"Measurement Time Series Analysis of Economic and Finance Data" Solving Chapter End Problems with Python

[Tatsuyoshi Okimoto "Measurement Time Series Analysis of Economic and Finance Data"](https://www.amazon.co.jp/gp/product/4254127928/ref=as_li_ss_tl?ie=UTF8&ref_=nav_ya_signin&&linkCode=ll1&tag=sankichi92-22&linkId = cda8aa8cd64ad2bda6a911e37a8c9ca1) I'm solving the end-of-chapter problem "using a computer" with ** Python **.

@aokikenichi wrote an article about what he solved with ** R ** as follows, so I decided to publish what I solved with Python before.

-"Measurement Time Series Analysis of Economic and Finance Data" Solving the End Problem with R-Chapter 1 Basic Concept of Time Series Analysis- -"Measurement time series analysis of economic and finance data" Solving the end problem with R-Chapter 2 ARMA process- -"Measurement time series analysis of economic and finance data" Solving the end-of-chapter problem with R-Chapter 4 VAR model-

However, it was troublesome to paste the resulting chart, so I am writing only the code here. For the output result, see ** Updating Jupyter Notebook to Gist **.

Library to use

import numpy as np
import pandas as pd
from statsmodels.tsa.api import stattools, AR, ARMA, VAR
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.stats.diagnostic import acorr_ljungbox
import matplotlib.pyplot as plt

In particular, I often use pandas and statsmodels.tsa. I referred to the following documents.

1. Basic concept of time series analysis

1.3

mu_sigma = [(0, 1), (2, 1), (-2, 1), (0, 2), (0, 3), (2, 2)]
white_noise = DataFrame()
for mu, sigma in mu_sigma:
    name = '$\mu={0}, \sigma={1}$'.format(mu, sigma)
    white_noise[name] = np.random.normal(mu, sigma, 100)
white_noise.plot(subplots=True, layout=(3,2), figsize=(12, 12))

1.5

economicdata = pd.read_excel('http://www.geocities.jp/tatsuyoshi_okimoto/books/tsa/economicdata.xls', index_col='date')

(1)

economicdata.plot(subplots=True, layout=(3,2), figsize=(12, 12))

(2)

economicdata_pct = np.log(economicdata).diff() * 100

(3)

economicdata_pct[['topix', 'exrate', 'indprod']].plot(subplots=True, figsize=(12, 12))

(4)

indprod = economicdata_pct.indprod.dropna()

plot_acf(indprod, lags=20)

def portmanteau_test(endog, lags=10):
    q_m, pvalues = acorr_ljungbox(endog, lags=lags)
    df = pd.DataFrame([q_m.round(2), pvalues.round(3)], index=['Q(m)', 'p-value'], columns=range(1, lags + 1))
    return df

print(portmanteau_test(indprod))

(5)

topix = economicdata_pct.topix.dropna()
print(portmanteau_test(topix))

exrate = economicdata_pct.exrate.dropna()
print(portmanteau_test(exrate))

2. ARMA process

2.5

(1)

def plot_acf_pacf(x, lags=20):
    fig = plt.figure(figsize=(12,4))
    ax1 = fig.add_subplot(121)
    plot_acf(x, ax=ax1, lags=lags)
    ax2 = fig.add_subplot(122)
    plot_pacf(x, ax=ax2, lags=lags)
    return fig

plot_acf_pacf(indprod)

ar4 = AR(indprod).fit(maxlag=4)
plot_acf(ar4.resid, lags=20)

arma12 = ARMA(indprod, (1,2)).fit()
plot_acf(arma12.resid, lags=20)

def arma_order_select(y, orders):
    df = pd.DataFrame(index=['AIC', 'SIC'])
    for order in orders:
        model = ARMA(y, order).fit()
        df[str(order)] = [round(model.aic, 1), round(model.bic, 1)]
    df['min'] = df.idxmin(axis=1)
    return df

orders = [(4,0), (0,3), (1,1), (2,1), (1,2), (2,2)]
print(arma_order_select(indprod, orders))

(2)

print(portmanteau_test(ar4.resid))
print(portmanteau_test(arma12.resid))

2.6

arma = pd.read_excel('http://www.geocities.jp/tatsuyoshi_okimoto/books/tsa/arma.xls')

(1)

y1 = arma.y1.values
plot_acf_pacf(y1)

(3)

order_select = stattools.arma_order_select_ic(y1, max_ar=2, max_ma=2,  ic=['aic', 'bic'])
print(order_select['aic'])
print(order_select['bic'])
print('AIC:', order_select['aic_min_order'], ', SIC:', order_select['bic_min_order'])

(4)

ar2 = AR(y1).fit(maxlag=2)
plot_acf(ar2.resid, lags=20)
print(portmanteau_test(ar2.resid))

arma21 = ARMA(y1, (2,1)).fit()
plot_acf(arma21.resid, lags=20)
print(portmanteau_test(arma21.resid))

(5)

y2 = arma.y2.values
plot_acf_pacf(y2)

order_select = stattools.arma_order_select_ic(y2, max_ar=2, max_ma=2, ic=['aic', 'bic'])
print(order_select['aic'])
print(order_select['bic'])
print('AIC:', order_select['aic_min_order'], ', SIC:', order_select['bic_min_order'])

arma21 = ARMA(y2, (2,1)).fit()
plot_acf(arma21.resid, lags=20)
print(portmanteau_test(arma21.resid))

y3 = arma.y3.values
plot_acf_pacf(y3)

orders = [(4,0), (8,0), (1,1), (1,2), (1,3), (2,1), (2,2), (2,3)]
print(arma_order_select(y3, orders))

arma23 = ARMA(y3, (2,3)).fit()
plot_acf(arma23.resid, lags=20)
print(portmanteau_test(arma23.resid))

arma11 = ARMA(y3, (1,1)).fit()
plot_acf(arma11.resid, lags=20)
print(portmanteau_test(arma11.resid))

4. VAR model

msci_day = pd.read_excel('http://www.geocities.jp/tatsuyoshi_okimoto/books/tsa/msci_day.xls', index_col='Date')
msci_pct = np.log(msci_day).diff().dropna() * 100

4.5

(1)

jp_uk_us = ['jp', 'uk', 'us']
var3 = VAR(msci_pct[jp_uk_us]).fit(3)

import itertools

df = pd.DataFrame(index=['Statistical test statistic', 'p-value'])
for pair in itertools.permutations(jp_uk_us, r=2):
    col = pair[1] + ' → ' + pair[0]
    res = var3.test_causality(*pair, verbose=False)
    df[col] = [res['statistic'].round(3), res['pvalue'].round(3)]
print(df)

var3.irf().plot(orth=True)

var3.fevd().plot()

4.6

(4)

model = VAR(msci_pct[['jp', 'fr', 'ca']])
model.select_order(10)
result = model.fit(maxlags=10, ic='aic')

(5)

result.test_causality('fr', 'jp')

result.test_causality('fr', 'ca')

(6)

result.irf().plot(impulse='fr', response='jp')

(7)

result.fevd().plot()