def __init__(self):
super(self.__class__, self).__init__() #initialize DGP
nobs = self.nobs
y_true, x, exog = self.y_true, self.x, self.exog
np.random.seed(8765993)
sigma_noise = 0.1
y = y_true + sigma_noise * np.random.randn(nobs)
m = AdditiveModel(x)
m.fit(y)
res_gam = m.results #TODO: currently attached to class
res_ols = OLS(y, exog).fit()
#Note: there still are some naming inconsistencies
self.res1 = res1 = Dummy() #for gam model
#res2 = Dummy() #for benchmark
self.res2 = res2 = res_ols #reuse existing ols results, will add additional
res1.y_pred = res_gam.predict(x)
res2.y_pred = res_ols.model.predict(res_ols.params, exog)
res1.y_predshort = res_gam.predict(x[:10])
slopes = [i for ss in m.smoothers for i in ss.params[1:]]
const = res_gam.alpha + sum([ss.params[1] for ss in m.smoothers])
#print const, slopes
res1.params = np.array([const] + slopes)
def setup_class(cls):
super(TestAdditiveModel, cls).setup_class() #initialize DGP
nobs = cls.nobs
y_true, x, exog = cls.y_true, cls.x, cls.exog
np.random.seed(8765993)
sigma_noise = 0.1
y = y_true + sigma_noise * np.random.randn(nobs)
m = AdditiveModel(x)
m.fit(y)
res_gam = m.results #TODO: currently attached to class
res_ols = OLS(y, exog).fit()
#Note: there still are some naming inconsistencies
cls.res1 = res1 = Dummy() #for gam model
#res2 = Dummy() #for benchmark
cls.res2 = res2 = res_ols #reuse existing ols results, will add additional
res1.y_pred = res_gam.predict(x)
res2.y_pred = res_ols.model.predict(res_ols.params, exog)
res1.y_predshort = res_gam.predict(x[:10])
slopes = [i for ss in m.smoothers for i in ss.params[1:]]
const = res_gam.alpha + sum([ss.params[1] for ss in m.smoothers])
#print const, slopes
res1.params = np.array([const] + slopes)
x1.sort()
x2 = R.standard_normal(nobs)
x2.sort()
y = R.standard_normal((nobs, ))
f1 = lambda x1: (x1 + x1**2 - 3 - 1 * x1**3 + 0.1 * np.exp(-x1 / 4.))
f2 = lambda x2: (x2 + x2**2 - 0.1 * np.exp(x2 / 4.))
z = standardize(f1(x1)) + standardize(f2(x2))
z = standardize(z) * 2 # 0.1
y += z
d = np.array([x1, x2]).T
if example == 1:
print("normal")
m = AdditiveModel(d)
m.fit(y)
x = np.linspace(-2, 2, 50)
print(m)
y_pred = m.results.predict(d)
plt.figure()
plt.plot(y, '.')
plt.plot(z, 'b-', label='true')
plt.plot(y_pred, 'r-', label='AdditiveModel')
plt.legend()
plt.title('gam.AdditiveModel')
if example == 2:
print("binomial")
x1 = np.linspace(lb, ub, nobs)
x2 = np.sin(2*x1)
x = np.column_stack((x1/x1.max()*2, x2))
exog = (x[:,:,None]**np.arange(order+1)[None, None, :]).reshape(nobs, -1)
idx = lrange((order+1)*2)
del idx[order+1]
exog_reduced = exog[:,idx] #remove duplicate constant
y_true = exog.sum(1) / 2.
z = y_true #alias check
d = x
y = y_true + sigma_noise * np.random.randn(nobs)
example = 1
if example == 1:
m = AdditiveModel(d)
m.fit(y)
y_pred = m.results.predict(d)
for ss in m.smoothers:
print(ss.params)
res_ols = OLS(y, exog_reduced).fit()
print(res_ols.params)
#assert_almost_equal(y_pred, res_ols.fittedvalues, 3)
if example > 0:
import matplotlib.pyplot as plt
x2 = R.standard_normal(nobs)
x2.sort()
y = R.standard_normal((nobs,))
f1 = lambda x1: (x1 + x1**2 - 3 - 1 * x1**3 + 0.1 * np.exp(-x1/4.))
f2 = lambda x2: (x2 + x2**2 - 0.1 * np.exp(x2/4.))
z = standardize(f1(x1)) + standardize(f2(x2))
z = standardize(z) * 2 # 0.1
y += z
d = np.array([x1,x2]).T
if example == 1:
print "normal"
m = AdditiveModel(d)
m.fit(y)
x = np.linspace(-2,2,50)
print m
y_pred = m.results.predict(d)
plt.figure()
plt.plot(y, '.')
plt.plot(z, 'b-', label='true')
plt.plot(y_pred, 'r-', label='AdditiveModel')
plt.legend()
plt.title('gam.AdditiveModel')
import scipy.stats, time
def trend_seasonality_spike_strength(x, freq):
"""Strength of trend and seasonality and spike"""
cont_x = x.dropna()
length_cont_x = len(cont_x)
season = peak = trough = np.nan
if length_cont_x < (2 * freq):
trend = linearity = curvature = season = spike = peak = trough = np.nan
else:
if freq > 1:
all_stl = sm.tsa.seasonal_decompose(cont_x, freq=freq)
trend0 = all_stl.trend
fits = trend0 + all_stl.seasonal
adj_x = cont_x - fits
v_adj = adj_x.var()
detrend = cont_x - trend0
deseason = cont_x - all_stl.seasonal
peak = all_stl.seasonal.max()
trough = all_stl.seasonal.min()
remainder = all_stl.resid
season = 0 if detrend.var() < 1e-10 else max(
0, min(1, 1 - v_adj / detrend.var()))
else: # No seasonal component
tt = np.array([range(length_cont_x)]).T
_trend0_values = AdditiveModel(tt).fit(cont_x.values).mu
trend0 = pd.Series(_trend0_values, index=cont_x.index)
remainder = cont_x - trend0
deseason = cont_x - trend0
v_adj = trend0.var()
trend = 0 if deseason.var() < 1e-10 else max(
0, min(1, 1 - v_adj / deseason.var()))
n = len(remainder)
v = remainder.var()
d = (remainder - remainder.mean())**2
varloo = (v * (n - 1) - d) / (n - 2)
spike = varloo.var()
pl = Poly()
pl.fit(range(length_cont_x), degree=2)
result_pl = pl.predict(range(length_cont_x)) # [:, 2]
X = sm.add_constant(result_pl, has_constant='add')
ols_data = trend0.copy()
ols_data = pd.concat(
[ols_data.reset_index(drop=True),
pd.DataFrame(X)],
axis=1,
ignore_index=True)
ols_data.columns = ['Y', 'Intercept', 'X1', 'X2', 'X3']
result_ols = ols('Y ~ X1 + X2 + X3', data=ols_data.dropna())
trend_coef = result_ols.fit().params
linearity = trend_coef[1]
curvature = trend_coef[2]
result = dict(trend=trend,
spike=spike,
peak=peak,
trough=trough,
linearity=linearity,
curvature=curvature)
if freq > 1:
result["season"] = season
return result
