自分の勉強用に、沖本竜義「経済・ファイナンスデータの計量経済分析」の章末問題をpythonで解いてみました。
jupyter notebook上で記述したものをほぼそのまま載せてあります。
ソースコードの細かい説明は省いてありますが、今後余裕があれば説明を加えようと思います。

こちらの記事は第5章の章末問題を解いたものになります。
第1章、第2章、第4章、第6章、第7章も公開しています。

各種設定・モジュールのインポート

%matplotlib inline
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from arch.unitroot import ADF
from arch.unitroot import PhillipsPerron

import matplotlib as mpl
font = {"family":"IPAexGothic"}
mpl.rc('font', **font)
plt.rcParams["font.size"] = 12

5.5

(1)

ファイルをインポートする

eco = pd.read_csv('./input/economicdata.csv')
print(eco.shape)
eco.head()

(364, 7)

	date	topix	exrate	indprod	cpi	saunemp	intrate
0	Jan-75	276.09	29.13	47.33	52.625	1.7	12.67
1	Feb-75	299.81	29.70	46.86	52.723	1.8	13.00
2	Mar-75	313.50	29.98	46.24	53.114	1.8	12.92
3	Apr-75	320.57	29.80	47.33	54.092	1.8	12.02
4	May-75	329.65	29.79	47.33	54.385	1.8	11.06

Date列をdatetime型に変換してecoのDatetimeIndexとする

eco.index=pd.to_datetime(eco.date.values,format='%b-%y')
eco.drop('date',axis=1,inplace=True)
eco.head()

	topix	exrate	indprod	cpi	saunemp	intrate
1975-01-01	276.09	29.13	47.33	52.625	1.7	12.67
1975-02-01	299.81	29.70	46.86	52.723	1.8	13.00
1975-03-01	313.50	29.98	46.24	53.114	1.8	12.92
1975-04-01	320.57	29.80	47.33	54.092	1.8	12.02
1975-05-01	329.65	29.79	47.33	54.385	1.8	11.06

topix,exrate,indprod,cpiの対数系列を追加する

logs=['topix','exrate','indprod','cpi'] 
for i in range(len(logs)):
    eco['%s_log'%logs[i]]=np.log(eco[logs[i]])
eco.head()

	topix	exrate	indprod	cpi	saunemp	intrate	topix_log	exrate_log	indprod_log	cpi_log
1975-01-01	276.09	29.13	47.33	52.625	1.7	12.67	5.620727	3.371769	3.857144	3.963191
1975-02-01	299.81	29.70	46.86	52.723	1.8	13.00	5.703149	3.391147	3.847164	3.965052
1975-03-01	313.50	29.98	46.24	53.114	1.8	12.92	5.747799	3.400530	3.833845	3.972441
1975-04-01	320.57	29.80	47.33	54.092	1.8	12.02	5.770101	3.394508	3.857144	3.990686
1975-05-01	329.65	29.79	47.33	54.385	1.8	11.06	5.798031	3.394173	3.857144	3.996088

プロットする

title=['topix_log','exrate_log','indprod_log','cpi_log','saunemp','intrate']

fig,ax = plt.subplots(nrows=3,ncols=2,figsize=[10,15])
for i in range(3):
    for j in range(2):
        ax[i,j].plot(eco[title].iloc[:,2*i+j])
        ax[i,j].set_title(title[2*i+j])
        ax[i,j].set_xlim(eco.index[0],eco.index[-1])
        ax[i,j].set_xticks(eco.index[eco.index.is_year_start][::3])
        ax[i,j].set_xticklabels(eco.index[eco.index.is_year_start][::3].strftime('%y'))
        ax[i,j].set_xlabel('year')
plt.subplots_adjust(wspace=0.2,hspace=0.3)
plt.show()

5.2の解答に従い、exrate_log,saunemp,intrateは場合2、topix_log,indeprod_log,cpi_logは場合3を仮定する

場合1...トレンドがなく、期待値が0
場合2...トレンドがなく、期待値が0ではない
場合3...トレンドがある

trend=['ct','c','ct','ct','c','c']
adf=[]
pp=[]
for i in range(len(title)):
    adf.append(ADF(eco[title[i]],trend=trend[i],max_lags=10,method='AIC'))
    pp.append(PhillipsPerron(eco[title[i]],trend=trend[i]))

ADF検定の結果を表示する

for i in range(len(title)):
    print(title[i])
    print(adf[i])
    print('')

topix_log
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -1.149
P-value                         0.921
Lags                                1
-------------------------------------

Trend: Constant and Linear Time Trend
Critical Values: -3.98 (1%), -3.42 (5%), -3.13 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

exrate_log
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -1.839
P-value                         0.361
Lags                                3
-------------------------------------

Trend: Constant
Critical Values: -3.45 (1%), -2.87 (5%), -2.57 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

indprod_log
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -2.299
P-value                         0.435
Lags                                4
-------------------------------------

Trend: Constant and Linear Time Trend
Critical Values: -3.98 (1%), -3.42 (5%), -3.13 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

cpi_log
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -3.824
P-value                         0.015
Lags                               10
-------------------------------------

Trend: Constant and Linear Time Trend
Critical Values: -3.98 (1%), -3.42 (5%), -3.13 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

saunemp
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -0.846
P-value                         0.805
Lags                               10
-------------------------------------

Trend: Constant
Critical Values: -3.45 (1%), -2.87 (5%), -2.57 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

intrate
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -2.226
P-value                         0.197
Lags                                3
-------------------------------------

Trend: Constant
Critical Values: -3.45 (1%), -2.87 (5%), -2.57 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

ADF検定では、cpi_logのみ単位根の帰無仮説が棄却された

PP検定の結果を表示する

for i in range(len(title)):
    print(title[i])
    print(pp[i])
    print('')

topix_log
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                 -1.269
P-value                         0.895
Lags                               17
-------------------------------------

Trend: Constant and Linear Time Trend
Critical Values: -3.98 (1%), -3.42 (5%), -3.13 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

exrate_log
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                 -1.856
P-value                         0.353
Lags                               17
-------------------------------------

Trend: Constant
Critical Values: -3.45 (1%), -2.87 (5%), -2.57 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

indprod_log
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                 -2.012
P-value                         0.595
Lags                               17
-------------------------------------

Trend: Constant and Linear Time Trend
Critical Values: -3.98 (1%), -3.42 (5%), -3.13 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

cpi_log
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                 -3.898
P-value                         0.012
Lags                               17
-------------------------------------

Trend: Constant and Linear Time Trend
Critical Values: -3.98 (1%), -3.42 (5%), -3.13 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

saunemp
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                 -0.733
P-value                         0.838
Lags                               17
-------------------------------------

Trend: Constant
Critical Values: -3.45 (1%), -2.87 (5%), -2.57 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

intrate
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                 -2.417
P-value                         0.137
Lags                               17
-------------------------------------

Trend: Constant
Critical Values: -3.45 (1%), -2.87 (5%), -2.57 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

ADF検定と同じくPP検定でも、cpi_logのみ単位根の帰無仮説が棄却された

(2)

cpi_log以外の系列の差分系列を作成する

for i in range(len(title)):
    if title[i]!='cpi_log':
        eco['%s_diff'%title[i]]=eco[title[i]].diff()
    else:
        pass

プロットする

diff=['topix_log_diff','exrate_log_diff','indprod_log_diff','saunemp_diff','intrate_diff']

fig,ax = plt.subplots(nrows=3,ncols=2,figsize=[10,15])
for i in range(3):
    for j in range(2):
        if i!=2 or j!=1:
            ax[i,j].plot(eco[diff].iloc[:,2*i+j])
            ax[i,j].set_title(diff[2*i+j])
            ax[i,j].set_xlim(eco.index[0],eco.index[-1])
            ax[i,j].set_xticks(eco.index[eco.index.is_year_start][::3])
            ax[i,j].set_xticklabels(eco.index[eco.index.is_year_start][::3].strftime('%y'))
            ax[i,j].set_xlabel('year')
        else:
            pass
plt.subplots_adjust(wspace=0.2,hspace=0.3)
plt.show()

全ての系列でトレンドがなく期待値が0であるように見えるので、全ての系列について場合1を仮定してADF検定及びPP検定を行う

場合1...トレンドがなく、期待値が0
場合2...トレンドがなく、期待値が0ではない
場合3...トレンドがある

trend=['nc','nc','nc','nc','nc']
adf=[]
pp=[]
for i in range(len(diff)):
    adf.append(ADF(eco[diff[i]][1:],trend=trend[i],max_lags=10,method='AIC'))
    pp.append(PhillipsPerron(eco[diff[i]][1:],trend=trend[i]))

ADF検定の結果を表示する

for i in range(len(diff)):
    print(diff[i])
    print(adf[i])
    print('')

topix_log_diff
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                -13.799
P-value                         0.000
Lags                                0
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

exrate_log_diff
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -8.762
P-value                         0.000
Lags                                2
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

indprod_log_diff
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -6.117
P-value                         0.000
Lags                                3
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

saunemp_diff
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -3.864
P-value                         0.000
Lags                                9
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

intrate_diff
   Augmented Dickey-Fuller Results   
=====================================
Test Statistic                 -7.681
P-value                         0.000
Lags                                2
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

ADF検定では、全ての系列で単位根の帰無仮説が棄却された

PP検定の結果を表示する

for i in range(len(diff)):
    print(diff[i])
    print(pp[i])
    print('')

topix_log_diff
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                -14.137
P-value                         0.000
Lags                               17
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

exrate_log_diff
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                -13.692
P-value                         0.000
Lags                               17
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

indprod_log_diff
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                -24.889
P-value                         0.000
Lags                               17
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

saunemp_diff
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                -21.391
P-value                         0.000
Lags                               17
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

intrate_diff
     Phillips-Perron Test (Z-tau)    
=====================================
Test Statistic                -14.303
P-value                         0.000
Lags                               17
-------------------------------------

Trend: No Trend
Critical Values: -2.57 (1%), -1.94 (5%), -1.62 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.

ADF検定と同じくPP検定でも、全ての系列で単位根の帰無仮説が棄却された
結論として、cpi_logは定常過程に従い、その他5つの系列は全て単位根過程（1次和分過程）に従うことが示唆された

参考サイト

ARCHのドキュメント: http://arch.readthedocs.io/en/latest/index.html