预测模型 - Python - SARIMA

Question

我在将 SARIMA 模型应用于 Python 中的数据集时遇到问题 - 我正在使用百货商店的商店销售数据，并希望预测明年的季度情况。数据具有稳定性，我已将历史数据分成四分之一。数据来源截至2017年12月31日。

请参阅下面的 Python 代码和输出

from statsmodels.tsa.statespace.sarimax import SARIMAX


model = SARIMAX(quarterly_sales, order=order, seasonal_order=seasonal_order)
results = model. Fit()

forecast = results.get_forecast(steps=4)
forecast_index = pd.date_range(start='2013-01-01', periods=4, freq='Q')
forecast_series = pd.Series(forecast.predicted_mean, index=forecast_index)


print(forecast_series)

# Plot the historical quarterly sales data
quarterly_sales.plot(kind='bar', figsize=(10, 6), label='Historical Quarterly Sales')

# Check if the forecast index aligns with the expected future quarters
print(forecast_series.index)

# Overlay the forecasted sales with more visibility
plt.plot(forecast_series.index, forecast_series, color='red', marker='o', linestyle='dashed', linewidth=2, label='Forecasted Quarterly Sales')


plt.ylim(0, max(quarterly_sales.max(), forecast_series.max()) * 1.1)


plt.title('Quarterly Sales with Forecast')
plt.xlabel('Quarter')
plt.ylabel('Sales')
plt.xticks(rotation=45)


plt.legend()

plt.show()


new_index = [f"Q{date.quarter} {str(date.year)[-2:]}" for date in forecast_series.index]
forecast_series.index = new_index

import matplotlib.pyplot as plt


historical_index = [f"Q{date.quarter} {str(date.year)[-2:]}" for date in quarterly_sales.index]
quarterly_sales.index = historical_index


quarterly_sales.plot(kind='bar', figsize=(10, 6), label='Historical Quarterly Sales')


plt.plot(forecast_series.index, forecast_series, color='red', marker='o', linestyle='dashed', label='Forecasted Quarterly Sales')

plt.title('Quarterly Sales with Forecast')
plt.xlabel('Quarter')
plt.ylabel('Sales')
plt.xticks(rotation=45)


plt.legend()

plt.show()

上面是我尝试过的方法，但我在可视化图表上看不到任何我对未来 12 个月的预测，尽管它显示在图例的屏幕截图中。

Answer 1

下面的示例显示了合成季度数据的预测和绘图。这是您想要的输出类型吗？

trn window: 2000-03-31 to 2009-12-31 [ 40 samples] | abs % err:   47.23 | target: -0.493, forecast: -0.260
trn window: 2000-03-31 to 2010-03-31 [ 41 samples] | abs % err:    8.14 | target: -0.624, forecast: -0.573
trn window: 2000-03-31 to 2010-06-30 [ 42 samples] | abs % err:   51.47 | target: -0.515, forecast: -0.780
trn window: 2000-03-31 to 2010-09-30 [ 43 samples] | abs % err:   21.35 | target: -0.892, forecast: -0.702
trn window: 2000-03-31 to 2010-12-31 [ 44 samples] | abs % err:   28.81 | target: -0.717, forecast: -0.924
trn window: 2000-03-31 to 2011-03-31 [ 45 samples] | abs % err:   18.18 | target: -0.629, forecast: -0.743
...

import pandas as pd
import numpy as np
from matplotlib import dates as mdates
from matplotlib import pyplot as plt
import statsmodels.tsa.api as tsa

#
# Synthetic quarterly data
#
dates = pd.date_range('1/1/2000', '1/1/2025', freq='QE')
t = np.linspace(0, 2*np.pi * 4, len(dates))
sine = np.sin(t) * np.exp(-0.03 * t)
data = sine + np.random.normal(0, 0.1, dates.size)

df = pd.DataFrame({'signal': data}, index=dates) #index is the date

#
# Define SARIMA model
#

#Training start date
train_start = df.index[0] #"31/03/2000"
min_train_size = 40

#Forecasting will start after 30 samples, until end of the data
forecast_start = train_start + min_train_size * df.index.freq
forecast_end = df.index[-1] #"31/12/2014"

forecasts = []
for train_end in pd.date_range(forecast_start, forecast_end, freq=df.index.freq).shift(-1):
    #the "shift(-1) is so we stop one sample before the forecast date
    train_data = df[train_start:train_end]
    
    #Fit the model and get the results object
    results = tsa.ARIMA(
        train_data,
        order=(3, 1, 0),
        seasonal_order=(1, 0, 0, 20)
    ).fit()
    
    #Use results object to forecast the next sample
    forecast = results.forecast()
    forecasts.append(forecast)

    #
    #Report results for each forecast
    #
    forecast_date = forecast.index.item().date()
    assert forecast_date == (train_end + df.index.freq).date()
    
    actual = df.loc[[forecast_date]].values.item()
    
    print(
        f'trn window: {train_start.date()} to {train_end.date()}',
        f'[{train_data.size:>3d} samples] |',
        f'abs % err: {abs(1 - forecast.item() / actual) * 100:>7.2f} |',
        f'target: {actual:>+5.3f},',
        f'forecast: {forecast.item():>+5.3f}',
    )

forecasts_df = pd.concat(forecasts, axis=0)

#
# Plot data and forecasts
#

#Plot the signal
ax = df.plot(
    y='signal', use_index=True, xlabel='date', ylabel='signal',
    marker='.', color='dodgerblue', linewidth=1, figsize=(8, 2)
)

#Plot the forecasts
forecasts_df.plot(
    use_index=True, label='forecast', color='crimson', ax=ax
)

#Add some visual lines marking various dates
[ax.axvline(date, ymax=0.05, linewidth=5, color='tab:green')
 for date in [train_start, forecast_start, forecast_end]
 ]

ax.legend(ncols=2, fontsize=8)