ARIMA时间序列预测-2

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import sys
import os
import pandas as pd
import numpy as np


import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.tsa.api as smt


import matplotlib.pylab as plt
import seaborn as sns

pd.set_option('display.float_format', lambda x:'%0.5f' %x)
np.set_printoptions(precision=5, suppress=True)

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

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

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filename_ts = 'data/series1.csv'
ts_df = pd.read_csv(filename_ts, index_col=0, parse_dates=[0])

n_samples = ts_df.shape[0]
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print(ts_df.shape)
print(ts_df.head())
(120, 1)
              value
2006-06-01  0.21507
2006-07-01  1.14225
2006-08-01  0.08077
2006-09-01 -0.73952
2006-10-01  0.53552

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n_train=int(0.95*n_samples) + 1
n_forecast = n_samples-n_train

ts_train = ts_df.iloc[:n_train]['value']
ts_test = ts_df.iloc[n_train:]['value']
print(ts_train.shape)
print(ts_test.shape)
print("Training Series:", "\n", ts_train.tail(), "\n")
print("Testing Series:", "\n", ts_test.head())
(115,)
(5,)
Training Series: 
 2015-08-01    0.60371
2015-09-01   -1.27372
2015-10-01   -0.93284
2015-11-01    0.08552
2015-12-01    1.20534
Name: value, dtype: float64 

Testing Series: 
 2016-01-01    2.16411
2016-02-01    0.95226
2016-03-01    0.36485
2016-04-01   -2.26487
2016-05-01   -2.38168
Name: value, dtype: float64

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def tsplot(y, lags=None, title='', figsize = (14,10)):
    fig = plt.figure(figsize=figsize)
    layout = (2,2)
    ts_ax = plt.subplot2grid(layout, (0,0))
    hist_ax = plt.subplot2grid(layout, (0,1))
    acf_ax = plt.subplot2grid(layout, (1,0))
    pacf_ax = plt.subplot2grid(layout, (1,1))
    
    y.plot(ax=ts_ax)
    ts_ax.tick_params(labelsize=15)
    ts_ax.set_title(title)
    y.plot(ax=hist_ax, kind='hist', bins=25)
    hist_ax.tick_params(labelsize=15)
    hist_ax.set_title('Histogram')
    smt.graphics.plot_acf(y, lags=lags, ax=acf_ax)
    acf_ax.tick_params(labelsize=15)
    smt.graphics.plot_pacf(y, lags=lags, ax=pacf_ax)
    pacf_ax.tick_params(labelsize=15)
    [ax.set_xlim(0) for ax in [acf_ax, pacf_ax]]
    sns.despine()
    fig.tight_layout()
    return ts_ax, acf_ax, pacf_ax
    
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tsplot(ts_train, title='A Given Training Series', lags=20)
(<matplotlib.axes._subplots.AxesSubplot at 0x1c21cf6080>,
 <matplotlib.axes._subplots.AxesSubplot at 0x1c2240c358>,
 <matplotlib.axes._subplots.AxesSubplot at 0x1c22432e10>)

png

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# 模型训练
arima200 = sm.tsa.SARIMAX(ts_train,order=(2,0,0)) #(p,b,q)
model_results = arima200.fit()
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)

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import itertools

p_min = 0
d_min = 0
q_min = 0
p_max = 4
d_max = 0
q_max = 4

results_bic = pd.DataFrame(index=['AR{}'.format(i) for i in range(p_min, p_max+1)],
                          columns=['MA{}'.format(i) for i in range(q_min, q_max+1)])

for p, d, q in itertools.product(range(p_min,p_max+1),
                                range(d_min, d_max+1),
                                range(q_min, q_max+1)):
    if p == 0 and d==0 and q==0:
        results_bic.loc['AR{}'.format(p), 'MA{}'.format(q)] = np.nan
        continue
    try:
        model = sm.tsa.SARIMAX(ts_train, order=(p,d,q))
        results = model.fit()
        results_bic.loc['AR{}'.format(p), 'MA{}'.format(q)] = results.bic
    except:
        continue
results_bic = results_bic[results_bic.columns].astype(float)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/statespace/sarimax.py:961: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/statespace/sarimax.py:949: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/base/model.py:512: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  "Check mle_retvals", ConvergenceWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/base/model.py:512: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  "Check mle_retvals", ConvergenceWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)

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fig,ax = plt.subplots(figsize=(10,8))
ax = sns.heatmap(results_bic,
                mask=results_bic.isnull(),
                ax = ax,
                annot=True,
                fmt='.2f')
ax.set_title("BIC")
Text(0.5,1,'BIC')

png

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train_results = sm.tsa.arma_order_select_ic(ts_train, ic=['aic', 'bic'], trend='nc', max_ar=4, max_ma=4)
print('AIC', train_results.aic_min_order)
print('BIC', train_results.bic_min_order)
//anaconda3/lib/python3.7/site-packages/statsmodels/base/model.py:492: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available
  'available', HessianInversionWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/base/model.py:512: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  "Check mle_retvals", ConvergenceWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/base/model.py:492: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available
  'available', HessianInversionWarning)
//anaconda3/lib/python3.7/site-packages/statsmodels/base/model.py:512: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  "Check mle_retvals", ConvergenceWarning)


AIC (4, 2)
BIC (1, 1)

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model_results.plot_diagnostics(figsize=(16,12))

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ARIMA时间序列预测-2
https://zhangfuli.github.io/2020/08/18/ARIMA时间序列预测-2/
作者
张富利
发布于
2020年8月18日
许可协议