ARIMA 模型中的负结果

Question

我正在尝试通过学习上个月来预测月底的每日收入。由于工作日和周末的收入行为不同，我决定在 Python.

中使用时间序列模型 (ARIMA)

这是我正在使用的 Python 代码：

import itertools
import pandas as pd
import numpy as np
from datetime import datetime, date, timedelta
import statsmodels.api as sm
import matplotlib.pyplot as plt
plt.style.use('fivethirtyeight')
import calendar

data_temp = [['01/03/2020',53921.785],['02/03/2020',97357.9595],['03/03/2020',95353.56893],['04/03/2020',93319.6761999999],['05/03/2020',88835.79958],['06/03/2020',98733.0856000001],['07/03/2020',61501.03036],['08/03/2020',74710.00968],['09/03/2020',156613.20712],['10/03/2020',131533.9006],['11/03/2020',108037.3002],['12/03/2020',106729.43067],['13/03/2020',125724.79704],['14/03/2020',79917.6726599999],['15/03/2020',90889.87192],['16/03/2020',160107.93834],['17/03/2020',144987.72243],['18/03/2020',146793.40641],['19/03/2020',145040.69416],['20/03/2020',140467.50472],['21/03/2020',69490.18814],['22/03/2020',82753.85331],['23/03/2020',142765.14863],['24/03/2020',121446.77825],['25/03/2020',107035.29359],['26/03/2020',98118.19468],['27/03/2020',82054.8721099999],['28/03/2020',61249.91097],['29/03/2020',72435.6711699999],['30/03/2020',127725.50818],['31/03/2020',77973.61724]] 
panel = pd.DataFrame(data_temp, columns = ['Date', 'revenue'])

pred_result=pd.DataFrame(columns=['revenue'])
panel['Date']=pd.to_datetime(panel['Date'])
panel.set_index('Date', inplace=True)
ts = panel['revenue']

p = d = q = range(0, 2)
pdq = list(itertools.product(p, d, q))

seasonal_pdq = [(x[0], x[1], x[2], 7) for x in list(itertools.product(p, d, q))]
aic = float('inf')
for es in [True,False]:
    for param in pdq:
      for param_seasonal in seasonal_pdq:
        try:
          mod = sm.tsa.statespace.SARIMAX(ts,
                                          order=param,
                                          seasonal_order=param_seasonal,
                                          enforce_stationarity=es,
                                          enforce_invertibility=False)
          results = mod.fit()
          if results.aic<aic:
            param1=param
            param2=param_seasonal
            aic=results.aic
            es1=es
          #print('ARIMA{}x{} enforce_stationarity={} - AIC:{}'.format(param, param_seasonal,es,results.aic))
        except:
          continue
print('Best model parameters: ARIMA{}x{} - AIC:{} enforce_stationarity={}'.format(param1, param2, aic,es1))

mod = sm.tsa.statespace.SARIMAX(ts,
                                order=param1,
                                seasonal_order=param2,
                                enforce_stationarity=es1,
                                enforce_invertibility=False)
results = mod.fit()

pred_uc = results.get_forecast(steps=calendar.monthrange(datetime.now().year,datetime.now().month)[1]-datetime.now().day+1)
pred_ci = pred_uc.conf_int()
ax = ts.plot(label='observed', figsize=(12, 5))
pred_uc.predicted_mean.plot(ax=ax, label='Forecast')
ax.fill_between(pred_ci.index,
                pred_ci.iloc[:, 0],
                pred_ci.iloc[:, 1], color='k', alpha=.25)
ax.set_xlabel('Date')
plt.legend()
plt.show()

predict=pred_uc.predicted_mean.to_frame()
predict.reset_index(inplace=True)
predict.rename(columns={'index': 'date',0: 'revenue_forcast'}, inplace=True)
display(predict)

输出如下：

如何看到预测结果由于负斜率而具有负值。

因为我是预测收入，所以结果不能低于零，而且负斜率看起来也很奇怪。

我的方法有什么问题吗？我该如何改进它？

Answer 1

您不能强制 ARIMA 模型只取正值。但是，当您想预测始终为正的值时，经典的 'trick' 是使用将正值转换为 R 中的任何值的函数。log 函数就是一个很好的例子。

panel['log_revenue'] = np.log(panel['revenue'])

现在预测 log_revenue 列。

现在，如果预测值为负，那没关系，因为您的预测实际上是 np.exp(predict)，这是正值。

Answer 2

解决办法是获取更多的历史数据。

ARIMA 模型中的负结果

Negative results in ARIMA model

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