[] ARIMA time series model

%load_ext autoreload
%autoreload 2
%matplotlib inline
%config InlineBackend.figure_format='retina'

from __future__ import absolute_import, division, print_function
# http://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
import sys
import os

import pandas as pd
import numpy as np

# # Remote Data Access
# import pandas_datareader.data as web
# import datetime
# # reference: https://pandas-datareader.readthedocs.io/en/latest/remote_data.html

# TSA from Statsmodels
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt

# Display and Plotting
import matplotlib.pylab as plt
import seaborn as sns

pd.set_option('display.float_format', lambda x: '%.5f' % x) # pandas
np.set_printoptions(precision=5, suppress=True) # numpy

pd.set_option('display.max_columns', 100)
pd.set_option('display.max_rows', 100)

# seaborn plotting style
sns.set(style='ticks', context='poster')

#Read the data
#美国消费者信心指数
Sentiment = 'data/sentiment.csv'
Sentiment = pd.read_csv(Sentiment, index_col=0, parse_dates=[0])

sentiment_short = Sentiment.loc['2005':'2016']

sentiment_short.plot(figsize=(12,8))
plt.legend(bbox_to_anchor=(1.25, 0.5))
plt.title("Consumer Sentiment")
sns.despine()

As it can be seen from the figure, a time series fluctuations, therefore this differential

#一阶差分
sentiment_short['diff_1'] = sentiment_short['UMCSENT'].diff(1)
#二阶差分
sentiment_short['diff_2'] = sentiment_short['diff_1'].diff(1)

sentiment_short.plot(subplots=True, figsize=(18, 12))

Pq determined by ACF PACF

fig = plt.figure(figsize=(12,8))

ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(sentiment_short, lags=20,ax=ax1)
ax1.xaxis.set_ticks_position('bottom')
fig.tight_layout();

ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(sentiment_short, lags=20, ax=ax2)
ax2.xaxis.set_ticks_position('bottom')
fig.tight_layout();