growth.

法国：
France:

狗的数量变化较小，从2019年的740万只增至2023年的990万只，年均增长率约为7.6%。
The number of dogs has changed slightly, increasing from 7.4 million in 2019 to 9.9 million in 2023, an average annual growth rate of about 7.6%.

变化分析：法国养宠人群逐渐倾向于养小型犬，适合城市家庭环境。
Change analysis: French pet owners tend to keep small dogs, suitable for urban family environment.

德国：
Germany:

狗的数量基本保持在1,010-1,070万只之间波动，2023年为1,050万只。
The number of dogs fluctuated between 10.1 million and 10.7 million, reaching 10.5 million in 2023.

变化分析：德国对大型犬种的养护和行为培训要求较高，可能限制了养狗数量的快速增长。
Change analysis: Germany has high requirements for maintenance and behavioral training of large dog breeds, which may limit the rapid growth of the number of dogs.

（3）全球总趋势
(3)Global trends

猫的数量增长率高于狗，尤其在欧洲，可能与城市化、养护成本和家庭偏好相关。
Cats are growing faster than dogs, especially in Europe, probably due to urbanization, maintenance costs and family preferences.

狗的数量较为稳定，但在北美地区养狗数量略有下降，可能受经济压力和城市化趋势影响。
Dog populations have been stable, but dog ownership has declined slightly in North America, possibly due to economic pressures and urbanization trends.

5.1.3.2宠物市场规模与类型分析
5.1.3.2Pet Market Size and Type Analysis

根据收集的数据，全球宠物市场在食品和医疗消费方面呈现显著的宠物类型偏好：
Based on the collected data, the global pet market presents significant pet type preferences in terms of food and medical consumption:

（1）猫的市场偏好
(1)Market preferences of cats

食品消费：
Food consumption:

猫粮市场逐年增长，尤其是湿粮和特种营养粮，反映了宠物主对猫健康的关注。
The cat food market is growing year by year, especially wet food and specialty nutrition food, reflecting pet owners 'concern for cat health.

2023年全球猫粮市场约占宠物食品市场的48%，较2019年增长了8个百分点。
The global cat food market accounted for approximately 48% of the pet food market in 2023, an increase of 8 percentage points from 2019.

医疗消费：
Medical consumption:

猫的医疗支出增速明显，高于狗的增长率。疫苗接种、绝育手术及老龄猫护理需求增加。
Cats 'health care spending is growing faster than dogs'. Vaccination, neutering and care for aged cats are on the rise.

2019-2023年全球猫的医疗支出年均增长率约为9%。
2019-2023 Global cat health care spending is growing at an average annual rate of about 9 percent.

（2）狗的市场偏好
(2)Market preferences of dogs

食品消费：
Food consumption:

狗粮市场稳定增长，干粮仍是主流，但定制化、功能性狗粮（如减肥粮、牙齿护理粮）需求增加。
The dog food market is growing steadily, dry food is still the mainstream, but the demand for customized, functional dog food (such as diet food, dental care food) is increasing.

2023年狗粮市场约占宠物食品市场的50%，比例虽高于猫，但增长速度较低。
In 2023, the dog food market accounted for about 50% of the pet food market, although the proportion was higher than that of cats, but the growth rate was lower.

医疗消费：
Medical consumption:

狗的医疗消费仍占主导地位，但增速放缓。疫苗、骨科和皮肤病治疗是主要消费领域。
Medical spending on dogs remains dominant, but growth is slowing. Vaccines, orthopedics and dermatological treatments are the main areas of consumption.

全球狗的医疗支出年均增长率约为5%，低于猫的增长率。
Global spending on dogs is growing at an average annual rate of about 5 percent, slower than that of cats.

（3）市场偏好总结
(3)Summary of Market Preferences

猫的食品和医疗市场增速均高于狗，特别是在城市化程度较高的国家，猫的市场潜力更大。
The food and medical markets for cats are growing faster than those for dogs, especially in highly urbanized countries, where the market potential for cats is greater.

狗的市场仍占据大部分份额，但增长逐渐趋于稳定。
Dogs still hold the majority of the market share, but growth is gradually stabilizing.

5.1.3.3影响宠物行业发展的驱动因素分析
5.1.3.3Analysis of Driving Factors Affecting the Development of Pet Industry

通过分析宠物数量、市场规模和消费偏好，可以归纳出以下驱动因素：
By analyzing pet numbers, market size, and consumer preferences, the following drivers can be identified:

（1）城市化
1)Urbanization

城市化程度高的国家和地区（如法国、德国）对猫的需求更高。
Countries and regions with a high degree of urbanization (such as France and Germany) have a higher demand for cats.

狗的需求更偏向于城市郊区或乡村地区。
Demand for dogs tends to be more in suburban or rural areas.

（2）经济水平
(2)Economic level

北美和欧洲地区因高经济水平，宠物人均支出远高于其他地区。
In North America and Europe, per capita pet spending is much higher than in other regions due to high economic levels.

高收入群体更倾向于为宠物选择高端食品和服务，推动市场增长。
High-income groups are more likely to choose high-end food and services for pets, driving market growth.

（3）消费者行为
(3)Consumer behavior

年轻一代更关注宠物的健康和个性化需求，推动功能性食品和高端医疗服务的兴起。
The younger generation is more concerned about the health and personalized needs of pets, driving the rise of functional foods and high-end medical services.

随着宠物被视为“家庭成员”，消费习惯逐渐转向更高质量的商品和服务。
As pets are treated as "family members," spending habits shift toward higher-quality goods and services.

5.1.3.4全球宠物行业发展情况总结
5.1.3.4 Summary of Global Pet IndustryDevelopment

全球宠物行业正处于快速增长阶段，猫的市场增速高于狗，城市化是关键驱动因素之一。
The global pet industry is in a period of rapid growth, with cats growing faster than dogs, and urbanization being one of the key drivers.

食品消费仍是市场的核心，但医疗消费的增长潜力不容忽视。
Food consumption remains at the heart of the market, but the growth potential of medical consumption cannot be ignored.

北美和欧洲地区为成熟市场，增长趋于稳定；亚太地区的宠物市场潜力巨大。
North America and Europe are mature markets with stable growth, while Asia Pacific has great pet market potential.

通过上述分析，可以为全球宠物食品和医疗市场的发展趋势提供数据支撑，为后续预测全球宠物食品需求的模型提供重要依据。
Through the above analysis, it can provide data support for the development trend of global pet food and medical market, and provide important basis for subsequent models to predict global pet food demand.

5.2模型构建
5.2Model construction

为了预测未来三年全球宠物食品市场需求，按宠物类型（猫和狗）构建模型。以下是详细的模型建立过程：
To predict global pet food market demand over the next three years, models were constructed by pet type (cats and dogs). The following is the detailed model building process:

1. 建模目标
1. modeling target

预测未来三年（2024-2026）全球宠物食品的需求量，具体分为：
Forecast global pet food demand for the next three years (2024-2026), specifically divided into:

猫粮需求量
cat food requirement

dog food demand

2. model select

Considering the characteristics of data time series and the influence of multivariate factors, the following two modeling methods are selected for prediction:

Time series models: use trends in pet populations and historical food consumption to predict future demand.

Multiple regression model: combine multiple drivers (e.g., pet population, urbanization rate, income level) to create a predictive model.

3. data input

Based on the results of data collection and data preprocessing, the following variables were selected:

Independent variables (impact factors):

Number of pets (cats, dogs)

城市化率（每年平均增长率）
Urbanization rate (average annual growth rate)

居民人均可支配收入（按国家分类）
Per capita disposable income (by country)

宠物食品人均消费支出
Per capita consumption expenditure on pet food

目标变量（预测指标）：
Target variables (predictors):

全球猫粮市场需求量
Global cat food market demand

全球狗粮市场需求量
Global dog food market demand

5.2.1 时间序列模型
5.2.1Time series models

（1）模型形式
(1) Model form

采用 ARIMA（AutoRegressive Integrated Moving Average）模型：

AR：自回归，考虑历史需求的滞后效应。
AR: Autoregression, taking into account the lag effect of historical demand.

I：差分，处理数据的非平稳性。
I: Difference, dealing with nonstationarity of data.

MA：移动平均，捕捉随机波动。
MA: Moving average, capturing random fluctuations.

（2）建模步骤
(2) Modeling steps

时间序列分解：
Time series decomposition:

分解宠物食品需求的历史数据，分析趋势、周期性和随机性。
Disaggregate historical data on pet food demand to analyze trends, periodicity and randomness.

例如，观察猫粮市场从2019到2023年的趋势增长，确认趋势线性增长。
For example, observing the trend growth of the cat food market from 2019 to 2023 confirms the trend linear growth.

平稳性检验：
Stationarity test:

通过 ADF（Augmented Dickey-Fuller）检验 检查时间序列的平稳性。
TheADF (Augmented Dickey-Fuller) test was used to checkthe stationarity of the time series.

若非平稳，进行差分处理（例如一阶或二阶差分）。
If not stationary, differential processing (e.g., first or second order differencing) is performed.

参数选择与优化：
Parameter selection and optimization:

使用 ACF（自相关函数）和 PACF（偏自相关函数）确定模型的参数 p、d、q。
ACF (Autocorrelation Function) and PACF (Partial Autocorrelation Function) are used to determine the parameters p, d, q of the model.

对不同的参数组合进行交叉验证，选择最低 AIC（Akaike Information Criterion）值的模型。
Cross-validation was performed on different parameter combinations to select the model with the lowest AIC (Akaike Information Criterion) value.

预测：
Forecast:

用模型预测未来三年的需求量，并对结果进行置信区间评估。
The model is used to predict demand for the next three years and confidence intervals are evaluated for the results.

5.2.2多元回归模型
5. 2.2Multiple regression model

（1）模型形式
(1) Model form

建立以下回归方程：
Establish the following regression equation:

（2）建模步骤
(2) Modeling steps

变量筛选：
Variable screening:

对宠物数量、城市化率和人均收入进行相关性分析，确定高相关的变量进入模型。
Correlation analysis was performed on pet population, urbanization rate, and per capita income to identify variables with high correlation to enter the model.

例如，猫粮需求量与猫的数量呈正相关，相关系数 r>0.8r > 0.8r>0.8。
For example, cat food demand is positively correlated with cat population, r % 3E 0. 8r % 3E 0. 8r % 3E 0. 8.

数据标准化：
Data standardization:

对变量进行标准化处理（如 z-score），减少量纲对模型的影响。
Normalize variables (e.g. z-score) to reduce the effect of dimensionality on the model.

模型拟合：
Model Fit:

使用多元线性回归拟合数据，评估模型的 R2R^2R2 值及回归系数的显著性（p 值）。
Multiple linear regression was used to fit the data to assess the significance (p-value) of the R2R^2R2 values and regression coefficients of the model.

模型验证：
Model validation:

使用训练集和测试集进行交叉验证，评估模型的预测准确性。
The predictive accuracy of the model was assessed by cross-validation using the training and test sets.

5.2.3 代码实现
5.2.3 Code implementation

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression

from sklearn.metrics import mean_squared_error, r2_score

# 数据输入
#Data Entry

data = {

'Year': [2019, 2020, 2021, 2022, 2023],

'Global_Cat_Count': [3.5, 3.7, 3.9, 4.1, 4.35], # 全球猫数量（亿只）
'Global_Cat_Count': [3.5, 3.7, 3.9, 4.1, 4.35], #Number of cats worldwide (100 million)

'Global_Dog_Count': [3.6, 3.65, 3.7, 3.75, 3.8], # 全球狗数量（亿只）
'Global_Dog_Count': [3.6, 3.65, 3.7, 3.75, 3.8], #Number of dogs worldwide (100 million)

'Cat_Food_Consumption_Per_Cat': [12, 12, 12, 12, 12], # 每只猫年均粮食消耗（公斤）
'Cat_Food_Consumption_Per_Cat':[12, 12, 12, 12], #Average annual food consumption per cat (kg)

'Dog_Food_Consumption_Per_Dog': [20, 20, 20, 20, 20], # 每只狗年均粮食消耗（公斤）
'Dog_Food_Consumption_Per_Dog':[20, 20, 20, 20], #Average annual food consumption per dog (kg)

}

# 转换为DataFrame
#Convert to DataFrame

df = pd.DataFrame(data)

#Calculate Pet Food Demand

df['Cat_Food_Demand'] = df['Global_Cat_Count'] * df['Cat_Food_Consumption_Per_Cat']

df['Dog_Food_Demand'] = df['Global_Dog_Count'] * df['Dog_Food_Consumption_Per_Dog']

#Modelling: Using linear regression predictions

years = np.array(df['Year']).reshape(-1, 1)

cat_food_demand = np.array(df['Cat_Food_Demand'])

dog_food_demand = np.array(df['Dog_Food_Demand'])

#Cat Food Market Demand Forecast

cat_model = LinearRegression()

cat_model.fit(years, cat_food_demand)

future_years = np.array([2024, 2025, 2026]).reshape(-1, 1)

cat_predicted = cat_model.predict(future_years)

#Dog food market demand forecast

dog_model = LinearRegression()

dog_model.fit(years, dog_food_demand)

dog_predicted = dog_model.predict(future_years)

#Show results

future_results = pd.DataFrame({

'Year': [2024, 2025, 2026],

'Predicted_Cat_Food_Demand': cat_predicted,

'Predicted_Dog_Food_Demand': dog_predicted

})

print(future_results)

#Visualize

plt.figure(figsize=(10, 6))

plt.plot(df['Year'], df['Cat_Food_Demand'], 'bo-', label='Historical Cat Food Demand')

plt.plot(future_years, cat_predicted, 'b--', label='Predicted Cat Food Demand')

plt.plot(df['Year'], df['Dog_Food_Demand'], 'ro-', label='Historical Dog Food Demand')

plt.plot(future_years, dog_predicted, 'r--', label='Predicted Dog Food Demand')

plt.xlabel('Year')

plt.ylabel('Food Demand (10,000 tons)')

plt.title('Global Pet Food Market Demand Prediction')

plt.legend()

plt.grid()

plt.show()

#Model Performance Evaluation

cat_r2 = r2_score(cat_food_demand, cat_model.predict(years))

dog_r2 = r2_score(dog_food_demand, dog_model.predict(years))

print(f"Cat Food Model R^2: {cat_r2:.2f}")

print(f"Dog Food Model R^2: {dog_r2:.2f}")

5.2.4 Output of results

1. Cat food demand forecast

Based on the global trend in cat population growth (5% annual growth) and per capita consumption of cat food (historical average of approximately 12 kg per cat per year), it is calculated that:

Forecasts show that global cat food market demand will reach6.048 million metric tonsby 2026, with a total growth of about 15.9% over three years.

2. dog food demand forecast

Based on global dog population growth trends (3% annual growth rate) and dog food consumption per capita (historical average of approximately 20 kg per dog per year), the following calculations are made:

Forecasts show that global dog food market demand will reach8.320 million metric tonsby 2026, with a total growth of approximately 9.5% over three years.

3. Overall demand trends

Combined with cat food and dog food forecasts, the general trends in global pet food market demand for the next three years are as follows:

In the next three years, the total global pet food market demand is expected to grow from12.82 million metric tons in 2023to14.368 million metric tonsin 2026, with an average annual growth rate of approximately3.87%.

Question 3

Data collection:

In order to analyze the development of pet food industry in China more comprehensively, we need to supplement the following data:

Global Pet Food Market Trends:

According to Grand View Research, the global pet food market is expected to grow at an annual rate of 5 -6%.

来源：Grand View Research - Pet Food Market Size

China economic data:

GDP growth rate: According to the National Bureau of Statistics, China's GDP growth rate has averaged about 5% annually over the past few years.

Source: National Statistical Office

Pet Industry Consumption Trends:

According to the White Paper on China Pet Industry, the average annual growth rate of pet industry in China is about 20%, especially the demand growth of pet food is relatively significant.

Source:China Pet Industry White Paper 2023

Exchange rate data:

Exchange rate between RMB and US dollar: The exchange rate of US dollar against RMB in 2020 is about 1 USD = 7 CNY; in 2023, it is 1 USD ≈ 7.3 CNY.

Source:People's Bank of China-Exchange Rate Query

Global Pet Food Market Demand:

Pet food consumption in Europeand the United States: The United States and Europe are the main markets for global pet food demand. Pet food consumption in the United States is about $30 billion a year, and the European market is about € 15 billion.

来源：Euromonitor - Pet Food Market Analysis

China pet food import and export data:

China Pet Food Import and Export Volume: According to the General Administration of Customs of China, China pet food exports totaled US$24.7 million in 2022 and US$12.2 million in 2021.

Source:General Administration of Customs of China-Import and Export Data

data pre-processing

2. data pre-processing

After data collection, the next step is data preprocessing. The purpose of data preprocessing is to ensure the accuracy and consistency of data and provide the required format for model building. The following are the specific pretreatment steps, one by one in order.

2.1 data cleansing

During the data cleansing phase, we need to ensure the quality of all data, eliminate outliers and missing values, and standardize inconsistent units. We first checked the data on China pet food production and export volume in Annex 3 to ensure consistency in units and formats.

Standardization of units: Annex 3 provides data from 2019 to 2023, where production value is in RMB and export value is in USD. For ease of analysis, we convert all data to the same units and adjust for exchange rates. Export data for 2020 and 2023 are expressed in RMB and USD respectively, so it is necessary to unify the unit into USD or RMB as follows:

2.2 outlier check

Next, we need outlier detection on the data. Among the data in Annex 3, the export value of pet food in 2019 (RMB 154.1 million) is unusually high, which is too large after exchange rate conversion, so we need to consider whether this data is an outlier.

According to the standards of the global pet food market, 22.01 million US dollars is relatively low, so we judge that this data may be due to data source problems or exchange rate changes caused by anomalies, so we can temporarily ignore this part of the data and keep only the data for the rest of the normal years. To ensure the stability of the results, we will adopt a relatively stable growth trend for forecasting.

2.3 Missing value handling

There are no significant missing values in the data in Annex 3, but some fluctuations in the export data for some years may cause errors in fitting the model. To eliminate the effects of this error, we can choose:

Interpolation: Linear interpolation can be used to fill in fluctuations in export data in a given year.

Weighted Average: Given the outlier problem with the 2019 data, we can choose to ignore the 2019 export data and use the 2020 - 2023 data to calculate the annual growth rate of exports and make projections.

2.4 data normalization

In order to avoid deviations of some eigenvalues in modeling, we need to normalize the data. Especially for features that involve multiple scales (such as production and exports), we useMin-Max normalizationto map all data between 0 and 1. The normalization formula is as follows:

This approach ensures that features are processed at the same scale, thus avoiding bias from features with different units or large numerical ranges.

2.5 Time series data formatting

For time series analysis, we sort the data by year. The time dimension (year) of the data is a key factor in analyzing trends over the next three years, especially when predicting trends in pet food production and exports in China. We organize the data in the following format:

Here, theGDP GrowthandGlobal Pet Food Demand Growthcolumns represent China's GDP growth rate and global pet food demand growth rate, respectively. These data will be used as external features (independent variables) of the prediction model to help us predict production and exports over the next three years.

2.6 tabulate data

Finally, we consolidate all the data into a unified data frame and normalize it. The goal of this process is to divide all the data by features, ensure the quality of the data, and format it into a format suitable for use by machine learning algorithms.

import pandas as pd

from sklearn.preprocessing import MinMaxScaler

#Data loading

data = pd.DataFrame({

'Year': [2019, 2020, 2021, 2022, 2023],

'Production_CNY': [440.7, 727.3, 1554, 1508, 2793], # 单位：百万人民币

'Exports_USD': [22.01, 9.8, 12.2, 24.7, 39.6], # 单位：百万美元

'GDP_Growth':[6.1, 2.3, 8.1, 3.0, 5.0], #Assumed GDP growth rate ( %)

'Global_Pet_Food_Demand_Growth':[0.06, 0.06, 0.06, 0.06] #Annual growth rate of global pet food demand

})

#Data Normalization

scaler = MinMaxScaler()

normalized_data = scaler.fit_transform(data[['Production_CNY', 'Exports_USD', 'GDP_Growth', 'Global_Pet_Food_Demand_Growth']])

#backfill normalized data into original data box

data[['Production_CNY', 'Exports_USD', 'GDP_Growth', 'Global_Pet_Food_Demand_Growth']] = normalized_data

#View processed data

print(data)

2.7 result checking

After data preprocessing, we check the integrity of the data again. In particular, there should be no problems with missing values, outliers, and unit-transformed data. All features should be compared at the same scale to ensure that the data format is suitable for further analysis and modeling.

Through the above steps, the data preprocessing process will provide clear and standardized input data for the subsequent establishment of mathematical models.

3. mathematical model is established

After data collection and data preprocessing, the next step is to build mathematical models based on the collected data. Our goal is to analyze the current situation of China pet food industry based on global pet food market demand trends and China economic development, and forecast the production and export of pet food in China for the next three years regardless of economic policy changes.

3.1 establishment of regression model

In order to predict the production and export of pet food industry in China, we can adopt Regression Analysis method. Regression models can help us reveal the relationship between independent variables (such as global pet food demand growth rate, GDP growth rate, etc.) and China pet food production and export volume. We will usemultiple linear regression modelsto establish this relationship.

3.1.1 Select Model Type

Since we have multiple factors (independent variables) affecting the development of China pet food industry, such asglobal pet food demand growth rateandChina GDP growth rate, we choose to usemultiple linear regressionmodel. This model allows for simultaneous consideration of multiple factors affecting production and exports. The basic regression equation is as follows:

3.1.2 Training models

We will use Python'sscikit-learnlibrary for regression analysis. The specific steps are as follows:

Prepare data set: Organize collected data into training set, features includeglobal pet food demand growth rate(Global_Pet_Food Demand_Growth) andChina GDP growth rate(GDP_Growth), target variables areChina pet food production value(Production_CNY) andexport value(Exports_USD).

Split Training Set and Test Set: To avoid overfitting, we split the data into Training Set (used to train the model) and Test Set (used to verify the accuracy of the model). Typically, 70% of the data can be used for training and the remaining 30% for testing.

Training the regression model: Train the regression model using the training set data to obtain regression coefficients and model intercepts.

Model Evaluation: Evaluate the fit of the model by calculating theR² value(coefficient of determination) andmean squared error(MSE). The higher the R² value, the better the model fits the data.

from sklearn.linear_model import LinearRegression

from sklearn.model_selection import train_test_split

from sklearn.metrics import mean_squared_error, r2_score

#Prepare data

X = data[['Global_Pet_Food_Demand_Growth', 'GDP_Growth']] # 特征变量

y_prod = data ['Production_CNY']#Target Variable-Production Amount

y_exp = data ['Exports_USD']#Target variable-Exports

#Split data sets

X_train, X_test, y_train_prod, y_test_prod = train_test_split(X, y_prod, test_size=0.3, random_state=42)

X_train_exp, X_test_exp, y_train_exp, y_test_exp = train_test_split(X, y_exp, test_size=0.3, random_state=42)

#Create Regression Model

reg_prod = LinearRegression()

reg_prod.fit(X_train, y_train_prod)

reg_exp = LinearRegression()

reg_exp.fit(X_train_exp, y_train_exp)

#Predicted results

y_pred_prod = reg_prod.predict(X_test)

y_pred_exp = reg_exp.predict(X_test_exp)

#Model evaluation

print("Production Model Evaluation: ")

print("R²:", r2_score(y_test_prod, y_pred_prod))

print("均方误差:", mean_squared_error(y_test_prod, y_pred_prod))

print("\nExit model evaluation: ")

print("R²:", r2_score(y_test_exp, y_pred_exp))

print("均方误差:", mean_squared_error(y_test_exp, y_pred_exp))

3.1.3 Model predictions

After the regression model is obtained, we can use it to predict the production and export of pet food in China for the next three years (2024-2026). To make the projections, we need to assume values forglobal pet food demand growth ratesandChina GDP growth ratesover the next three years. These assumptions can be set based on historical trends and expert forecasts.

Assumptions:

Global pet food demand growth rate remains at6%;

China GDP growth rates are projected to be 5.0%, 5.2% and 5.5% over the next three years(these figures can be adjusted according to the latest China economic forecast).

Based on these assumptions, we can use a well-trained regression model to predict production and export values for the next three years.

#Assuming GDP growth and global demand growth over the next three years

future_data = pd.DataFrame({

'Global_Pet_Food_Demand_Growth': [0.06, 0.06, 0.06],

'GDP_Growth': [0.05, 0.052, 0.055]

})

#Use regression models for forecasting

future_prod = reg_prod.predict(future_data)

future_exp = reg_exp.predict(future_data)

#Output forecast results

print("China pet food production forecast for the next three years (millions of RMB):", future_prod)

print("China pet food export forecast for the next three years (millions of US dollars):", future_exp)

3.2 result analysis

Production forecast: According to the forecast result of regression model, we can get the expected value of pet food production in China in the next three years. By looking at trends in these forecasts, we can determine whether China pet food production can keep pace with global demand growth or whether it will be affected by other factors.

Export projections: Similarly, projected export data will help us assess China's competitiveness in the global pet food market, especially market share changes in Europe and the United States.

3.3 Model Improvement and Optimization

To further improve the accuracy and stability of the model, we can consider:

Introduce more influencing factors: such as domestic consumption trends in China, price fluctuations of pet food, etc.

More complex models, such asrandom forest regressionorsupport vector regression(SVR), are used to further improve prediction accuracy.

3.4 conclusion

Through regression analysis model, we can accurately predict the production and export trend of China pet food industry in the next three years according to the global pet food market demand trend and China GDP growth rate. These forecast results will provide decision support for enterprises in China pet food industry and help them gain advantages in future market competition.

Question 4

4. A Model for Analyzing the Impact of External Economic Policies on China Pet Food Industry

data collection

To comprehensively analyze the challenges and opportunities facing China's pet food industry in the next three years and predict its production and export situation, we have collected the following key types of data. These data provide the necessary information basis for mathematical modeling and help us to quantitatively analyze the impact of external economic policies (such as tariff policies) on China's pet food industry.

1. China Pet Food Production and Export Data

Data sources:China Customs,China Statistical YearbookandIndustry Reports.

We collected data on China's total pet food production and export value from 2019 to 2023, as follows:

Pet Food GDP: includes the annual total amount of all pet food produced in China, measured in RMB. This data reflects the size and growth trend of China's pet food industry.

Pet Food Export Value: Includes the annual value of pet food exported by China to other countries and regions, usually measured in US dollars. This data reflects the competitiveness and demand changes of China pet food in the international market.

The data show that China's pet food industry has shown a growth trend since 2019, especially in 2020, when it was affected by the global epidemic, exports experienced brief fluctuations. Since 2021, with the global economic recovery and the growth of pet industry demand, China's pet food production and export volume have rebounded significantly.

Table 1: Production and export data of pet food in China (unit: RMB 100 million)

2. Global Pet Food Market Demand Data

Data sources:International Pet Food Association (IPSA),National Pet Industry Associations,Market Research Reports.

Changes in global pet food market demand directly affect China's pet food export performance. We collected data on pet food demand in key markets such as the United States, Europe (particularly France and Germany), as follows:

US Market: As one of the largest pet food consumer markets in the world, pet food demand in the US experienced fluctuations of varying degrees during 2019-2023. We collected annual pet food demand data for the US market and analyzed the annual growth rate of demand.

European markets: Pet food demand data for major European markets including France and Germany. Pet food consumption in France and Germany, in particular, has shown an increasing trend in recent years, but is still affected by tariff policies and consumer behavior in different countries.

Table 2: Pet food demand data of European and American countries (unit: 10,000)

3. Tariff Policy Data of European and American Countries

Source:World Trade Organization (WTO),Office of the United States Trade Representative (USTR),EU Trade Policy Database,official announcements of governments.

Global trade policies, especially the tariff policies of European and American countries, have a direct impact on China's pet food exports. In recent years, the tariff policies of European and American countries have experienced changes to varying degrees, especially under the background of trade wars and international economic frictions, the tariff policies of pet food industry have also undergone corresponding changes. We have collected data on tariff changes in the United States, Europe and other countries from 2019 to 2023, focusing on import tariff policies for China pet food.

We also pay special attention to the impact of tariff changes during the Sino-US trade war on China's pet food exports, and analyze the impact of tariff increases or decreases on export volume.

Table 3: Changes in Tariffs of European and American Countries on China Pet Food (Unit: %)

4. Global Economic Growth Data

Source:World Bank (WB),International Monetary Fund (IMF),United Nations Department of Economic and Social Affairs (UNDESA).

Global economic growth has a direct impact on the demand of the global pet food market. We collected global economic growth data from 2019 to 2023, with a special focus on growth in Europe and the United States. These data provide a reference for analyzing the relationship between the global economy and the demand of pet food market.

Table 4: Global economic growth data (in %)

5. data summary

Through the above data collection, we can fully understand the position of China pet food industry in the global market and the extent to which it is affected by external economic policies (especially tariff policies). We collected China pet food production and export data, global pet food demand data, tariff policy change data of European and American countries and global economic growth data, which provided solid data support for mathematical model establishment and subsequent analysis.

Next, based on these data, we will preprocess the data and build mathematical models to analyze the impact of tariff policies, global demand and economic growth on China's pet food industry and predict the industry's production and exports in the next three years.

data pre-processing

Before data preprocessing, we first confirm the quality and integrity of all collected data. Next, according to the type and source of the collected data, the following detailed preprocessing steps are carried out:

1. data cleansing

First, we cleaned all collected data to remove erroneous values, missing data, and non-compliant data. The cleaning steps are as follows:

Missing data handling: For records containing missing values, we applied different imputation strategies:

For production and export data: Missing values are imputed using linear interpolation. Data for missing years are extrapolated based on data trends for the previous two years.

For global market demand data: missing values are imputed using market averages to ensure continuity and stability of data.

For tariff policy data: tariff data for missing years are imputed as the average of data for the previous or subsequent year.

Abnormal data processing: Data points in the data that significantly deviate from the normal distribution (such as obvious abnormally high or abnormally low data) are deleted or replaced with abnormal values. This includes removing abnormally high production and export figures for individual years.

2. data standardization

For accurate mathematical modeling, we need to normalize all data to the same units for comparison and analysis. Specific operations include:

Unit Conversion: Convert data for China Renminbi (CNY) and US Dollar (USD) to a uniform Renminbi (CNY) to ensure consistent use of the same monetary unit in the model.

Annualization: annualizes all annual data to actual values. For example, quarterly production and export data are converted to annual values for comparison and analysis.

3. data merge

Combine data from different sources to create a comprehensive dataset. Consolidated data includes:

China pet food production and export data: Combined with global market demand data to create a complete dataset for analyzing China pet food performance in the global market.

Pet Food Market Demand Data for Europe and the UnitedStates: Combine pet food market demand data from the United States, France and Germany to provide a comprehensive view of the global market.

Data consolidation steps:

Year-based consolidation: market demand data for different countries and regions are consolidated by year for trend analysis and forecasting purposes.

Discordant data removal: Ensure consistency and comparability of data and eliminate differences due to different data sources.

4. data integration

Finally, we integrate all processed data into a unified data framework. This data framework includes:

Year: From 2019 to 2023.

China production and export data: including annual China pet food production value (RMB) and export value (USD).

Global market demand data: including the annual pet food market demand in the United States, France and Germany (in thousands).

Tariff policy data for European and American countries: including tariff policy by year (percentage).

Global economic growth data: includes annual global, US and EU GDP growth rates (percentage).

Examples of data frameworks:

Through data cleansing, standardization, consolidation, and integration, we create an exhaustive data framework that provides a solid foundation for further mathematical modeling and predictive analysis. Next, we will use this data framework to establish mathematical models, and analyze and predict the production and export situation of China pet food industry in the next three years through regression analysis and time series prediction.

Model-building section

In solving how China's pet food industry will be affected by new foreign economic policies (such as tariff policies) in European and American countries, we need to establish a suitable mathematical model to quantify the impact of tariff policies on China's pet food production and exports. The model will be based on existing historical data, global market demand trends, and growth in China's pet food industry, further combined with changes in economic policies.

This part will introduce the process of establishing the model in detail, including the selection of variables, the construction of regression model, the implementation of regression analysis and the specific method of prediction analysis.

1. model assumes

To simplify the analysis and calculations, we assume:

Direct impact of tariff policy: Tariff policy directly affects the production and export volume of pet food in China. Tariff increases may reduce demand for China products by increasing import costs; tariff decreases may boost export volume growth.

Changes in market demand: In addition to tariffs, global demand for pet food is also influenced by factors such as the state of each country's economy, consumer preferences, and the pace of development of the pet industry. Therefore, we assume that factors such as global economic growth, changes in demand in the European and American markets, and pet food consumption habits are significantly related to production and export volumes.

Linear assumption of data: We assume a linear relationship between influencing factors, although in practice this relationship may be more complex, and linear regression models are a simplified modeling method.

2. variable definition

To build the regression model, we define the following variables:

3. Regression Model Construction

Based on the defined dependent variables and independent variables, we construct the following regression model:

4. Data Processing and Regression Analysis

After building the regression model, we will process the historical data and estimate the regression coefficients through regression analysis. The steps are as follows:

Data Normalization: To eliminate the effect of unit differences in each variable on the regression results, we will normalize all independent variables so that their mean is 0 and their standard deviation is 1. The standardized formula is as follows:

Data split: Split the 2019-2023 data into a training set (2019-2022) and a test set (2023), fit the model with the training set, and verify the prediction effect of the model with the test set. The goal of data splitting is to avoid overfitting and ensure the generalization of the model.

Regression analysis: Perform regression analysis using statistical software such as statsmodels in Pythonor the lm function in R. The regression coefficients are calculated by fitting the model to obtain the weights of the variables.

Model Evaluation: Calculate the R2R^2 value of the model to measure the fitness of the model and calculate the mean squared error (MSE) to evaluate the predictive power. High R2R^2 values and low MSE values indicate that the model fits the data well and is able to make accurate predictions.

5. predictive parsing

By training the regression model, we can predict the production and export of pet food in China in the next three years (2024-2026). The specific steps are as follows:

Forecast input data: forecast independent variables (such as GDP growth rate of the United States and the European Union, tariff level, etc.) for the next three years based on global economic forecasts, European and American pet food demand forecasts and tariff policy changes.

For example, forecast GDP growth rates and tariff policy changes in the US and EU for 2024-2026. These forecasts can be obtained by consulting relevant economic reports or using expert forecasts.

Substitute regression model: substitute predicted independent variable values into trained regression model to calculate predicted values of pet food production and export in China from 2024 to 2026.

Validation of results: Verify the accuracy of the prediction model by comparing it with known data such as actual production and export values in 2023. If the predicted values differ significantly from the actual values, further model adjustments may be required.

6. strategy recommendations

Based on the forecast results, we propose the following sustainable development strategies for the pet food industry in China:

Diversified market strategy: If the European and American markets are affected by tariff increases, China enterprises can diversify their risks and reduce their dependence on the single market by exploring other markets (such as Southeast Asia, Latin America, etc.).

Increase the added value of products: The increase of tariffs may increase the cost of pet food in China. Enterprises can increase the market competitiveness by improving the added value of products (such as innovative products, improving product quality, introducing environmentally friendly packaging, etc.).

Optimize supply chain management: Optimize supply chain, reduce production costs and offset the negative impact of tariffs through more efficient production and logistics management.

Strengthen domestic market development: With the rapid development of pet industry in China, the domestic market has great potential. Enterprises can enhance their domestic market share by enhancing brand awareness and improving product quality.

sum up

By establishing linear regression model, we can quantitatively analyze the impact of tariff policy changes in European and American countries on the production and export of China pet food industry. Using historical data and forecasted economic data, the model provides us with a forecast of China pet food market for the next three years. Based on these forecasts, we propose strategies for the pet food industry in China such as diversifying the market, enhancing product added value, optimizing supply chain management and strengthening the domestic market to ensure the sustainable development of the industry.

Development of Pet Industry in China in the Next Three Years

5.1 data

5.2 Prediction Model of Pet Industry Development in China

5.2.1 influence factor

5.2.2 ARIMA time series prediction

5.2.3 Results

6. Global demand for pet food in the next three years

6.1 data declaration

6.1.1 Data collection

6.1.2 Data preprocessing

6.2 Impact Analysis Model: Global Pet Development by Pet Type

6.2.1 Optimal Species Competition Model in Mathematical Modeling

6.2.2 结果

7.未来三年（无论经济政策如何变化）其宠物食品生产和出口情况。

7.1 数据说明

7.1.1 Data collection

7.1.2 Data preprocessing

7.2 Impact Analysis Model: Global Pet Development by Pet Type

7.2.1 Optimal Species Competition Model in Mathematical Modeling

7.2.2 Results

8. Economic Policy Impact on China Pet Industry

8.1 index settings

8.2 double difference model

8.3 result

9. Sensitivity analysis and error analysis

10. Model evaluation and further discussion

10.1 model evaluation

10.1.1 the advantages of

10.1.2 Weaknesses of the model

10.2 generalization of the model

11. reference data

12. appendix

Zhong Cuixia"TheRise of Pet Economy, How Operators Leverage the Hundred Billion Market"