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diebold_Li_helpers.py
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diebold_Li_helpers.py
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import Quandl
import pandas as pd
from numpy import *
import statsmodels.api as sm
import matplotlib.pylab as plt
import plotly.graph_objs as go
import plotly as py
import cufflinks as cf
import datetime as dt
import seaborn as sns
from sklearn import linear_model
from plotly.offline import download_plotlyjs, init_notebook_mode, iplot
import scipy
import os
import pywt
maturities = asarray([3, 6, 9, 12, 15, 18,21, 24, 30, 36, \
48, 60, 72, 84, 96, 108, 120])
beta_names = ['beta1', 'beta2', 'beta3']
lam_t = .0609
_load2 = lambda x: (1.-exp(-lam_t*x)) / (lam_t*x)
_load3 = lambda x: ((1.-exp(-lam_t*x)) / (lam_t*x)) - \
exp(-lam_t*x)
def loadData():
# load datasets + define parameters
lam_t = .0609
# filter where we only get the last day of every month
tau = ['Date', '1 MO', '3 MO', '6 MO', '9 MO', '12 MO', '15 MO', '18 MO', '21 MO', \
'24 MO', '30 MO', '36 MO', '48 MO', '60 MO', '72 MO', '84 MO', '96 MO', \
'108 MO', '120MO']
__location__ = os.path.realpath(os.path.join(os.getcwd(), os.path.dirname(__file__)))
loc = os.path.join(__location__ + '/Data/FBFitted.csv')
ratedata = pd.read_csv(loc, index_col=0)
_load2 = lambda x: (1.-exp(-lam_t*x)) / (lam_t*x)
_load3 = lambda x: ((1.-exp(-lam_t*x)) / (lam_t*x)) - \
exp(-lam_t*x)
ratedata = ratedata.drop('1', axis=1)
# convert ratedatea indices into datetiems
ratedata.index = pd.to_datetime(ratedata.index, format='%Y%m%d')
# Diebold and Li only use Jan 1980 to Dec 2000
start_idx = ratedata.index.get_loc(dt.datetime.strptime('1985-01-31', '%Y-%m-%d'))
ratedata = ratedata.iloc[start_idx:]
# make 2D matrix of all of the beta coeff. for each maturity
X = zeros((len(maturities), 2))
# X[:,0] = sm.add_constant(ones(len(maturities)))
X[:,0] = _load2(maturities)
X[:,1] = _load3(maturities)
X = sm.add_constant(X)
# for each observation, fit the maturity curve
beta_fits = zeros((len(ratedata), 3))
residuals = zeros((len(ratedata), 17))
for i in range(0, len(ratedata)):
model = sm.regression.linear_model.OLS(ratedata.iloc[i], X)
results = model.fit()
beta_fits[i,:3] = results.params
residuals[i,:] = results.resid
# convert into a dataframe for conv.
beta_fits = pd.DataFrame(beta_fits, columns=beta_names)
residuals = pd.DataFrame(residuals, columns=[str(mat) for mat in maturities])
beta_fits.index = ratedata.index
residuals.index = ratedata.index
return beta_fits, residuals, ratedata
def table2(residuals):
table2 = zeros((len(maturities), 9)) # initialize a matrix
table2 = pd.DataFrame(table2, index=[str(mat) for mat in maturities])
table2.columns = ['Mean', 'Std', 'Min', 'Max', 'MAE', 'RMSE', 'ACF(1)', 'ACF(12)', 'ACF(30)']
for mat in maturities:
table2.ix[str(mat), 0] = residuals.ix[:,str(mat)].mean()
table2.ix[str(mat), 1] = residuals.ix[:,str(mat)].std()
table2.ix[str(mat), 2] = residuals.ix[:,str(mat)].min()
table2.ix[str(mat), 3] = residuals.ix[:,str(mat)].max()
table2.ix[str(mat), 4] = abs(residuals.ix[:,str(mat)]).mean() # MAE
table2.ix[str(mat), 5] = sqrt(pow(residuals.ix[:,str(mat)],2).mean())
table2.ix[str(mat), 6] = sm.tsa.stattools.acf(residuals.ix[:,str(mat)], nlags=31)[1]
table2.ix[str(mat), 7] = sm.tsa.stattools.acf(residuals.ix[:,str(mat)], nlags=31)[13]
table2.ix[str(mat), 8] = sm.tsa.stattools.acf(residuals.ix[:,str(mat)], nlags=31)[-1]
return table2
def table3(beta_fits):
table3 = pd.DataFrame(zeros((3, 8)), index=beta_names)
table3_columns = ['Mean', 'Std', 'Min', 'Max', 'ACF(1)', 'ACF(12)', 'ACF(30)', 'ADF']
table3.columns = table3_columns
for beta in beta_names:
table3.ix[beta, 0] = beta_fits.ix[:,beta].mean()
table3.ix[beta, 1] = beta_fits.ix[:,beta].std()
table3.ix[beta, 2] = beta_fits.ix[:,beta].min()
table3.ix[beta, 3] = beta_fits.ix[:,beta].max()
table3.ix[beta, 4] = sm.tsa.stattools.acf(beta_fits.ix[:, beta], nlags=31)[1]
table3.ix[beta, 5] = sm.tsa.stattools.acf(beta_fits.ix[:, beta], nlags=31)[13]
table3.ix[beta, 6] = sm.tsa.stattools.acf(beta_fits.ix[:, beta], nlags=31)[-1]
table3.ix[beta, -1] = sm.tsa.adfuller(beta_fits.ix[:,beta])[0] # note the ADF assumes [maxlag = 12*(nobs/100)^.25]
return table3
def table4(forecast, actual, naive):
idx_1994 = actual.index.get_loc(dt.datetime.strptime('1994-01-31', '%Y-%m-%d'))
idx_2000 = actual.index.get_loc(dt.datetime.strptime('2000-12-29', '%Y-%m-%d'))
if naive == False:
forecast = roll(forecast.ix[:,:], -1, axis=0)
forecast = pd.DataFrame(forecast)
forecast.index = actual.index[idx_1994:idx_2000]
forecast.columns = actual.columns
err = actual.ix[idx_1994:idx_2000-1,:] - forecast.ix[:-1,:]
table = pd.DataFrame(zeros((5, 5)), index=['3', '12' ,'36', '60', '120'], \
columns=['mean', 'std. dev.', 'RMSE', 'ACF(1)', 'ACF(12)'])
for idx in table.index:
table.ix[idx, 'mean' ] = err.ix[:,idx].mean()
table.ix[idx, 'std. dev.' ] = err.ix[:,idx].std()
table.ix[idx, 'RMSE' ] = sqrt(pow(err.ix[:,idx],2).mean())
table.ix[idx, 'ACF(1)' ] = sm.tsa.acf(err.ix[:, idx])[1]
table.ix[idx, 'ACF(12)' ] = sm.tsa.acf(err.ix[:, idx])[13]
return table
def yieldContors(ratedata):
data = [
go.Contour(
z = ratedata.as_matrix(),
x = ratedata.columns,
y = ratedata.index)
]
layout = go.Layout(
title='Yields vs. Maturities',
width=640,
height=480,
xaxis=dict(
title='Maturity (months)',
titlefont=dict(
size=16)
),
yaxis=dict(
title='Date',
titlefont=dict(
size=16)
)
)
fig = go.Figure(data=data, layout=layout)
return fig
def exampleYield(ratedata, loc):
if type(loc) != list:
print('You must input a list')
if len(loc) ==1:
tit = str('Fig 3: '+ ratedata.index[loc[0]])
else:
tit = "Sample Yield Curves"
layout = go.Layout(
width=640,
height=480,
title=tit,
titlefont=dict(
size=24),
xaxis=dict(
title='Maturity (months)',
titlefont=dict(
size=20)
),
yaxis=dict(
title='Yield (percent)',
titlefont=dict(
size=20)
),
legend=dict(
font=dict(
size=12))
)
trace1 = go.Scatter(
y = ratedata.ix[loc[0], :],
x = ratedata.index)
trace2 = go.Scatter(
y = ratedata.ix[loc[1], :],
x = ratedata.index)
trace3 = go.Scatter(
y = ratedata.ix[loc[2], :],
x = ratedata.index)
data = [trace1, trace2, trace3]
return go.Figure(data=data, layout=layout)
def beta_resid(residuals):
resid_interest = residuals.ix[:,['3','6', '12', '24', '60', '120']]
layout = go.Layout(
title='Residuals for selected maturities (months)',
titlefont=dict(
size=18),
legend= dict(
font=dict(
size=16)),
# title='Residuals for selected maturity periods',
width=640,
height=480,
)
trace1 = go.Scatter(
y = resid_interest.iloc[0, :],
x = resid_interest.index,
name='3 MO')
trace2 = go.Scatter(
y = resid_interest.iloc[1, :],
x = resid_interest.index,
name = '6 MO')
trace3 = go.Scatter(
y = resid_interest.iloc[2, :],
x = resid_interest.index,
name= '12 MO')
trace4 = go.Scatter(
y = resid_interest.iloc[3, :],
x = resid_interest.index,
name='24 MO')
trace5 = go.Scatter(
y = resid_interest.iloc[4, :],
x = resid_interest.index,
name='60 MO')
trace6 = go.Scatter(
y = resid_interest.iloc[5, :],
x = resid_interest.index,
name='120 MO')
fig = py.tools.make_subplots(rows=3, cols=2, print_grid=False)
fig.append_trace(trace1,1,1)
fig.append_trace(trace2, 2,1)
fig.append_trace(trace3, 3,1)
fig.append_trace(trace4, 1,2)
fig.append_trace(trace5, 2,2)
fig.append_trace(trace6, 3,2)
fig['layout'].update(layout)
return fig
def beta_dist(beta_fits):
fig, axes = plt.subplots(1,3, figsize=(10,7))
fig.suptitle('Fitted Parameters Histogram')
sns.set(font_scale=1)
d = sns.distplot(beta_fits.ix[:,'beta1'], ax=axes[0])
d = sns.distplot(beta_fits.ix[:,'beta2'], ax=axes[1])
d = sns.distplot(beta_fits.ix[:,'beta3'], ax=axes[2])
return fig
def fig7(ratedata, beta_fits):
beta1_hat = ratedata.ix[:, '120']
beta2_hat = ratedata.ix[:,'120'] - ratedata.ix[:,'3']
beta3_hat = 2*ratedata.ix[:,'24'] - \
(ratedata.ix[:,'120'] + ratedata.ix[:,'3'])
layout = go.Layout(
title='Residuals for selected maturities (months)',
titlefont=dict(
size=18),
legend= dict(
font=dict(
size=16)),
width=640,
height=480,
)
fig = py.tools.make_subplots(rows=3,
shared_xaxes=True, print_grid=False,subplot_titles=(
'Level', 'Slope', 'Curvature' ))
beta1a = go.Scatter(
x = beta1_hat.index,
y = beta1_hat,
name = 'Emprical')
beta1b = go.Scatter(
x = beta_fits.index,
y = beta_fits.ix[:,'beta1'],
name='Fitted')
beta2a = go.Scatter(
x = beta2_hat.index,
y = beta2_hat,
name = 'Emprical')
beta2b = go.Scatter(
x = beta_fits.index,
y = -beta_fits.ix[:,'beta2'],
name='Fitted')
beta3a = go.Scatter(
x = beta3_hat.index,
y = beta3_hat,
name = 'Emprical')
beta3b = go.Scatter(
x = beta_fits.index,
y = .3*beta_fits.ix[:,'beta3'],
name='Fitted')
fig.append_trace(beta1a,1,1)
fig.append_trace(beta1b, 1,1)
fig.append_trace(beta2a,2,1)
fig.append_trace(beta2b, 2,1)
fig.append_trace(beta3a,3,1)
fig.append_trace(beta3b, 3,1)
fig['layout'].update(layout)
return fig
def ACF_beta(beta_fits, fitted_resid):
titlefont = {'fontsize': 14}
fig = plt.figure(figsize=(20,12))
ax1 = fig.add_subplot(321)
f = sm.graphics.tsa.plot_acf(beta_fits.ix[:,0].values.squeeze(),\
lags=60, ax=ax1)
ax1.set_title('ACF for Level', **titlefont)
ax2 = fig.add_subplot(322)
f = sm.graphics.tsa.plot_pacf(beta_fits.ix[:,0].values.squeeze(),\
lags=60, ax=ax2)
ax2.set_title('PACF for Level', **titlefont)
ax3 = fig.add_subplot(323)
f = sm.graphics.tsa.plot_acf(beta_fits.ix[:,1].values.squeeze(),\
lags=60, ax=ax3)
ax3.set_title('ACF for Slope', **titlefont)
ax4 = fig.add_subplot(324)
f = sm.graphics.tsa.plot_pacf(beta_fits.ix[:,1].values.squeeze(),\
lags=60, ax=ax4)
ax4.set_title('PACF for Slope', **titlefont)
ax5 = fig.add_subplot(325)
f = sm.graphics.tsa.plot_acf(beta_fits.ix[:,2].values.squeeze(),\
lags=60, ax=ax5)
ax5.set_title('ACF for Curvature', **titlefont)
ax6 = fig.add_subplot(326)
f = sm.graphics.tsa.plot_pacf(beta_fits.ix[:,2].values.squeeze(),\
lags=60, ax=ax6)
ax6.set_title('PACF for Curvature', **titlefont)
fig.tight_layout()
def ARforecast(ratedata, beta_fits):
# clip the data to only go to 1994
idx_1994 = ratedata.index.get_loc(dt.datetime.strptime('1994-01-31', '%Y-%m-%d'))
idx_2000 = ratedata.index.get_loc(dt.datetime.strptime('2000-12-29', '%Y-%m-%d'))
# from the CWT, predict each level using an AR model
N_out = idx_2000 - idx_1994 # N out of sample
beta_predict = pd.DataFrame(zeros((N_out, 3)), \
index=beta_fits.index[idx_1994:idx_2000], columns=beta_fits.columns)
yield_forecast = pd.DataFrame(zeros((N_out, len(ratedata.columns))), \
index=beta_fits.index[idx_1994:idx_2000], columns=ratedata.columns)
beta_predict_nieve = pd.DataFrame(zeros((N_out, 3)), \
index=beta_fits.index[idx_1994:idx_2000], columns=beta_fits.columns)
yield_forecast_nieve = pd.DataFrame(zeros((N_out, len(ratedata.columns))), \
index=beta_fits.index[idx_1994:idx_2000
], columns=ratedata.columns)
beta_predict_random = pd.DataFrame(zeros((N_out, 3)), \
index=beta_fits.index[idx_1994:idx_2000], columns=beta_fits.columns)
yield_forecast_random = pd.DataFrame(zeros((N_out, len(ratedata.columns))), \
index=beta_fits.index[idx_1994:idx_2000
], columns=ratedata.columns)
def perDone(i, length, goal):
if i != 0:
if (float(i)/length) *100 > goal:
print("{}% done".format(goal))
return 10.;
else:
return 0
else: return 0
# we want to save all the fits so we can analyze the noise spectrum
saveRuns =[]
# for each date in the withheld series
d = 10.
wavelet = 'db2'
i = 0;
for date in range(0, N_out):
d_updt = perDone(date, N_out, d)
d = d_updt + d
now = idx_1994+date # step each turn to fit
for beta in beta_fits.columns:
testb = beta_fits.ix[i:(now),beta]
coeff = pywt.swt(testb, wavelet)
# coeff will return a list of [level, 2, len(data)]
# each of the levels will have the trend and stochiastic componet
# so we will predict the trend via AR and add a random var
# make the nieve AR forecast
model = sm.tsa.AR(beta_fits.ix[:now,beta]).fit(maxlag=1, \
method='cmle')
# the len of the data must be even, so shift forward one
try:
beta_predict_nieve.ix[date, beta] = \
model.predict(len(beta_fits.ix[:now,beta])-1\
,len(beta_fits.ix[:now,beta])).iloc[-1]
beta_predict_random.ix[date, beta] = \
beta_fits.ix[now-1, beta] +\
(beta_fits.ix[now-1, beta].std())*random.randn()
except KeyError:
pdb.set_trace()
# for each of the levels in wavelet
for level in coeff:
for detail in range(0,len(level)):
model = sm.tsa.AR(level[detail])# fit the model
params = model.fit(maxlag=1, method='cmle').params
# predict the next beta
prediction = model.predict(params, len(level[detail])-1, len(level[detail]))[-1]
# roll append the predicted data and roll forward
level[detail][:] = hstack((level[detail][1:], prediction))
# reconstruct the og signal from the wavlet
try:
pred = []
N_lvl = shape(coeff)[0]
# starts with N, so counting back all the way to sqrt(2)
for t in range(0, N_lvl):
try:
# pdb.set_trace()
# make the stochasitic shock
pred.append((coeff[t][0][-1] + (coeff[t][1][-5])) / sqrt(2)**(N_lvl-t))
# pred.append((coeff[t][0][-1] + coeff[t][1][-1]) / sqrt(2)**(N_lvl-t))
except IndexError:
pdb.set_trace()
beta_predict.ix[date,beta] = mean(pred)
except ValueError:
pdb.set_trace()
# forecast the yields at specific maturities
try:
yield_forecast.ix[date,:] = beta_predict.ix[date, 'beta1'] + \
beta_predict.ix[date, 'beta2']*_load2(asarray(maturities)) +\
beta_predict.ix[date, 'beta3']*_load3(asarray(maturities))
yield_forecast_nieve.ix[date,:] = beta_predict_nieve.ix[date, 'beta1'] + \
beta_predict_nieve.ix[date, 'beta2']*_load2(asarray(maturities)) +\
beta_predict_nieve.ix[date, 'beta3']*_load3(asarray(maturities))
yield_forecast_random.ix[date,:] = beta_predict_random.ix[date, 'beta1'] + \
beta_predict_random.ix[date, 'beta2']*_load2(asarray(maturities)) +\
beta_predict_random.ix[date, 'beta3']*_load3(asarray(maturities))
saveRuns.append(coeff)
except TypeError:
pdb.set_trace()
i = i +1
return yield_forecast_nieve, yield_forecast, yield_forecast_random, saveRuns
def cwtGraph(beta_fits):
fig = plt.figure(figsize=(10,7))
ax1 = fig.add_subplot(131)
cwtmatr= scipy.signal.cwt(beta_fits.ix[:,'beta1'], scipy.signal.ricker, arange(1, 100))
ax1.imshow(cwtmatr, extent=[0, cwtmatr.shape[1], 1, cwtmatr.shape[0]], cmap='PRGn', \
aspect='auto', vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max())
ax1.set_xlabel('Time (months)')
ax1.set_title('Beta1')
ax1.set_ylabel('Scale')
ax2 = fig.add_subplot(132)
cwtmatr= scipy.signal.cwt(beta_fits.ix[:,'beta2'], scipy.signal.ricker, arange(1, 100))
ax2.imshow(cwtmatr, extent=[0, cwtmatr.shape[1], 1, cwtmatr.shape[0]], cmap='PRGn', \
aspect='auto', vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max())
ax2.set_xlabel('Time (months)')
ax2.set_ylabel('Scale')
ax2.set_title('Beta2')
ax3 = fig.add_subplot(133)
cwtmatr= scipy.signal.cwt(beta_fits.ix[:,'beta3'], scipy.signal.ricker, arange(1, 100))
ax3.imshow(cwtmatr, extent=[0, cwtmatr.shape[1], 1, cwtmatr.shape[0]], cmap='PRGn', \
aspect='auto', vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max())
ax3.set_xlabel('Time (months)')
ax3.set_ylabel('Scale')
ax3.set_title('Beta3')
plt.show()
def meanError(actual, naive, wavelet):
idx_1994 = actual.index.get_loc(dt.datetime.strptime('1994-01-31', '%Y-%m-%d'))
idx_2000 = actual.index.get_loc(dt.datetime.strptime('2000-12-29', '%Y-%m-%d'))
err = roll(wavelet.ix[:,:], -1, axis=0)
trace1 = go.Scatter(
x = maturities,
y = (err[:-1,:]-actual.ix[idx_1994:idx_2000-1]).mean().abs(),
name='Wavelet-extended')
trace2 = go.Scatter(
x = maturities,
y = (naive - \
actual.ix[idx_1994:idx_2000]).mean().abs(),
name='Naive')
layout = go.Layout(
titlefont=dict(
size=16),
legend= dict(
font=dict(
size=18)),
title='Mean Absolute Error',
width=600,
height=480,
xaxis=dict(
title='Maturity (months)'),
yaxis=dict(
title='Mean Error (yield percentage)')
)
data = [trace1, trace2]
return go.Figure(data=data, layout=layout)