﻿ 时间序列分析在福建省茶叶产量预测中的应用

# 时间序列分析在福建省茶叶产量预测中的应用Application of Time Series Analysis in Tea Yield Prediction in Fujian Province

Abstract: Based on the time series analysis theory and the SAS software, the total output of tea in Fujian Province from 1986 to 2015 was processed and analyzed. After the data processing, the time series was fitted with ARIMA(1,1,0) model and ARIMA(1,2,1) model. Model test and parameter test are carried out for the model respectively. After the test is passed, the two models are compared with the actual tea production of Fujian Province in 2016~2019, and the model with better fitting is determined by combining AIC criterion. Finally, using SAS software, we choose ARIMA(1,2,1) model to effectively predict the total output of tea in Fujian Province from 2020 to 2025.

1. 引言

2. 茶叶产量数据的预处理

2.1. 平稳性判断

Table 1. Table of tea production in Fujian Province in 1986~2019

Figure 1. Time sequence of total tea production in Fujian Province from 1986 to 2015

Cramer分解定理里说明了任何一个序列的波动都可以视为同时受到了确定性影响和随机影响的综合作用 [4]。平稳序列要求这两方面的影响都是稳定的，而非平稳序列产生的机理则在于它所受到的这两方面的影响至少有一方面是不平稳的。

2.2. 平稳化处理

Figure 2. Time sequence diagram of the first-order difference of the total output of tea in Fujian Province from 1986 to 2015

Figure 3. Unit root test after first order difference of sequence

2.3. 纯随机性检验

$\text{LB}=n\left(n+2\right){\sum }_{k=1}^{m}\left(\frac{{\stackrel{^}{\rho }}_{k}^{2}}{n-k}\right)$ (1)

Table 2. White noise test chart

3. ARIMA(1,1,0)模型识别及参数估计

3.1. 模型识别

Figure 4. Autocorrelation graph after first order difference of sequence

Figure 5. Partial autocorrelation graph after first order difference of sequence

3.2. 模型参数估计

$\stackrel{˜}{\beta }={\left({\phi }_{1},\cdots ,{\phi }_{p},{\theta }_{1},\cdots ,{\theta }_{q}\right)}^{\prime }$ (2)

${F}_{t}\left(\stackrel{˜}{\beta }\right)={\phi }_{1}{x}_{t-1}+\cdots +{\phi }_{p}{x}_{t-p}-{\theta }_{1}{\epsilon }_{t-1}-\cdots -{\theta }_{q}{\epsilon }_{t-q}$ (3)

$Q\left(\stackrel{˜}{\beta }\right)={\sum }_{t=1}^{n}{\left[{x}_{t}-{\sum }_{i=1}^{t}{\pi }_{i}{x}_{t-i}\right]}^{2}$ (4)

Table 3. Parameter estimation table

$\nabla {x}_{t}=1.03544+\frac{{\epsilon }_{t}}{1-0.71939B}$ (5)

${x}_{t}=0.29056+1.71939{x}_{t-1}-0.71939{x}_{t-2}+{\epsilon }_{t}$ (6)

4. ARIMA(1,1,0)模型检验及预测

4.1. 模型检验

Table 4. Model significance test table

Table 5. Parameter significance test table

4.2. 模型预测及数据对比

Table 6. Prediction table of total output value of tea in Fujian Province in 2016~2019

Table 7. Comparison table of total output value of tea in Fujian Province in 2016~2019

5. ARIMA(1,2,1)模型识别及参数估计

5.1. 平稳性检验

Figure 6. Sequence diagram after second order difference

Figure 7. Unit root test after second order difference of sequence

5.2. 纯随机性检验

Table 8. Second order difference pure random test table

6. ARIMA(1,2,1)模型识别及参数估计

6.1. 模型识别

Figure 8. Autocorrelation graph after second order difference of sequence

Figure 9. Partial autocorrelation graph after second order difference of sequence

6.2. 模型参数估计

Table 9. Parameter estimation table after second order difference

${\nabla }^{2}{x}_{t}=0.04228+\frac{1-B}{1-0.47205B}{\epsilon }_{t}$ (7)

7. ARIMA(1,2,1)模型检验及预测

Table 10. Significance test table of second-order difference model

Table 11. Test table of parameter significance after second-order difference

Table 12. Parameter significance test table after parameter elimination

Table 13. Parameter estimation table after parameter elimination

${x}_{t}=2{x}_{t-1}-{x}_{t-2}+0.50424{\epsilon }_{t}$ (8)

Table 14. Prediction table of total output value of tea in Fujian Province in 2016~2019

Table 15. Comparison table of total output value of tea in Fujian Province in 2016~2019

8. 模型对比及预测

Table 16. Comparison table of model results

Table 17. Prediction table of total output value of tea in Fujian Province from 2020 to 2025

9. 结论

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