基于ARIMA模型对第三产业GDP进行分析预测并给出代码

首先，我们需要先导入一些必要的库，包括pandas、matplotlib、statsmodels等。代码如下：

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.arima_model import ARIMA
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

接下来，我们可以通过pandas读取第三产业GDP数据，并且对数据进行预处理和可视化。

df = pd.read_csv('third_industry_GDP.csv')
df = df.fillna(method='ffill')
df['date'] = pd.to_datetime(df['date'])
df.set_index('date', inplace=True)
df.plot(figsize=(12,8))
plt.show()

接下来，我们可以对数据进行平稳性检验，如果数据不平稳，我们需要对数据进行差分处理。

from statsmodels.tsa.stattools import adfuller

def test_stationarity(timeseries):
    #Determing rolling statistics
    rolmean = timeseries.rolling(window=12).mean()
    rolstd = timeseries.rolling(window=12).std()

    #Plot rolling statistics:
    orig = plt.plot(timeseries, color='blue',label='Original')
    mean = plt.plot(rolmean, color='red', label='Rolling Mean')
    std = plt.plot(rolstd, color='black', label = 'Rolling Std')
    plt.legend(loc='best')
    plt.title('Rolling Mean & Standard Deviation')
    plt.show(block=False)

    #Perform Dickey-Fuller test:
    print('Results of Dickey-Fuller Test:')
    dftest = adfuller(timeseries, autolag='AIC')
    dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])
    for key,value in dftest[4].items():
        dfoutput['Critical Value (%s)'%key] = value
    print(dfoutput)

test_stationarity(df['GDP'])

如果数据是非平稳的，我们可以通过差分操作来使其平稳。在这里，我们使用一阶差分（即对原数据做一次差分）：

df_diff = df.diff().dropna()
test_stationarity(df_diff['GDP'])

接下来，我们可以使用ACF图和PACF图来选择ARIMA模型的参数。

plot_acf(df_diff, lags=20)
plot_pacf(df_diff, lags=20)
plt.show()

根据ACF和PACF图，我们可以选择p=2，q=1来训练ARIMA模型。接下来，我们可以使用ARIMA模型来对数据进行训练和预测。

model = ARIMA(df, order=(2,1,1))
results = model.fit(disp=-1)
plt.plot(df_diff)
plt.plot(results.fittedvalues, color='red')
plt.title('RSS: %.4f'% sum((results.fittedvalues-df_diff['GDP'])**2))
plt.show()

最后，我们可以使用ARIMA模型来对未来的第三产业GDP进行预测。

forecast = results.forecast(steps=12)[0]
print(forecast)

完整代码如下：

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.arima_model import ARIMA
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.stattools import adfuller

df = pd.read_csv('third_industry_GDP.csv')
df = df.fillna(method='ffill')
df['date'] = pd.to_datetime(df['date'])
df.set_index('date', inplace=True)
df.plot(figsize=(12,8))
plt.show()

def test_stationarity(timeseries):
    #Determing rolling statistics
    rolmean = timeseries.rolling(window=12).mean()
    rolstd = timeseries.rolling(window=12).std()

    #Plot rolling statistics:
    orig = plt.plot(timeseries, color='blue',label='Original')
    mean = plt.plot(rolmean, color='red', label='Rolling Mean')
    std = plt.plot(rolstd, color='black', label = 'Rolling Std')
    plt.legend(loc='best')
    plt.title('Rolling Mean & Standard Deviation')
    plt.show(block=False)

    #Perform Dickey-Fuller test:
    print('Results of Dickey-Fuller Test:')
    dftest = adfuller(timeseries, autolag='AIC')
    dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])
    for key,value in dftest[4].items():
        dfoutput['Critical Value (%s)'%key] = value
    print(dfoutput)

test_stationarity(df['GDP'])

df_diff = df.diff().dropna()
test_stationarity(df_diff['GDP'])

plot_acf(df_diff, lags=20)
plot_pacf(df_diff, lags=20)
plt.show()

model = ARIMA(df, order=(2,1,1))
results = model.fit(disp=-1)
plt.plot(df_diff)
plt.plot(results.fittedvalues, color='red')
plt.title('RSS: %.4f'% sum((results.fittedvalues-df_diff['GDP'])**2))
plt.show()

forecast = results.forecast(steps=12)[0]
print(forecast)