【学习笔记-时间序列预测】prophet-使用.4乘法季节性/假期性、不确定区间

1.乘法季节性

默认情况下，Prophet 适合加法季节性，即可以将季节性的影响添加到趋势项中。

但有的情况下，时间序列有一个明显的年周期，但是预测的季节性波动较大，可能在时间序列开始时太大而结束时太小。 于是在这种情况下，季节性并不是 Prophet 中假设的恒定附加因素，而是随趋势增长。这就体现了乘法季节性。

导入数据集，完成初始化设置

import pystan
import fbprophet
import pandas as pd
from fbprophet import Prophet

df = pd.read_csv('D:\Machine learning\prophet-main\example_air_passengers.csv')
m = Prophet()
m.fit(df)
future = m.make_future_dataframe(50, freq='MS')
forecast = m.predict(future)
fig = m.plot(forecast)

设置乘法季节性，训练模型

m = Prophet(seasonality_mode='multiplicative')
m.fit(df)
forecast = m.predict(future)
fig = m.plot(forecast)

并画图

fig.show()

训练结果与图像如下

INFO:numexpr.utils:Note: NumExpr detected 16 cores but "NUMEXPR_MAX_THREADS" not set, so enforcing safe limit of 8.
INFO:numexpr.utils:NumExpr defaulting to 8 threads.
INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
Initial log joint probability = -2.46502
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
      99       401.677     0.0020169       115.615           1           1      130
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
     144       401.793  1.05996e-005       59.3202  2.224e-007       0.001      238  LS failed, Hessian reset
     199       401.842  8.23524e-007       78.4056      0.2832           1      311
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
     253       401.843  3.04642e-008       64.9714        0.22           1      385
Optimization terminated normally:
  Convergence detected: relative gradient magnitude is below tolerance

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
Initial log joint probability = -2.46502
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
      99       501.604   0.000654695       77.4368      0.7922      0.7922      139
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
     199       503.323   2.7516e-005       73.7442           1           1      260
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
     224       503.365   0.000152713       82.0492  1.951e-006       0.001      320  LS failed, Hessian reset
     271       503.376  5.07205e-006       94.1896  6.533e-008       0.001      418  LS failed, Hessian reset
     299       503.377  7.57048e-008       54.4034      0.8718      0.8718      460
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
     301       503.377  8.09861e-009       72.6659      0.1896      0.1896      463
Optimization terminated normally:
  Convergence detected: absolute parameter change was below tolerance

 可以看到震荡越来越明显，拟合结果与数据匹配度高，适合用乘法季节性。

2.乘法假期性

使用seasonality_mode='multiplicative'，假期效应也被建模为乘法。

默认情况下，季节性或回归量都与seasonality_mode匹配；但可以添加季节性或回归量时指定 mode='additive' 或 mode='multiplicative' 作为参数以覆盖原有默认的seasonality_mode。

m = Prophet(seasonality_mode='multiplicative')
m.add_seasonality('quarterly', period=91.25, fourier_order=8, mode='additive')
m.add_regressor('regressor', mode='additive')

3.不确定区间

默认情况下，Prophet 将返回预测 yhat 的不确定区间。 

预测中不确定性的来源包括：趋势的不确定性、季节性估计中的不确定性、额外的观测噪声。

模型中假设未来的趋势变化到与历史的趋势变化相似；未来趋势变化的平均频率和幅度将与我们在历史的相同；

3.1趋势的不确定性

趋势的不确定性是最大的预测不确定性来源。可以通过向前预测趋势变化，通过计算它们趋势的分布获得不确定区间。

增加 changepoint_prior_scale ，即选用历史中更多的变化点进行建模，会使不确定性区间成为过拟合的有用指标，使趋势变化的平均速率灵活性更高，增加预测的不确定性。

可以使用参数 interval_width 设置不确定区间的宽度（默认为 80%）

forecast = Prophet(interval_width=0.95).fit(df).predict(future)

结果 

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
Initial log joint probability = -2.46502
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
      99       401.677     0.0020169       115.615           1           1      130
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
     144       401.793  1.05996e-005       59.3202  2.224e-007       0.001      238  LS failed, Hessian reset
     199       401.842  8.23524e-007       78.4056      0.2832           1      311
    Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes
     253       401.843  3.04642e-008       64.9714        0.22           1      385
Optimization terminated normally:
  Convergence detected: relative gradient magnitude is below tolerance

画图

fig=m.plot(forecast)
fig.show()

3.2季节性的不确定性

默认情况下，Prophet 只会返回趋势和观察噪声的不确定性。 获得季节性的不确定性，要进行完整的贝叶斯抽样。

m = Prophet(mcmc_samples=300)
forecast = m.fit(df).predict(future)