import pandas as pd
from pandas_datareader.data import DataReader
import matplotlib.pyplot as plt
from datetime import date
from statsmodels.tsa.stattools import acf
from statsmodels.graphics.tsaplots import plot_acf
series = 'DGS10'
datasource = 'fred'
start = date(1984, 1, 1)
end = date(2017, 1, 1)
data = DataReader(series, datasource, start)
data['dailydiff'] = data.diff()
autocorrelation_daily = data['dailydiff'].autocorr()
print("The autocorrelation of daily " + str(series) + " changes is %4.2f" %
(autocorrelation_daily))
weekly_data = data[series].resample('W').last()
weekly_data['weeklydiff'] = weekly_data.diff()
autocorrelation_weekly = weekly_data['weeklydiff'].autocorr()
print("The autocorrelation of weekly " + str(series) + " changes is %4.2f" %
(autocorrelation_weekly))
monthly_data = data[series].resample('M').last()
monthly_data['monthlydiff'] = monthly_data.diff()
autocorrelation_monthly = monthly_data['monthlydiff'].autocorr()
print("The autocorrelation of monthly " + str(series) + " changes is %4.2f" %
(autocorrelation_monthly))
annual_data = data[series].resample('A').last()
annual_data['annualdiff'] = annual_data.diff()
#
# As described above, the goal of this model was to create an
# interpretable series which could be used to understand the current status
# of the macroeconomy. This is what the coincident index is designed to do.
# It is constructed below. For readers interested in an explanation of the
# construction, see Kim and Nelson (1999) or Stock and Watson (1991).
#
# In essense, what is done is to reconstruct the mean of the (differenced)
# factor. We will compare it to the coincident index on published by the
# Federal Reserve Bank of Philadelphia (USPHCI on FRED).
usphci = DataReader(
'USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI']
usphci.plot(figsize=(13, 3))
dusphci = usphci.diff()[1:].values
def compute_coincident_index(mod, res):
# Estimate W(1)
spec = res.specification
design = mod.ssm['design']
transition = mod.ssm['transition']
ss_kalman_gain = res.filter_results.kalman_gain[:, :, -1]
k_states = ss_kalman_gain.shape[0]
W1 = np.linalg.inv(
np.eye(k_states) -
np.dot(np.eye(k_states) - np.dot(ss_kalman_gain, design), transition)
).dot(ss_kalman_gain)[0]
#
# As described above, the goal of this model was to create an
# interpretable series which could be used to understand the current status
# of the macroeconomy. This is what the coincident index is designed to do.
# It is constructed below. For readers interested in an explanation of the
# construction, see Kim and Nelson (1999) or Stock and Watson (1991).
#
# In essense, what is done is to reconstruct the mean of the (differenced)
# factor. We will compare it to the coincident index on published by the
# Federal Reserve Bank of Philadelphia (USPHCI on FRED).
usphci = DataReader('USPHCI', 'fred', start='1979-01-01',
end='2014-12-01')['USPHCI']
usphci.plot(figsize=(13, 3))
dusphci = usphci.diff()[1:].values
def compute_coincident_index(mod, res):
# Estimate W(1)
spec = res.specification
design = mod.ssm['design']
transition = mod.ssm['transition']
ss_kalman_gain = res.filter_results.kalman_gain[:, :, -1]
k_states = ss_kalman_gain.shape[0]
W1 = np.linalg.inv(
np.eye(k_states) -
np.dot(np.eye(k_states) - np.dot(ss_kalman_gain, design), transition)
).dot(ss_kalman_gain)[0]
def dynamic_factor_model_example():
np.set_printoptions(precision=4, suppress=True, linewidth=120)
# Get the datasets from FRED.
start = '1979-01-01'
end = '2014-12-01'
indprod = DataReader('IPMAN', 'fred', start=start, end=end)
income = DataReader('W875RX1', 'fred', start=start, end=end)
sales = DataReader('CMRMTSPL', 'fred', start=start, end=end)
emp = DataReader('PAYEMS', 'fred', start=start, end=end)
#dta = pd.concat((indprod, income, sales, emp), axis=1)
#dta.columns = ['indprod', 'income', 'sales', 'emp']
#HMRMT = DataReader('HMRMT', 'fred', start='1967-01-01', end=end)
#CMRMT = DataReader('CMRMT', 'fred', start='1997-01-01', end=end)
#HMRMT_growth = HMRMT.diff() / HMRMT.shift()
#sales = pd.Series(np.zeros(emp.shape[0]), index=emp.index)
# Fill in the recent entries (1997 onwards).
#sales[CMRMT.index] = CMRMT
# Backfill the previous entries (pre 1997).
#idx = sales.loc[:'1997-01-01'].index
#for t in range(len(idx)-1, 0, -1):
# month = idx[t]
# prev_month = idx[t-1]
# sales.loc[prev_month] = sales.loc[month] / (1 + HMRMT_growth.loc[prev_month].values)
dta = pd.concat((indprod, income, sales, emp), axis=1)
dta.columns = ['indprod', 'income', 'sales', 'emp']
dta.loc[:, 'indprod':'emp'].plot(subplots=True, layout=(2, 2), figsize=(15, 6));
# Create log-differenced series.
dta['dln_indprod'] = (np.log(dta.indprod)).diff() * 100
dta['dln_income'] = (np.log(dta.income)).diff() * 100
dta['dln_sales'] = (np.log(dta.sales)).diff() * 100
dta['dln_emp'] = (np.log(dta.emp)).diff() * 100
# De-mean and standardize.
dta['std_indprod'] = (dta['dln_indprod'] - dta['dln_indprod'].mean()) / dta['dln_indprod'].std()
dta['std_income'] = (dta['dln_income'] - dta['dln_income'].mean()) / dta['dln_income'].std()
dta['std_sales'] = (dta['dln_sales'] - dta['dln_sales'].mean()) / dta['dln_sales'].std()
dta['std_emp'] = (dta['dln_emp'] - dta['dln_emp'].mean()) / dta['dln_emp'].std()
# Get the endogenous data.
endog = dta.loc['1979-02-01':, 'std_indprod':'std_emp']
# Create the model.
mod = sm.tsa.DynamicFactor(endog, k_factors=1, factor_order=2, error_order=2)
initial_res = mod.fit(method='powell', disp=False)
res = mod.fit(initial_res.params, disp=False)
print(res.summary(separate_params=False))
# Estimated factors.
fig, ax = plt.subplots(figsize=(13, 3))
# Plot the factor.
dates = endog.index._mpl_repr()
ax.plot(dates, res.factors.filtered[0], label='Factor')
ax.legend()
# Retrieve and also plot the NBER recession indicators.
rec = DataReader('USREC', 'fred', start=start, end=end)
ylim = ax.get_ylim()
ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1)
# Post-estimation.
res.plot_coefficients_of_determination(figsize=(8, 2))
# Coincident index.
usphci = DataReader('USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI']
usphci.plot(figsize=(13, 3))
dusphci = usphci.diff()[1:].values
fig, ax = plt.subplots(figsize=(13, 3))
# Compute the index.
coincident_index = compute_coincident_index(mod, res, dta, usphci, dusphci)
# Plot the factor.
dates = endog.index._mpl_repr()
ax.plot(dates, coincident_index, label='Coincident index')
ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')
ax.legend(loc='lower right')
# Retrieve and also plot the NBER recession indicators.
ylim = ax.get_ylim()
ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1)
# Extended dynamic factor model.
# Create the model.
extended_mod = ExtendedDFM(endog)
initial_extended_res = extended_mod.fit(maxiter=1000, disp=False)
extended_res = extended_mod.fit(initial_extended_res.params, method='nm', maxiter=1000)
print(extended_res.summary(separate_params=False))
extended_res.plot_coefficients_of_determination(figsize=(8, 2))
fig, ax = plt.subplots(figsize=(13,3))
# Compute the index.
extended_coincident_index = compute_coincident_index(extended_mod, extended_res, dta, usphci, dusphci)
# Plot the factor.
dates = endog.index._mpl_repr()
ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model')
ax.plot(dates, extended_coincident_index, '--', linewidth=3, label='Extended model')
ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')
ax.legend(loc='lower right')
ax.set(title='Coincident indices, comparison')
# Retrieve and also plot the NBER recession indicators.
ylim = ax.get_ylim()
ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1)
