数学建模

 

编程知识点

模型第三方库-prophet

 

Wang Haihua

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Prophet Model Incorporated with Bayesian Analysis

The manager notes from previous surveys that many American customers who previously stayed at their hotel traveled to Portugal via London with British Airways.

You are tasked with building a Prophet model that can forecast passenger numbers traveling from San Francisco to London with British Airways as accurately as possible.

Specifically, your managers want to maximize the accuracy of the Prophet model through the defining of "changepoints", or points that mark a significant change in cancellation trends.

Additionally, they would also like the Prophet model to account for uncertainty in the trend and seasonality components.

In this notebook

• Milestone 1: Forecasting Air Passenger Numbers
  • Fit the model
  • Plot the forecast components of the model
  • Calculate the RMSE
• Milestone 2: AR(1) Time Series Analysis
• Milestone 3: Forecasting Volatility with Bayesian Time Series Methods

import pandas as pd
import numpy as np

from fbprophet import Prophet

import statsmodels.api as sm
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.seasonal import seasonal_decompose
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

from sklearn.metrics import mean_squared_error

%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns

np.random.seed(42)
idx = pd.IndexSlice

import fbprophet
fbprophet.__version__

'0.7.1'

Milestone 1: Forecasting Air Passenger Numbers

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You are tasked with building a Prophet model that can forecast passenger numbers traveling from San Francisco to London with British Airways as accurately as possible.

• Quick Start - Python API
• Trend Changepoints

df = (pd.read_csv('data/british_airways.csv', parse_dates=['Date'])
      .rename(columns={'Date': 'ds', 'Adjusted Passenger Count': 'y'}))

df.info()
df.head(2)
df.tail(2)

_ = df.plot(x='ds', y='y', figsize=(12, 4), title='Adjusted Passenger Count')

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 129 entries, 0 to 128
Data columns (total 2 columns):
 #   Column  Non-Null Count  Dtype         
---  ------  --------------  -----         
 0   ds      129 non-null    datetime64[ns]
 1   y       129 non-null    int64         
dtypes: datetime64[ns](1), int64(1)
memory usage: 2.1 KB

	ds	y
0	2005-07-01	21686
1	2005-08-01	20084

	ds	y
127	2016-02-01	16230
128	2016-03-01	18392

train, test = df.iloc[:115], df.iloc[115:]

len(train), len(test)

(115, 14)

Fit the model

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m = Prophet()
m.fit(train)

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.

<fbprophet.forecaster.Prophet at 0x7fe132cc6ca0>

Predictions are then made on a dataframe with a column ds containing the dates for which a prediction is to be made.
You can get a suitable dataframe that extends into the future a specified number of days using the helper method Prophet.make_future_dataframe.

future = m.make_future_dataframe(periods=len(test), freq='M')
future.tail(2)

	ds
127	2016-01-31
128	2016-02-29

forecast = m.predict(future)
forecast.tail(2)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	additive_terms	additive_terms_lower	additive_terms_upper	yearly	yearly_lower	yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yhat
127	2016-01-31	18089.307220	12843.423767	15198.180296	18050.655292	18121.616087	-4111.614690	-4111.614690	-4111.614690	-4111.614690	-4111.614690	-4111.614690	0.0	0.0	0.0	13977.69253
128	2016-02-29	18105.011939	14568.818318	17044.917821	18062.220859	18141.574588	-2325.227709	-2325.227709	-2325.227709	-2325.227709	-2325.227709	-2325.227709	0.0	0.0	0.0	15779.78423

Plot the forecast components of the model

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fig1 = m.plot(forecast)

ax = fig1.gca()
ax = test.plot(x='ds', y='y', ls='--', color='C3', ax=ax, label='True TS')

fig2 = m.plot_components(forecast)

Calculate the RMSE

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test.head(2)

	ds	y
115	2015-02-01	14372
116	2015-03-01	17304

round(np.sqrt(mean_squared_error(test['y'], forecast['yhat'].iloc[-len(test):])), 4)

2346.5605