ETS 模型在拟合值中具有标准差和置信区间

Question

我将 ETS 模型应用于该时间序列。我需要拟合值的标准差和置信区间。

import os
import numpy as np
import pandas as pd
import datetime as dt
import matplotlib.pyplot as plt
from statsmodels.tsa.exponential_smoothing.ets import ETSModel

df_air = pd.read_csv('https://raw.githubusercontent.com/AileenNielsen/TimeSeriesAnalysisWithPython/master/data/AirPassengers.csv',
         parse_dates=['Month'], 
         date_parser=lambda x: pd.to_datetime(x, format='%Y-%m', errors = 'coerce'))
df_air = df_air.set_index('Month')
data = df_air['#Passengers']

model_mul = ETSModel(data, error="mul", trend="mul", seasonal="mul", damped_trend=True, seasonal_periods=12)
fit_mul = model_mul.fit(maxiter=10000)

print(fit_mul.fittedvalues)

如何获得拟合值的标准差和置信区间？

Answer 1

在文档中，您可以使用函数

get_prediction()

获取模型预测以及置信区间。

pred = fit_mul.get_prediction()
df = pred.summary_frame(alpha=0.05)
print(df.head())
#                 mean  mean_numerical    pi_lower    pi_upper
#1949-01-01  113.241964      113.306568  105.861134  121.671326
#1949-02-01  111.889290      111.871512  104.055665  119.540671
#1949-03-01  134.951988      135.038488  125.197954  143.861504
#1949-04-01  130.773432      130.740944  121.976745  139.822335
#1949-05-01  131.279296      131.257138  121.549210  140.543643

print(fit_mul.sse)
# 0.19104403079657817

data.plot(label="data")
fit_mul.fittedvalues.plot(label="statsmodels fit")
pred.predicted_mean.plot(label="predicted mean")
df["mean"].plot(label="mean prediction")
df["pi_lower"].plot(linestyle="--", color="tab:blue", label="95% interval")
df["pi_upper"].plot(linestyle="--", color="tab:blue", label="_")
plt.legend()
plt.show()