Python 使用统计模型的指数平滑插值

我正在使用statsmodels中的

指数平滑

对时间序列运行Holt Winters方法。 我得到预测值，但无法提取计算值并将其与观测值进行比较

from pandas import Series
from scipy import stats
import statsmodels.api as sm
from statsmodels.tsa.api import ExponentialSmoothing

modelHW = ExponentialSmoothing(np.asarray(passtrain_df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()

y_hat_avg['Holt_Winter'] = modelHW.forecast(prediction_size)

所以这里，

prediction\u size=预测数据点的数量

（在我的例子中是4个）

passtrain_df

是一个具有观测值（140个数据点）的数据帧，在此基础上建立霍尔特_冬季模型（回归）

我可以轻松显示4个预测值

from pandas import Series
from scipy import stats
import statsmodels.api as sm
from statsmodels.tsa.api import ExponentialSmoothing

modelHW = ExponentialSmoothing(np.asarray(passtrain_df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()

y_hat_avg['Holt_Winter'] = modelHW.forecast(prediction_size)

如何提取140个计算值

尝试使用：

print(ExponentialSmoothing.predict(np.asarray(passtrain_df), start=0, end=139))

但我可能在某个地方有语法错误

谢谢大家!

编辑：

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

• 用OP中的样本数据替换合成数据集

• 固定的功能，建立新的预测期

• 根据OPs请求固定x轴日期格式

回答：

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

如果要在估算期内查找计算值，则应使用

modelHW.fittedvalues

而不是

modelHW.forecast（）

。后者会给你它所说的；预测。这真是太棒了。让我告诉你如何做这两件事：

地块1-估算期内的模型

地块2-预测

代码：

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

---

以前的尝试：

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

1。如何在估算期内绘制观测值与估算值：

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

下面的代码片段将提取所有拟合值，并根据观察到的值进行绘制

from pandas import Series
from scipy import stats
import statsmodels.api as sm
from statsmodels.tsa.api import ExponentialSmoothing

modelHW = ExponentialSmoothing(np.asarray(passtrain_df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()

y_hat_avg['Holt_Winter'] = modelHW.forecast(prediction_size)

片段2:

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

绘图1:

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

2。如何生成和绘制一定长度的模型预测：

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

下面的代码片段将根据您的模型生成10个预测，并将其绘制为一个与您的观察者值相比的延长期

片段3:

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

绘图2:

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

---

下面是简单复制和粘贴的全部内容：

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

# Load data
pass_df = pd.read_csv('https://raw.githubusercontent.com/dacatay/time-series-analysis/master/data/passengers.csv', sep=';')
pass_df = pass_df.set_index('month')
type(pass_df.index)

df = pass_df.copy()

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model = df_model.set_index(pd.DatetimeIndex(df_model.index))

# Model, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_model.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# Forecasts
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)

# Forecasts, build new period 
forecast_start = df.index[-1]
forecast_start = pd.to_datetime(forecast_start, format='%Y-%m-%d')
forecast_period = pd.period_range(forecast_start, periods=prediction_size+1, freq='M')
forecast_period = forecast_period[1:]

# Forecasts, create dataframe
df_forecast = pd.Series(forecast_values, index = forecast_period.values).to_frame()
df_forecast.columns = ['HWforecast']

# merge input and forecast dataframes
df_all = pd.merge(df,df_forecast, how='outer', left_index=True, right_index=True)
#df_all = df_all.set_index(pd.DatetimeIndex(df_all.index.values))
ix = df_all.index
ixp = pd.PeriodIndex(ix, freq = 'M')
df_all = df_all.set_index(ixp)

# Forecast, plot
fig, ax = plt.subplots()
myFmt = mdates.DateFormatter('%Y-%m')
df_all.plot(ax = ax, x_compat=True)
ax.xaxis.set_major_formatter(myFmt)

# imports
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

# imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from statsmodels.tsa.api import ExponentialSmoothing

# Data that matches your setup, but with a random
# seed to make it reproducible
np.random.seed(42)

# Time
date = pd.to_datetime("1st of Jan, 2019")
dates = date+pd.to_timedelta(np.arange(140), 'D')

# Data
n_passengers = np.random.normal(loc=0.0, scale=5.0, size=140).cumsum()
n_passengers = n_passengers.astype(int) + 100
df = pd.DataFrame({'n_passengers':n_passengers},index=dates)

# Model
modelHW = ExponentialSmoothing(np.asarray(df['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()
modelHW.summary()

# Model, fitted values
model_values = modelHW.fittedvalues
model_period = df.index
df_model = pd.concat([df['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
df_model.columns = ['n_passengers', 'HWmodel']
df_model.plot()

# Forecast
prediction_size = 10
forecast_values = modelHW.forecast(prediction_size)
forecast_period = df.index[-1] + pd.to_timedelta(np.arange(prediction_size+1), 'D')
forecast_period  = forecast_period[1:]

df_forecast = pd.concat([df['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
df_forecast.columns = ['n_passengers', 'HWforecast']
df_forecast.plot()

@维斯特兰-以下是代码和错误：

y_train = passtrain_df.copy(deep=True)

model_HW = ExponentialSmoothing(np.asarray(y_train['n_passengers']), seasonal_periods=12, trend='add', seasonal='mul',).fit()

model_values = model_HW.fittedvalues
model_period = y_train.index

hw_model = pd.concat([y_train['n_passengers'], pd.Series(model_values, index = model_period)], axis = 1)
hw_model.columns = ['Observed Passengers', 'Holt-Winters']

plt.figure(figsize=(18,12))
hw_model.plot()

forecast_values = model_HW.forecast(prediction_size)
forecast_period = y_train.index[-1] + pd.to_timedelta(np.arange(prediction_size+1),'D')
forecast_period  = forecast_period[1:]

hw_forecast = pd.concat([y_train['n_passengers'], pd.Series(forecast_values, index = forecast_period)], axis = 1)
hw_forecast.columns = ['Observed Passengers', 'HW-Forecast']
hw_forecast.plot()

错误：

NullFrequencyError     Traceback (most recent call last)
<ipython-input-25-5f37a0dd0cfa> in <module>()
     17 
     18 forecast_values = model_HW.forecast(prediction_size)
---> 19 forecast_period = y_train.index[-1] +  pd.to_timedelta(np.arange(prediction_size+1),'D')
     20 forecast_period  = forecast_period[1:]
     21 

/anaconda3/lib/python3.6/site- packages/pandas/core/indexes/datetimelike.py in __radd__(self, other)
    879         def __radd__(self, other):
    880             # alias for __add__
--> 881             return self.__add__(other)
    882         cls.__radd__ = __radd__
    883 

/anaconda3/lib/python3.6/site- packages/pandas/core/indexes/datetimelike.py in __add__(self, other)
    842                 # This check must come after the check for  np.timedelta64
    843                 # as is_integer returns True for these
--> 844                 result = self.shift(other)
    845 
    846             # array-like others

/anaconda3/lib/python3.6/site-packages/pandas/core/indexes/datetimelike.py in shift(self, n, freq)
   1049 
   1050         if self.freq is None:
-> 1051             raise NullFrequencyError("Cannot shift with no freq")
   1052 
   1053         start = self[0] + n * self.freq

NullFrequencyError: Cannot shift with no freq

NullFrequencyError回溯（最近一次调用）
在（）
17
18预测值=模型硬件预测（预测大小）
--->19预测周期=y序列指数[-1]+pd到时间增量（np.arange（预测大小+1），'D'）
20预测期=预测期[1:]
21
/anaconda3/lib/python3.6/site-packages/pandas/core/index/datetimelike.py in_u______________（self，other）
879 def_uuuradd_uuu（自身、其他）：
880#添加的别名__
-->881返回自我。添加（其他）
882 cls.\uuuu radd\uuuuuu=\uuuuuu radd__
883
/anaconda3/lib/python3.6/site-packages/pandas/core/index/datetimelike.py in\uuuu添加（self，other）
842#此检查必须在np.timedelta64检查之后进行
843#as is#u integer为这些
-->844结果=自换档（其他）
845
846#像其他阵列一样
/anaconda3/lib/python3.6/site-packages/pandas/core/indexes/datetimelike.py in-shift（self，n，freq）
1049
1050如果self.freq为无：
->1051 raise NullFrequencyError（“无频率时无法移位”）
1052
1053启动=自[0]+n*自频率
NullFrequencyError:无法在没有频率的情况下移动

谢谢您，很抱歉耽搁了您。第一部分工作得很好（modelHW.fittedvalues）。问题是第二部分（预测）有一个错误：-见上文。无法在此正确格式化。也不清楚为什么你建议使用“D”，而数据有每月的频率。然而，我尝试了“M”，但得到了相同的错误预测值=模型预测（预测大小）预测时段=y列车索引[-1]+pd.到时间增量（np.arange（预测大小+1），'D'）预测时段=预测时段[1:]HW预测=pd.concat（[y列车['n乘客]），pd.系列（预测值，索引=预测时段）]，轴=1）hw_forecast.columns=['观察乘客'，'hw forecast']hw_forecast.plot（）感谢您的反馈！我明天可以建立一个聊天室，我们可以从那里开始。当然！乐意效劳！我提供了代码和错误。这是提取命令：pass_df=pd.read_csv（“”，header=0，parse_dates=True，sep='））我刚刚修复了x轴时间格式以表示原始数据的格式。@vesland-遗憾的是，仍然有一个错误--------------------NameErrorTraceback（上次调用）在（）22#Plot 23图中，ax=plt.subplot（）-->24 myFmt=mdates.DateFormatter（“%Y-%m”）25 df#u all.Plot（ax=ax，x#u compat=True）26 ax.xaxis.set_major#u formatter（myFmt）name错误：名称“mdates”未定义您运行的matplotlib版本是什么？运行

matplotlib.\uuuuu版本\uuuu

并检查。我在

2.2.2

上，我看到您的错误消息中有一个名为

Plot 23

的东西。如果您只是在自己的代码之上添加我的代码的一部分，它可能不起作用。尝试一个新的开始，只使用我提供的代码，看看它是否适用于mdate。在任何情况下，请确保在代码的开头添加此行

import matplotlib.dates as mdate