使用来自 statsmodels 的指数平滑进行插值

Question

我正在使用来自 statsmodels 的ExponentialSmoothing 在时间序列上运行 Holt-Winters 方法。 我得到了预测值，但无法提取计算值并将它们与观察值进行比较。

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)

所以在这里，prediction_size = number of forecasted datapoints（在我的例子中是 4 个） passtrain_df 是一个包含观测值（140 个数据点）的数据框，基于该模型构建 Holt_Winter 模型（回归）。

我可以轻松显示 4 个预测值。

如何提取 140 个计算值？

尝试使用：

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

但我可能在某处有语法错误

谢谢！

Answer 1

编辑：

• 用来自 OP 的样本数据替换合成数据集

• 构建新预测期的固定函数

• 根据 OP 请求修复 x 轴日期格式

答案：

如果您要查找估算期内的计算值，则应使用modelHW.fittedvalues 而不是modelHW.forecast()。后者会给你它所说的；预测。它非常棒。让我告诉你如何做这两件事：

图 1 - 估计期内的模型

情节 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)

---

之前的尝试：

# 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)

1.如何在估计期内绘制观察值与估计值：

以下 sn-p 将提取所有拟合值并将其与您的观察值进行对比。

片段 2：

# 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()

情节 1：

2。如何生成和绘制一定长度的模型预测：

以下 sn-p 将从您的模型中生成 10 个预测，并将其绘制为与您的观察者值相比的延长周期。

片段 3：

# 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()

情节 2：

---

以下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

# 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()

@vestland - 这是代码和错误：

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