def backward_elimination(X_opt, y, significant_level):
import statsmodels.regression.linear_model as sm
num_var = len(X_opt[0])
while (num_var > 0):
regressor = sm.OLS(y, X_opt).fit()
max_Pvalue = max(regressor.pvalues).astype(float)
if (max_Pvalue > significant_level):
real_num_var = num_var
for i in range(num_var):
prev_X_opt = X_opt
cur_adjusted_rvalue = regressor.rsquared_adj
if (regressor.pvalues[i] == max_Pvalue):
X_opt = np.delete(X_opt, i, 1)
temp_regressor = sm.OLS(y, X_opt).fit()
new_adjusted_rvalue = temp_regressor.rsquared_adj
if (new_adjusted_rvalue < cur_adjusted_rvalue):
return prev_X_opt
real_num_var -= 1
num_var = real_num_var
else:
break
return X_opt
def backwards_elimination(X, y, sl):
#print("\n\n\n")
X = np.append(
arr=np.ones((50, 1)).astype(int), values=X, axis=1
) #adding x0=1 for coeff b0 in the multiple linear regression equation
#X_opt=X[:,[0,3]] #starting with all independent variables, eliminating ivs one by one
X_opt = X
SL = 0.05
maxP = 0
rows, cols = X_opt.shape
#print("\t\tX_opt\n\n\n",X_opt)
for i in range(0, cols):
#print("\n\n")
regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()
p_len = len(regressor_OLS.pvalues)
#print("pvalue array is = ",regressor_OLS.pvalues)
#print("length of p value array is ",p_len)
maxP = find_max(regressor_OLS.pvalues, p_len)
#maxP = max(regressor_OLS.pvalues).astype(float)
if (maxP > SL):
#print("inside mxp>sl")
for j in range(0, cols - i):
#print("inside j loop")
if (regressor_OLS.pvalues[j].astype(float) == maxP):
#print("inside main condition")
#print("print col to be deleted is ",X_opt[:,j])
X_opt = np.delete(X_opt, j, 1)
#print("\n\nfinal X_opt is \n",X_opt)
regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()
return regressor_OLS
def vif_sub(x, regressors):
x_i = regressors.iloc[:, x]
mask = np.arange(k) != x
x_not_i = regressors.iloc[:, mask]
rsq = linear_model.OLS(x_i, x_not_i, missing="drop").fit().rsquared_adj
vif = 1.0 / (1.0 - rsq)
return vif
def backwardElimination(
x,
y,
sl,
con=True): # con implies if the constent matrix is added ao not
import matplotlib.pyplot as plt
import numpy as np
import statsmodels.regression.linear_model as lmd
if con == False:
x = np.append(arr=np.ones((len(x), 1)).astype(int), values=x, axis=1)
numVars = len(x[0])
r_sq = 0
for i in range(0, numVars):
regressor_OLS = lmd.OLS(endog=y, exog=x).fit()
if regressor_OLS.rsquared_adj > r_sq: # To see the Complete graph replace r_sq by 0
r_sq = regressor_OLS.rsquared_adj
maxVar = max(regressor_OLS.pvalues).astype(float)
if maxVar > sl:
for j in range(0, numVars - i):
if (regressor_OLS.pvalues[j].astype(float) == maxVar):
x = np.delete(x, j, 1)
print(regressor_OLS.rsquared_adj)
plt.scatter(i, regressor_OLS.rsquared_adj)
plt.draw()
plt.pause(0.2)
plt.show()
print(regressor_OLS.summary())
return x
def cluster_vs_meta_granger_TM(c, X, M, Ml, lags=7, thresh=0.05):
# use the Toda Yamamoto method (environmental data is stationary, but clusters are not)
x1 = X[c].sum(0)
adf = stattools.adfuller(x1, maxlag=lags)
if (adf[0] > adf[4]['5%']):
m1 = adf[2]
else:
m1 = 0
R = []
for j, x2 in enumerate(M):
have_values = np.isfinite(x2)
xi = x1[have_values]
x2i = x2[have_values]
adf = stattools.adfuller(x2i, maxlag=lags)
if (adf[0] > adf[4]['5%']):
m2 = adf[2]
else:
m2 = 0
m = max(m1, m2)
y = [
xi[i + max(0, m2 - m1):len(xi) + i - (m1 + lags)]
for i in range(m1 + lags)
] + [
x2i[i + max(0, m1 - m2):len(xi) + i - (m2 + lags)]
for i in range(m2 + lags)
]
y = np.array(y).T
lm = linear_model.OLS(xi[max(m1, m2) + lags:], y)
result = lm.fit()
Restr = np.eye(y.shape[1])[m + lags:]
wald = result.wald_test(Restr)
if wald.pvalue < thresh:
R.append((wald.pvalue, Ml[j]))
return m, sorted(R)
def _za_thread(x, regression, start, end, nobs, basecols, baselags, res,
residx):
# first-diff y
dy = np.diff(x, axis=0)[:, 0]
zastat = bpidx = np.inf
for bp in range(start, end):
# reserve exog space
exog = np.zeros((dy[baselags:].shape[0], basecols + baselags))
# constant
exog[:, 0] = 1
# intercept dummy / trend / trend dummy
if regression != 't':
exog[(bp - (baselags + 1)):, 1] = 1
exog[:, 2] = np.arange(baselags + 2, nobs + 1)
if regression == 'ct':
exog[(bp - (baselags + 1)):, 3] = np.arange(1, nobs - bp + 1)
else:
exog[:, 1] = np.arange(baselags + 2, nobs + 1)
exog[(bp - (baselags + 1)):, 2] = np.arange(1, nobs - bp + 1)
# lagged y
exog[:, basecols - 1] = x[baselags:(nobs - 1), 0]
# lagged dy
exog[:, basecols:] = tsa.lagmat(
dy, baselags, trim='none')[baselags:exog.shape[0] + baselags]
stat = lm.OLS(dy[baselags:], exog).fit().tvalues[basecols - 1]
if stat < zastat:
zastat = stat
bpidx = bp - 1
crit = zacrit.za_crit(zastat, regression)
pval = crit[0]
cvdict = crit[1]
res[residx] = [zastat, pval, cvdict, bpidx]
def polynomial_regression() -> List[float]:
""" Define the model directly through the design matrix.
Similar to MATLAB's "regress" command.
Returns
-------
params : coefficients for the quadratic model
"""
# Generate the data: a noisy second order polynomial
# To get reproducable values, I provide a seed value
np.random.seed(987654321)
t = np.arange(0, 10, 0.1)
y = 4 + 3 * t + 2 * t**2 + 5 * np.random.randn(len(t))
# --- >>> START stats <<< ---
# Make the fit. Note that this is another "OLS" than the one in
# "model_formulas", as it works directly with the design matrix!
M = np.column_stack((np.ones(len(t)), t, t**2))
res = sm.OLS(y, M).fit()
# --- >>> STOP stats <<< ---
# Display the results
print('Summary:')
print((res.summary()))
print(('The fit parameters are: {0}'.format(str(res.params))))
print('The confidence intervals are:')
print((res.conf_int()))
return res.params # should be [ 4.74244177, 2.60675788, 2.03793634]
def test_arch_lm(simulated_data):
zm = ZeroMean(simulated_data, volatility=GARCH())
res = zm.fit(disp=DISPLAY)
wald = res.arch_lm_test()
nobs = simulated_data.shape[0]
df = int(np.ceil(12.0 * np.power(nobs / 100.0, 1 / 4.0)))
assert wald.df == df
assert "Standardized" not in wald.null
assert "Standardized" not in wald.alternative
assert "H0: Standardized" not in wald.__repr__()
assert "heteroskedastic" in wald.__repr__()
resids2 = pd.Series(res.resid ** 2)
data = [resids2.shift(i) for i in range(df + 1)]
data = pd.concat(data, 1).dropna()
lhs = data.iloc[:, 0]
rhs = smtools.add_constant(data.iloc[:, 1:])
ols_res = smlm.OLS(lhs, rhs).fit()
assert_almost_equal(wald.stat, nobs * ols_res.rsquared)
assert len(wald.critical_values) == 3
assert "10%" in wald.critical_values
wald = res.arch_lm_test(lags=5)
assert wald.df == 5
assert_almost_equal(wald.pval, 1 - stats.chi2(5).cdf(wald.stat))
wald = res.arch_lm_test(standardized=True)
assert wald.df == df
assert "Standardized" in wald.null
assert "Standardized" in wald.alternative
assert_almost_equal(wald.pval, 1 - stats.chi2(df).cdf(wald.stat))
assert "H0: Standardized" in wald.__repr__()
def cohort_1d_regressions(configs):
for fpath in sorted(
glob.glob(os.path.join(configs["metagroup_path"], "*.csv"))):
groupname = fpath.split("/")[-1][:-4]
print("Group: {}".format(groupname))
with open(fpath, 'r') as fp:
csv_fp = csv.reader(fp, delimiter=',')
next(csv_fp)
x = []
y = []
for line in csv_fp:
if line[0].strip(
) == "held_out" or line[1] == "" or line[2] == "":
continue
x.extend([1, 0])
y.extend([float(line[1]), float(line[2])])
lm = statslm.OLS(y,
statstools.add_constant(
np.array(x).reshape(len(x), 1)),
missing='raise',
hasconst=True)
results = lm.fit()
print(
"Group result for group {} intercept/group effect: {}, t-test p-val: {}"
.format(groupname, results.params, results.pvalues))
def interaction_effects(data, dep_variable, threshold):
# remove date variable and booking/click depending on dep_variable
data = data.iloc[:, 1:].copy()
if dep_variable == "click_bool":
data = data.drop("booking_bool", axis=1)
elif dep_variable == "booking_bool":
data = data.drop("click_bool", axis=1)
# choose dependent variable
X = data.drop(dep_variable, axis=1)
y = data[dep_variable]
# Generate interaction terms
poly = PolynomialFeatures(interaction_only=True, include_bias=False)
X_interaction = poly.fit_transform(X)
# Get names of these terms
names = PolynomialFeatureNames(poly.get_feature_names(), X)
# Fit model to check importance of features
model = linear_model.OLS(y, X_interaction).fit()
# save results
with open("output/interaction_effects/modelsummary.csv", "w") as f:
f.write(model.summary().as_csv())
# show significant results
results = pd.read_csv(
"output/interaction_effects/modelsummary.csv",
skiprows=10,
skipfooter=10,
index_col=0,
)
results.index = names
sign_results = results[results["P>|t| "] < threshold]
print(sign_results.sort_values(by=" coef ", ascending=False))
def calculate(self, key, return_data=False):
lob = self._lobagent.get(key).get_data()
price = self._priceagent.get(key).get_data().price[0]
lob_buy = lob.loc[lob.buysell == 'B',
['price', 'volume']].sort_values(by='price',
ascending=False)
lob_sell = lob.loc[lob.buysell == 'S',
['price', 'volume']].sort_values(by='price',
ascending=True)
tr_costs_sell = copy.copy(lob_buy)
tr_costs_buy = copy.copy(lob_sell)
tr_costs_sell['costs'] = np.cumsum(
np.abs(tr_costs_sell.price - price) * tr_costs_sell.volume)
tr_costs_sell.volume = np.cumsum(tr_costs_sell.volume)
tr_costs_buy['costs'] = np.cumsum(
np.abs(tr_costs_buy.price - price) * tr_costs_buy.volume)
tr_costs_buy.volume = -np.cumsum(tr_costs_buy.volume)
tr_costs = pd.concat(
(tr_costs_buy,
tr_costs_sell)).sort_values(by='volume').reset_index(drop=True)
tr_costs = tr_costs[['volume', 'costs']]
if return_data:
return tr_costs
try:
DIV = DIVIDER[key[1]]
except KeyError:
DIV = 1
V = np.array(tr_costs.volume) / DIV
costs = np.array(tr_costs.costs)
y = costs
X = np.stack([V, V**2, V**3, V**4], axis=1)
model = linear_model.OLS(y, X)
results = model.fit()
params = np.array([results.params])
covparams = results.cov_params()
column_names = self._transactioncoststable.get_column_names()
key_names = self._transactioncoststable.get_key()
row = pd.DataFrame(columns=column_names)
row[key_names[0]] = [key[0]]
row[key_names[1]] = [key[1]]
row[key_names[2]] = [key[2]]
row['params'] = [params.tolist()]
row['cov_params'] = [covparams.tolist()]
transactioncosts = TransactionCosts()
transactioncosts.set_key(key)
transactioncosts.set_data(row)
return transactioncosts
def get_vif(exog):
vif = {}
for col in exog.columns:
endog = exog.loc[:, col]
exog_coef = exog.drop([col], axis=1)
exog_coef = sm.add_constant(exog_coef)
model = smlr.OLS(endog, exog_coef).fit()
vif[col] = 1 / (1 - model.rsquared)
return vif
def regression_affine(X, Y, details=True):
Xreg = add_constant(X) #Add a constant to fit tan affine model
model = linear_model.OLS(Y, Xreg) #Linear regression
results = model.fit()
[b, a] = results.params #parameters of the affine curve
Yreg = a * X + b #regression curve
return Yreg, a, b, results.summary()
def calculate_vif(data):
vif_df = pd.DataFrame(columns=['Var', 'Vif'])
x_var_names = data.columns
for i in range(0, x_var_names.shape[0]):
y = data[x_var_names[i]]
x = data[x_var_names.drop([x_var_names[i]])]
r_squared = sm.OLS(y, x).fit().rsquared
vif = round(1 / (1 - r_squared), 2)
vif_df.loc[i] = [x_var_names[i], vif]
return vif_df.sort_values(by='Vif', axis=0, ascending=False, inplace=False)
def stepwise_selection(X,
y,
initial_list=[],
threshold_in=0.01,
threshold_out=0.05,
verbose=True):
""" Perform a forward-backward feature selection based on p-values"""
included = list(initial_list)
while True:
changed = False
# forward step
excluded = list(set(X.columns) - set(included))
new_pval = pd.Series(index=excluded)
for new_column in excluded:
model = sm.OLS(
y, sm.add_constant(pd.DataFrame(X[included +
[new_column]]))).fit()
new_pval[new_column] = model.pvalues[new_column]
best_pval = new_pval.min()
if best_pval < threshold_in:
best_feature = new_pval.idxmin()
included.append(best_feature)
changed = True
if verbose:
print('Add {:30} with p-value {:.6}'.format(
best_feature, best_pval))
# backward step
model = sm.OLS(y, sm.add_constant(pd.DataFrame(X[included]))).fit()
# use all coefs except intercept
pvalues = model.pvalues.iloc[1:]
worst_pval = pvalues.max() # null if pvalues is empty
if worst_pval > threshold_out:
changed = True
worst_feature = pvalues.argmax()
included.remove(worst_feature)
if verbose:
print('Drop {:30} with p-value {:.6}'.format(
worst_feature, worst_pval))
if not changed:
break
return included
def backwardElimination(X, sl):
epochs = len(X[0])
for i in range(0, epochs):
regressor_OLS = sm.OLS(y, X).fit()
varWithMaxPValue = max(regressor_OLS.pvalues).astype(float)
if varWithMaxPValue > sl:
for j in range(0, epochs - 1):
if (regressor_OLS.pvalues[j].astype(float) == varWithMaxPValue):
X = np.delete(X, j, 1)
regressor_OLS.summary()
return X
def backwardElimination(x, sl):
numVars = len(x[0])
for i in range(0, numVars):
regressor_OLS = sm.OLS(y, x).fit()
maxVar = max(regressor_OLS.pvalues).astype(float)
if maxVar > sl:
for j in range(0, numVars - i):
if (regressor_OLS.pvalues[j].astype(float) == maxVar):
x = np.delete(x, j, 1)
regressor_OLS.summary()
return x
def CAPM(ticker, benchmark, start='2016-09-27'):
import statsmodels.regression.linear_model as lm
import statsmodels.tools.tools as ct
df = make_portfolio([ticker, benchmark], start=start)
ticker_df = df[ticker].pct_change()[1:]
bench_df = df[benchmark].pct_change()[1:]
const = ct.add_constant(bench_df)
capm = lm.OLS(ticker_df, const)
results = capm.fit()
return results.summary()
def backwardElimination(x, sl):
numVars = len(x[0])
for i in range(0, numVars):
regressor_OLS = sm.OLS(y, x).fit()
maxVar = max(regressor_OLS.pvalues).astype(float)
if maxVar > sl:
for j in range(0, numVars - i):
if (regressor_OLS.pvalues[j].astype(float) == maxVar):
x = np.delete(x, j, 1)
mdl = regressor_OLS.get_robustcov_results(cov_type='HAC', maxlags=1)
print(mdl.summary())
return x
def get_regression(x, y) -> RegressionResults:
y = y.values
x = x.values
x = add_constant(x)
# intialize the model
model = linear_model.OLS(y, x, missing='drop')
# fit the regression
fit_result = model.fit()
return fit_result
def backwardelimination(x, sl):
numvar = len(x[1])
for i in range(0, numvar):
regressor_ols = lm.OLS(y, x).fit()
maxpval = max(regressor_ols.pvalues).astype(float)
if maxpval > sl:
for j in range(0, numvar - i):
if (regressor_ols.pvalues[j].astype(float) == maxpval):
x = np.delete(x, j, 1)
regressor_ols.summary()
return x
def backwardElimination(x, SL):
numVars = len(x[0])
temp = np.zeros((50,6)).astype(int)
for i in range(0, numVars):
regressor_OLS = sm.OLS(y, x.tolist()).fit()
maxVar = max(regressor_OLS.pvalues).astype(float)
adjR_before = regressor_OLS.rsquared_adj.astype(float)
if maxVar > SL:
for j in range(0, numVars - i):
if (regressor_OLS.pvalues[j].astype(float) == maxVar):
temp[:,j] = x[:, j]
x = np.delete(x, j, 1)
tmp_regressor = sm.OLS(y, x.tolist()).fit()
adjR_after = tmp_regressor.rsquared_adj.astype(float)
if (adjR_before >= adjR_after):
x_rollback = np.hstack((x, temp[:,[0,j]]))
x_rollback = np.delete(x_rollback, j, 1)
print (regressor_OLS.summary())
return x_rollback
else:
continue
regressor_OLS.summary()
return x
def cohort_one_regression(configs):
group_idxs = []
for idx, fpath in enumerate(
sorted(glob.glob(os.path.join(configs["metagroup_path"],
"*.csv")))):
groupname = fpath.split("/")[-1][:-4]
group_idxs.append((idx, groupname))
x = []
y = []
for fpath in sorted(
glob.glob(os.path.join(configs["metagroup_path"], "*.csv"))):
groupname = fpath.split("/")[-1][:-4]
print("Group: {}".format(groupname))
with open(fpath, 'r') as fp:
csv_fp = csv.reader(fp, delimiter=',')
next(csv_fp)
for line in csv_fp:
if line[1] == "":
continue
x.append([(1 if group_idxs[idx][1] == groupname else 0)
for idx in range(len(group_idxs))])
y.extend([float(line[1])])
y.append(0.9)
y = np.array(y)
x.append(np.zeros(len(group_idxs)))
x = np.array(x)
print("Size of design matrix: {}".format(x.shape))
lm = statslm.OLS(y,
statstools.add_constant(x),
missing='raise',
hasconst=None)
results = lm.fit()
print("Intercept, Coefficient: {}, p-value: {}".format(
results.params[0], results.pvalues[0]))
for idx in range(len(group_idxs)):
pval = results.pvalues[idx + 1]
print("Group: {}, Coefficient: {}, p-value: {}".format(
group_idxs[idx][1], results.params[idx + 1],
results.pvalues[idx + 1]))
def fit(self, x, y, cens, verbose=False):
"""
Fit a maximum-likelihood Tobit regression
:param x: Pandas DataFrame (n_samples, n_features): Data
:param y: Pandas Series (n_samples,): Target
:param cens: Pandas Series (n_samples,): -1 indicates left-censored samples, 0 for uncensored, 1 for right-censored
:param verbose: boolean, show info from minimization
:return:
"""
x_copy = x.copy()
with warnings.catch_warnings():
warnings.filterwarnings("ignore")
init_reg = sm.OLS(y, x_copy).fit()
b0 = init_reg.params.values
y_pred = init_reg.predict(x_copy)
resid = y - y_pred
resid_var = np.var(resid)
s0 = np.sqrt(resid_var)
params0 = np.append(b0, s0)
#params0 = b0
xs, ys = split_left_right_censored(x_copy, y, cens)
result = minimize(
lambda params: tobit_neg_log_likelihood(xs, ys, params),
params0,
method='BFGS',
jac=lambda params: tobit_neg_log_likelihood_der(xs, ys, params),
options={'disp': verbose})
if verbose:
print(result)
self.ols_coef_ = b0[1:]
self.ols_intercept = b0[0]
if self.fit_intercept:
self.intercept_ = result.x[1]
self.coef_ = result.x[1:-1]
else:
self.coef_ = result.x[:-1]
self.intercept_ = 0
self.sigma_ = result.x[-1]
self.result = result
return self
def backwardElimination(x, Y, sl, columns):
numVars = len(columns.columns)
numVars2 = len(columns.columns)
print("\nStarting backward elimination...")
for i in range(0, numVars):
regressor_OLS = sm.OLS(endog = Y.astype(float), exog = columns.astype(float)).fit()
maxVar = float(max(regressor_OLS.pvalues))
print("Highest P value is: "+str(maxVar))
if maxVar > sl:
for j in range(0, numVars2):
if (regressor_OLS.pvalues[j].astype(float) == maxVar):
print("Removing column "+str(j))
columns = columns.drop(columns.columns[j], axis=1)
numVars2 -= 1
print(regressor_OLS.summary())
return columns
def polynomial_regression():
''' Define the model directly through the design matrix. Similar to MATLAB's "regress" command '''
# Generate the data
t = np.arange(0, 10, 0.1)
y = 4 + 3 * t + 2 * t**2 + 5 * np.random.randn(len(t))
# Make the fit. Note that this is another "OLS" than the one in "model_formulas"!
M = np.column_stack((np.ones(len(t)), t, t**2))
res = sm.OLS(y, M).fit()
# Display the results
print 'Summary:'
print res.summary()
print 'The fit parameters are: {0}'.format(str(res.params))
print 'The confidence intervals are:'
print res.conf_int()
def smart_regression(df, ignore_cols):
endog = df.iloc[:, 0]
exog = df.iloc[:, 1:]
exog = exog.drop(ignore_cols, axis=1)
vifs = get_vif(exog)
large_vifs = {k: vifs[k] for k in vifs.keys() if vifs[k] > 10}
coef = {}
if len(large_vifs) != 0:
max_vif = max(large_vifs, key=large_vifs.get)
ignore_cols.append(max_vif)
coef = smart_regression(df, ignore_cols)
else:
exog = sm.add_constant(exog)
model = smlr.OLS(endog, exog).fit()
coef = model.params
return coef
def apply_OLS(self, ):
y_fit = np.log(self.data[self.column_y])
if not hasattr(self, 'X'):
self.create_X_variables()
with warnings.catch_warnings():
warnings.filterwarnings("ignore")
model = sm.OLS(y_fit, self.X.astype(float)).fit()
predictions = model.predict(self.X.astype(float))
print_model = model.summary()
prstd, iv_l, iv_u = wls_prediction_std(model)
# salvando informacoes do OLS
self.fit_ols_predictions = predictions
self.fit_ols_stats = print_model
self.fit_ols_iv_l = iv_l
self.fit_ols_iv_u = iv_u
self.fit_ols_stats = prstd
return model
def iteration(e0, depth):
y_star = y_data
Wald_iter_df = pd.DataFrame(index=range(depth), columns=y_star.columns)
for d in range(depth):
e = e0.sample(frac=1).reset_index(drop=True)
for i in range(34):
ei = e.iloc[:, i]
y_star_lag = pd.Series(index=y_star.index)
y_star_lag[1:] = y_star.iloc[:-1, i]
y_star.iloc[1:, i] = ei + Params_df.loc[
'const', i] + Params_df.loc[0, i] * y_star_lag[1:] # 生成y-star
# y_star.iloc[0, i] = y_data.iloc[0, i]
x_lag1 = pd.Series(index=y_star.index)
y_lag1 = pd.Series(index=y_star.index)
x_lag1[1:] = X_data.iloc[:-1, i]
y_lag1[1:] = y_star.iloc[:-1, i]
y_reg = y_star.iloc[:, i]
X_exo = pd.concat([y_lag1, x_lag1], axis=1)
X_exo = lm.add_constant(X_exo)
model = lm.OLS(y_reg, X_exo, missing='drop')
res = model.fit()
R = np.eye(len(res.params))[2]
# print(res.wald_test(R).fvalue[0][0])
# Wald_iter_df.iloc[d, i] = res.wald_test(R).fvalue[0][0]
try:
wald_i = res.wald_test(R).fvalue[0][0]
except ValueError:
Wald_iter_df.iloc[d, i] = np.nan
print(d, i, "Appear")
# print(X_exo)
else:
Wald_iter_df.iloc[d, i] = wald_i
return Wald_iter_df
def polynomial_regression():
''' Define the model directly through the design matrix. Similar to MATLAB's "regress" command '''
# Generate the data
# To get reproducable values, I provide a seed value
np.random.seed(987654321)
t = np.arange(0, 10, 0.1)
y = 4 + 3 * t + 2 * t**2 + 5 * np.random.randn(len(t))
# Make the fit. Note that this is another "OLS" than the one in "model_formulas"!
M = np.column_stack((np.ones(len(t)), t, t**2))
res = sm.OLS(y, M).fit()
# Display the results
print 'Summary:'
print res.summary()
print 'The fit parameters are: {0}'.format(str(res.params))
print 'The confidence intervals are:'
print res.conf_int()
return res.params # should be [ 4.74244177, 2.60675788, 2.03793634]
