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Analysis and Prediction of Egg Price in Guangdong Province Based on ARIMA Model and Auto-Regressive Model
DOI: 10.12677/sa.2024.132036, PDF, HTML, XML, 下载: 123  浏览: 186

Abstract: Based on the egg price of Guangdong province in the China Animal Husbandry Yearbook, the ARIMA model and the auto-regressive model are constructed in this paper. According to the theoretical basis of the model and evaluation indicators, such as goodness of fit, mean square error, mean absolute error and information criteria, the optimal model is selected to predict egg price. The optimal forecasting model is the product season model . The model is used to measure the future price of eggs in Guangdong Province, and some practical suggestions are put forward for the government, breeders, investors and consumers. This paper not only enriched the theoretical basis of egg price forecasting but also provided a valuable reference for the decision-making of related subjects.

1. 引言

1.1. 研究背景

1.2. 研究现状

2. 数据预处理

2.1. 数据概况

2.2. 白噪音检验

Table 1. White noise test of egg price sequence in Guangdong Province

2.3. 平稳性检验

Figure 1. Time series of egg price in Guangdong Province from January 2003 to December 2011

Table 2. ADF unit root test results of egg price sequence in Guangdong Province

3. ARIMA模型的构建

3.1. 差分平稳化

Figure 2. Time sequence diagram of egg price in Guangdong Province after first order twelve-step difference

3.2. ARIMA模型定阶

3.3. ARIMA模型参数估计及检验

3.4. ARIMA模型确定

Table 3. Comparison of ARIMA models

3.5. ARIMA模型优化

$\left\{\begin{array}{l}\left(1-B\right)\left(1-{B}^{12}\right){X}_{t}=\left(1+0.33275{B}^{8}\right)\left(1-0.81571{B}^{12}\right){\epsilon }_{t}\\ {\epsilon }_{t}\sim WN\left(0,0.077987\right)\end{array}$ (1)

3.6. ARIMA模型预测

Table 4. ARIMA model egg price forecast in Guangdong Province from January to December 2012 (unit: Yuan)

Figure 3. ARIMA model fitting and prediction renderings

4. 残差自回归模型的构建

${\epsilon }_{t}={\Phi }_{1}{\epsilon }_{t-1}+\cdots +{\Phi }_{p}{\epsilon }_{t-p}+{a}_{t}$ (2)

4.1. 拟合季节效应

Table 5. Seasonal index of egg price in Guangdong Province by month

$\frac{{X}_{t}}{{S}_{t}}={T}_{t}+{\epsilon }_{t}$ (3)

4.2. 拟合趋势效应

${T}_{t}={\beta }_{0}+{\beta }_{1}\cdot t+\cdots +{\beta }_{k}\cdot {t}^{k}+{\epsilon }_{t}$ (4)

${T}_{t}=-19.5007+0.001601t$ (5)

Figure 4. The trend effect is fitted with the power function of time t as the independent variable

4.3. 拟合残差序列

${\epsilon }_{t}=-0.907264{\epsilon }_{t-1}+{a}_{t},\text{\hspace{0.17em}}{a}_{t}~NID\left(0,0.08411\right)$ (6)

4.4. 残差自回归模型的确定

$\left\{\begin{array}{l}\frac{{X}_{t}}{{S}_{t}}=-19.5007+0.001601t+{\epsilon }_{t}\\ {\epsilon }_{t}=0.907264{\epsilon }_{t-1}+{a}_{t}\\ {a}_{t}~NID\left(0,0.08411\right)\end{array}$ (7)

4.5. 残差自回归模型预测

Figure 5. Auto-regressive model fitting and prediction renderings

Table 6. Prediction of egg price in Guangdong Province from January to December 2012 by auto-regressive model (unit: Yuan)

5. 模型对比

5.1. 模型理论层面

5.2. 评价指标对比

Table 7. Comparison of evaluation index values of two models

5.3. 预测效果对比

6. 结论

Table 8. ARIMA model forecast of egg price in Guangdong Province from 2012 to 2013 (unit: Yuan)

Figure 6. ARIMA model fitting and prediction renderings

Table A1. Raw data

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