ARIMA 模型中的负面结果

Question

I'm trying to predict daily revenue to end of month by learning previous month. Due to different behavior of the revenue between workdays and weekends I decided to use time series model (ARIMA) in Python.

This is the my Python code that I'm using:

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)

The output looks like:

How you can see the prediction results have negative value as result of negative slope.

Since I'm trying to predict income, the result cannot be lower than zero, and the negative slope also looks very strange.

What's wrong with my method? How can I improve it?

Answer 1

You can't force an ARIMA model to take only positive values. However, a classic 'trick' when you want to predict something that's always positive is to use a function that converts positive values to any value in R. The log function is a good example of this.

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

And predict now log_revenue column.

Now if the predictions take negative values, that's ok because your prediction is actually np.exp(predict) , which is positive.

Answer 2

The solution is to take more data history.