def get_linear_regression_results(x, y, intercept=False, rolling_window=-1):
"""
:type x: pd.Series
:type y: pd.Series
"""
if rolling_window != -1:
model = pd.ols(x=x,
y=y,
intercept=intercept,
window=rolling_window,
window_type='rolling')
else:
model = pd.ols(x=x, y=y, intercept=intercept)
# The type of 'beta' actually changes.. if rolling then DataFrame, else Series
slope = model.beta['x'] if rolling_window != -1 else model.beta[0]
const = model.beta['intercept'] if intercept else 0
result = pd.concat([x, y], axis=1)
# remove the start that cannot be fit using rolling window mode:
if rolling_window != -1:
result = result.iloc[rolling_window - 1:, :]
result.loc[:, 'slope'] = slope
result.loc[:, 'const'] = const
result.loc[:, 'f(x)'] = result.iloc[:, 0] * slope + const
result.loc[:, 'error'] = result.loc[:, 'f(x)'] - result.iloc[:, 1]
return result
def dd_plot(self):
data = ps.merge(self.temp,
self.degd,
left_index=True,
right_index=True,
how='inner')
hdd = data[ps.notnull(data['HDD'])]
cdd = data[ps.notnull(data['CDD'])]
hday = hdd[hdd['temp'] < 60]
cday = cdd[cdd['temp'] > 55]
model = ps.ols(x=hday['temp'], y=hday['HDD'])
mH, cH = model.beta.x, model.beta.intercept
print model
model = ps.ols(x=cday['temp'], y=cday['CDD'])
mC, cC = model.beta.x, model.beta.intercept
print model
xH = hday['temp']
xC = cday['temp']
vs_temp = ps.DataFrame({
'temp': hdd['temp'],
'hdd scatter': hdd['HDD']
}).merge(ps.DataFrame({
'temp': cdd['temp'],
'cdd scatter': cdd['CDD']
}),
on='temp',
how='outer',
suffixes=('', '')).merge(ps.DataFrame({
'temp':
xH,
'hdd regression':
line(xH, mH, cH)
}),
on='temp',
how='outer',
suffixes=('',
'')).merge(ps.DataFrame({
'temp':
xC,
'cdd regression':
line(xC, mC, cC)
}),
on='temp',
how='outer',
suffixes=('',
''))
data = data.fillna(0)
vs_time = ps.DataFrame({
'time': data.index,
'HDD': data['HDD'],
'CDD': data['CDD']
})
return vs_temp.set_index('temp'), vs_time.set_index('time')
def movingLR(fr_xzdf, fr_xydf, fr_xdf, window_period):
ts_xz=fr_xzdf.reset_index()
ts_xy=fr_xydf.reset_index()
ts_x=fr_xdf.reset_index()
tdelta=ts_xz['Time']-ts_xz['Time'][0]
tdelta=tdelta.astype('timedelta64[s]')/(60*60*24.) #in days
for col in fr_xzdf.columns:
print col
#if col!=7:continue
ts_xz[col].plot()
model=pd.ols(y=ts_xz[col], x=tdelta,window_type='rolling', window=window_period, intercept=True)
ts_xz[col]=np.round(model.beta.x,3)
ts_xz[col].plot()
model=pd.ols(y=ts_xy[col], x=tdelta,window_type='rolling', window=window_period, intercept=True)
ts_xy[col]=np.round(model.beta.x,3)
model=pd.ols(y=ts_x[col], x=tdelta,window_type='rolling', window=window_period, intercept=True)
ts_x[col]=np.round(model.beta.x,3)
plt.show()
ts_xz.index=ts_xz['Time']
ts_xy.index=ts_xz['Time']
ts_x.index=ts_xz['Time']
def _run_regressions(self):
self.model_capm = pd.ols(y=self.est_data['RETX'],
x=self.est_data[['mkt']])
self.model_ff3f = pd.ols(y=self.est_data['RETX'],
x=self.est_data[['mkt', 'smb', 'hml']])
self.model_ff4f = pd.ols(y=self.est_data['RETX'],
x=self.est_data[['mkt', 'smb', 'hml', 'umd']])
self._has_models = True
def half_life(y, x):
"""calculate the half_life for a pair"""
model = pd.ols(y=y, x=x, intercept=False)
res = model.resid
dres = res.shift(1)[1:] - res[1:]
resmodel = pd.ols(y=dres, x=res, intercept=False)
half = -np.log(2) / resmodel.beta[0]
return half
def degree_day_regression(df, x_opt='both'):
'''
Function that runs the weather normalization regression on energy use data
df: dataframe that includes
use per day (upd)
heating degree days per day (hddpd)
cooling degree days per day (cddpd)
x_opt: options for the regression function
'hdd': run regression with just heating degree days
'cdd': run regression with just cooling degree days
'both' (default):
'''
if x_opt == 'hdd':
covar = {'HDD': df.hdd_per_day}
results = pd.ols(y=df.use_per_day, x=covar)
return pd.DataFrame([[
results.beta[1], results.std_err[1], results.beta[0],
results.std_err[0], results.r2, results.r2_adj, results.nobs
]],
columns=[
'intercept', 'intercept_std_err', 'HDD',
'HDD_std_err', 'R2', 'R2_adj', 'N_reads'
])
elif x_opt == 'cdd':
covar = {'CDD': df.cdd_per_day}
results = pd.ols(y=df.use_per_day, x=covar)
return pd.DataFrame([[
results.beta[1], results.std_err[1], results.beta[0],
results.std_err[0], results.r2, results.r2_adj, results.nobs
]],
columns=[
'intercept', 'intercept_std_err', 'CDD',
'CDD_std_err', 'R2', 'R2_adj', 'N_reads'
])
elif x_opt == 'both':
covar = {'CDD': df.cdd_per_day, 'HDD': df.hdd_per_day}
results = pd.ols(y=df.use_per_day, x=covar)
return pd.DataFrame([[
results.beta[2], results.std_err[2], results.beta[0],
results.std_err[0], results.beta[1], results.std_err[1],
results.r2, results.r2_adj, results.nobs
]],
columns=[
'intercept', 'intercept_std_err', 'CDD',
'CDD_std_err', 'HDD', 'HDD_std_err', 'R2',
'R2_adj', 'N_reads'
])
def compute_hedge_ratios(self, **kwargs):
rolling_beta_com = self.settings.get('rolling_beta_com')
# Predict long term volatility move as a function of short
fd = self.settings['fd']
y = self.strat_data['cm_vol_fut_returns'][fd[1]]
x = pd.DataFrame(index=self.strat_data['cm_vol_fut_returns'].index)
x['front_return'] = self.strat_data['cm_vol_fut_returns'][fd[0]]
x['front_level'] = self.strat_data['cm_vol_fut_prices'][fd[0]].shift(1)
x['interaction'] = x['front_return'] * x['front_level']
exog_vars = ['front_return', 'front_level', 'interaction']
# OLS to start
r1 = pd.ols(y=y, x=x)
# Now use OLS residuals for WLS
r2 = pd.ols(y=np.log(r1.resid**2), x=x[exog_vars])
pred_sq_err = np.exp(r2.y_fitted)
weights = 1. / pred_sq_err
reg_data = x
reg_data['endog'] = y
reg_data['weights'] = weights
reg_data = reg_data[np.isfinite(reg_data).all(axis=1)]
reg_data = sm.add_constant(reg_data)
r3 = sm.WLS(endog=reg_data['endog'],
exog=reg_data[['const'] + exog_vars],
weights=reg_data['weights']).fit()
# Historical front/back betas
self.calc['front_back_beta'] = (
r3.params.front_return + x['front_level'] * r3.params.interaction)
self.calc['rolling_front_back_beta'] = \
y.ewm(com=rolling_beta_com).cov(x['front_return']
.ewm(com=rolling_beta_com)) \
/ x['front_return'].ewm(com=rolling_beta_com).var()
buff = 21
self.calc['rolling_front_back_beta'].iloc[0:buff] \
= self.calc['rolling_front_back_beta'].iloc[buff]
self.calc['r1'] = r1
self.calc['r2'] = r2
self.calc['r3'] = r3
def regress():
if True:
pid=session["pid"]
regs=[]
csvf=data[pid]
reg=pd.DataFrame()
outs=session['rout']
inps=session['rinp']
controls=session['rcont']
count=0
for o in outs:
r=[]
inputData=[]
controlData=[]
y=csvf[o]
for i in inps:
reg[i]=csvf[i]
for control in controls:
reg[control]=csvf[control]
model=pd.ols(y=y,x=reg)
formula="Measuring the impact of \""+', '.join(inps)+"\" on \""+o+"\" while controlling for variables such as \""+', '.join(controls)+"\""
res=model.summary_as_matrix
r.append(formula)
r.append(round(model.r2_adj,2))
r.append(round(model.f_stat['f-stat'],2))
r.append(round(model.f_stat['p-value'],5))
r.append(model.df)
r.append(model.nobs)
for i in inps:
idata=[]
idata.append(i)
coef=round(res.ix['beta'][i],4)
idata.append(coef)
pval=round(res.ix['p-value'][i],4)
idata.append(pval)
stderr=round(res.ix['std err'][i],2)
idata.append(stderr)
tstat=round(res.ix['t-stat'][i],2)
idata.append(tstat)
inputData.append(idata)
r.append(inputData)
for c in controls:
cdata=[]
cdata.append(c)
coef=round(res.ix['beta'][c],4)
cdata.append(coef)
pval=round(res.ix['p-value'][c],4)
cdata.append(pval)
stderr=round(res.ix['std err'][c],2)
cdata.append(stderr)
tstat=round(res.ix['t-stat'][c],2)
cdata.append(tstat)
controlData.append(cdata)
r.append(controlData)
regs.append(r)
count+=1
data["regs"]=regs
return render_template("regression.html",regs=regs)
else:
return redirect(url_for("logout"))
def find_cointergrate_stocks(self,stockList):
stocks_pair = {}
price_df = history(g.adfTest_period, unit='1d', field='close', security_list=stockList, df=True, skip_paused=False, fq='pre')
for i in range(len(stockList)):
stock1 = stockList[i]
stock1_price = price_df[stock1]
for j in range(i+1,len(stockList)):
stock2 = stockList[j]
stock2_price = price_df[stock2]
combined_df = pd.concat([stock1_price,stock2_price],axis=1)
print ('combined_df is ', combined_df)
combined_df = combined_df.dropna()
if len(combined_df) < 500:
continue
stock2_price = combined_df[stock2]
stock1_price = combined_df[stock1]
model = pd.ols(y=stock2_price, x=stock1_price, intercept=True) # perform ols on these two stocks
spread = stock2_price - stock1_price*model.beta['x']
spread = spread.dropna()
spread = spread.values
sta = sts.adfuller(spread, 1)
if sta[1] < 0.05 and sta[0] < sta[4]['5%'] and model.beta['x'] > 0:
stocks_pair[(stock1,stock2, model.beta[1], model.beta['x'],np.std(spread), np.mean(spread))] = sta[0]
rank = sorted(stocks_pair.items(),key=operator.itemgetter(1))
return rank[:1]
def regress_by_year(isi, in_sample, osi, out_sample):
"""
Docstring if I can get it working....
"""
for year in in_sample['yearID'].unique():
no_yr = in_sample.columns.drop('yearID')
d_too = {}
is_yr = in_sample['yearID'] == year
os_yr = out_sample['yearID'] == year
ols = pandas.ols(x = in_sample.loc[is_yr, no_yr], y = ys[isi][is_yr])
df = ols.summary_as_matrix
is_sig = df.loc['p-value', df.loc['p-value', :] < .01].index
if 'intercept' in is_sig:
is_sig = is_sig.drop('intercept')
clf = ensemble.RandomForestRegressor(n_estimators = 15)
clf.fit(in_sample.loc[is_yr, is_sig], ys[isi][is_yr])
is_score = clf.score(in_sample.loc[is_yr, is_sig], ys[isi][is_yr])
d_too['is-r2'] = is_score
os_score = clf.score(out_sample.loc[os_yr, is_sig], ys[osi][os_yr])
d_too['os-r2'] = os_score
eps = ys[osi][os_yr].sub(clf.predict(out_sample.loc[os_yr, is_sig]))
d_too['mae'] = eps.abs().sum()/(len(ys[osi][os_yr]) - 2.)
d[year] = pandas.Series(d_too)
return pandas.DataFrame(d).transpose()
def mv_regression(xs, ys, in_sample_size):
"""
Test a multi-variate regression creating the coefficients in sample
and then using those coefficients to test the regression out of sample
Args:
-----
- xs: `pandas.DataFrame` of the xs
- ys: `pandas.Series` of the variable we're attempting to predit
- in_sample_size: integer of the size of the `in sample` we want
to use to train our regression
Returns:
---------
float of the MSE or Mean Squared Error
"""
isi, in_sample, osi, out_sample = create_in_out_samples(xs, in_sample_size)
#run the regression and predict the new values
ols = pandas.ols(x = in_sample, y = ys[isi])
betas = ols.beta
intercept = betas['intercept']
betas = betas[betas.index != 'intercept']
#make our prediction on out of sample
pred = out_sample.dot(betas) + intercept
eps = (pred - ys[osi]).apply(numpy.abs)
mse = eps.sum()/( eps.shape[0] - 2)
return mse
def test_window_ols_full(ols_data):
y, x = ols_data['y'], ols_data['x']
res1 = _window_ols(y, x, window_type='full_sample')
res2 = _window_ols(y, x)
res3 = pd.ols(y=y, x=x, window_type='full_sample')
assert_ols_equal(res1, res2)
assert_ols_equal(res1, res3)
def PowerFit_CI(x, y, xspace=None, ax=plt, **kwargs):
datadf = pd.DataFrame.from_dict({
'x': x,
'y': y
}).dropna().apply(
np.log10
) ## put x and y in a dataframe so you can drop ones that don't match up
regression = pd.ols(y=datadf['y'], x=datadf['x'])
## Develop power function for x and y
powfunc = powerfunction(x, y) ## x and y should be Series
a, b = powfunc['a'].values, powfunc['b'].values
#print a,b
if xspace == None:
xvals = np.linspace(0, x.max() * 1.2)
#print 'No xspace, calculating xvals: '+str(x.max())+'*1.5= '+str(x.max()*1.5)
else:
xvals = xspace
ypred = a * (xvals**b)
ax.plot(xvals, ypred, **kwargs)
## Confidence interals
ci = .5
a_cilo, a_ciup = 10**regression.sm_ols.conf_int(
alpha=ci)[1][0], 10**regression.sm_ols.conf_int(alpha=ci)[1][1]
b_cilo, b_ciup = regression.sm_ols.conf_int(
alpha=ci)[0][0], regression.sm_ols.conf_int(alpha=ci)[0][1]
ypred_cilo = a_cilo * (xvals**b_cilo)
ypred_ciup = a_ciup * (xvals**b_ciup)
ax.fill_between(xvals, ypred_cilo, ypred_ciup, alpha=0.5, **kwargs)
plt.draw()
return powfunc
def compute_exposures(factor_returns=None, target_returns=None):
"""
:param factor_returns: Pandas DataFrame indexed on date,
with columns = factors
:param target_returns: a series index on date, or a DataFrame
indexed on date with columns for the various time series you want
exposure for
:return:
"""
if isinstance(target_returns, pd.Series):
target_returns = pd.DataFrame(target_returns)
regressions = dict()
coefs = pd.DataFrame(index=target_returns.columns,
columns=factor_returns.columns)
t_stats = pd.DataFrame(index=target_returns.columns,
columns=factor_returns.columns)
for col in target_returns.columns:
regressions[col] = pd.ols(y=target_returns[col], x=factor_returns)
coefs.loc[col] = regressions[col].beta
t_stats.loc[col] = regressions[col].t_stat
return coefs, t_stats, regressions
def calculate_signals(self, event):
"""
generate pair trading signal
:param event:
:return:
"""
if event.type == 'MARKET' \
and self.bars.get_current_bar_total_number(self.y_symbol) > self.look_back \
and self.bars.get_current_bar_total_number(self.x_symbol) > self.look_back:
y_bars = self.bars.get_latest_bars_values(
self.y_symbol, "adj_close", N=self.look_back)
x_bars = self.bars.get_latest_bars_values(
self.x_symbol, "adj_close", N=self.look_back)
# Use the pandas Ordinary Least Squares method to fit a rolling
# linear regression between the two closing price time series
model = pd.ols(y=y_bars, x=x_bars)
# Construct the hedge ratio and eliminate the first
# lookback-length empty/NaN period
hedge_ratio = model.beta['x']
# Create the spread and then a z-score of the spread
spread = y_bars - hedge_ratio*x_bars
zscore = (spread - np.mean(spread))/np.std(spread)
print(zscore)
def ar_periodogram(x, window='hanning', window_len=7):
"""
Compute periodogram from data x, using prewhitening, smoothing and
recoloring. The data is fitted to an AR(1) model for prewhitening,
and the residuals are used to compute a first-pass periodogram with
smoothing. The fitted coefficients are then used for recoloring.
Parameters:
* x is a NumPy array containing time series data
* window is a string indicating window type
* window_len is an odd integer
See the periodogram function documentation for more details on the window
arguments.
"""
# === run regression === #
x_current, x_lagged = x[1:], x[:-1] # x_t and x_{t-1}
x_current, x_lagged = Series(x_current), Series(x_lagged) # pandas series
results = ols(y=x_current, x=x_lagged, intercept=True, nw_lags=1)
e_hat = results.resid.values
phi = results.beta['x']
# === compute periodogram on residuals === #
w, I_w = periodogram(e_hat, window=window, window_len=window_len)
# === recolor and return === #
I_w = I_w / np.abs(1 - phi * np.exp(1j * w))**2
return w, I_w
def model(self, dd, city_code, business_class, per_meter):
'''
Regress usage data to heating and cooling degree days
:param dd: heating and cooling degree days
:param city_code: 'PRINCETON TWP' or 'PRINCETON BORO'
:param business_class: a single business_class or a collection thereof
- if a collection is given, the values are summed up
:param per_meter: True for consumption per meter, False for aggregate
:return: series of first differences
'''
data = ps.DataFrame(self.select(city_code, business_class, per_meter))
data['year'] = data.index.map(lambda d: d.year)
data = data[data['year'] > 2009]['usage']
#
# index degree days frame for correspondence to usage data
#
dd = dd.ix[data.index].fillna(0.0)
#
# regress to heating and cooling degree days
#
model = ps.ols(x=dd, y=data)
print city_code, business_class, per_meter
print model
print '-' * 60
return model.beta.intercept, model.beta.HDD, model.beta.CDD
def ts_regrFn(df, dep, indep, min_periods, max_periods):
if not (max_periods): max_periods = len(df[dep])
indx = df.index
names = indx.names
cols = [col + '_beta' for col in indep] + ['intercept']
df = df.reset_index([0])
X = df[indep + [dep]].dropna(how='any')
if min(X.count()) >= min_periods:
model = pd.ols(y=df[dep],
x=df[indep],
window_type='rolling',
window=max_periods,
min_periods=min_periods)
X = model.beta
X = pd.merge(df,
X,
left_index=True,
right_index=True,
how='outer',
suffixes=['', '_beta'])
X = X.reset_index()
X = X.set_index(names)
return X[cols]
else:
return DataFrame(nan, index=indx, columns=cols)
def regress_by_year(isi, in_sample, osi, out_sample):
"""
Docstring if I can get it working....
"""
for year in in_sample['yearID'].unique():
no_yr = in_sample.columns.drop('yearID')
d_too = {}
is_yr = in_sample['yearID'] == year
os_yr = out_sample['yearID'] == year
ols = pandas.ols(x=in_sample.loc[is_yr, no_yr], y=ys[isi][is_yr])
df = ols.summary_as_matrix
is_sig = df.loc['p-value', df.loc['p-value', :] < .01].index
if 'intercept' in is_sig:
is_sig = is_sig.drop('intercept')
clf = ensemble.RandomForestRegressor(n_estimators=15)
clf.fit(in_sample.loc[is_yr, is_sig], ys[isi][is_yr])
is_score = clf.score(in_sample.loc[is_yr, is_sig], ys[isi][is_yr])
d_too['is-r2'] = is_score
os_score = clf.score(out_sample.loc[os_yr, is_sig], ys[osi][os_yr])
d_too['os-r2'] = os_score
eps = ys[osi][os_yr].sub(clf.predict(out_sample.loc[os_yr, is_sig]))
d_too['mae'] = eps.abs().sum() / (len(ys[osi][os_yr]) - 2.)
d[year] = pandas.Series(d_too)
return pandas.DataFrame(d).transpose()
def get_alpha_beta(self, bm_rets):
if isinstance(bm_rets, pd.Series):
bm = CumulativeRets(bm_rets)
elif isinstance(bm_rets, CumulativeRets):
bm = bm_rets
else:
raise ValueError('bm_rets must be series or CumulativeRetPerformace not %s' % (type(bm_rets)))
bm_freq = guess_freq(bm_rets)
if self.pds_per_year != bm.pds_per_year:
tgt = {'B': 'dly', 'W': 'weekly', 'M': 'monthly', 'Q': 'quarterly', 'A': 'annual'}.get(bm_freq, None)
if tgt is None:
raise ValueError('No mapping for handling benchmark with frequency: %s' % bm_freq)
tmp = getattr(self, tgt)
y = tmp.rets
y_ann = tmp.ltd_ann
else:
y = self.rets
y_ann = self.ltd_ann
x = bm.rets.truncate(y.index[0], y.index[-1])
x_ann = bm.ltd_ann
model = pd.ols(x=x, y=y)
beta = model.beta[0]
alpha = y_ann - beta * x_ann
return pd.Series({'alpha': alpha, 'beta': beta}, name=bm_freq)
def mv_regression(xs, ys, in_sample_size):
"""
Test a multi-variate regression creating the coefficients in sample
and then using those coefficients to test the regression out of sample
Args:
-----
- xs: `pandas.DataFrame` of the xs
- ys: `pandas.Series` of the variable we're attempting to predit
- in_sample_size: integer of the size of the `in sample` we want
to use to train our regression
Returns:
---------
float of the MSE or Mean Squared Error
"""
isi, in_sample, osi, out_sample = create_in_out_samples(xs, in_sample_size)
#run the regression and predict the new values
ols = pandas.ols(x=in_sample, y=ys[isi])
betas = ols.beta
intercept = betas['intercept']
betas = betas[betas.index != 'intercept']
#make our prediction on out of sample
pred = out_sample.dot(betas) + intercept
eps = (pred - ys[osi]).apply(numpy.abs)
mse = eps.sum() / (eps.shape[0] - 2)
return mse
def fit(x, y, funcstr, *args, **kwargs):
x = pandas.Series(array(x))
y = pandas.Series(array(y))
x, y = remove_nan(x, y)
if funcstr == 'linear':
result = fit(x, y, 'power', 1)
result.type = 'linear'
elif funcstr == 'quadratic':
result = fit(x, y, 'power', 2)
result.type = 'quadratic'
elif funcstr == 'exponential':
y2 = np.log(y)
result = fit(x, y2, 'linear')
result.params = [np.exp(result.params[1]), result.params[0]]
p = result.params
labelstr = 'y= %.4e exp(%.4e x)' % (p[0], p[1])
result.label = labelstr
result.type = 'exponential'
elif funcstr == 'power':
data = pandas.DataFrame({'x': x, 'y': y})
power = args[0]
keys = ['x']
for i in range(power - 1):
exponent = (i + 2)
key = 'x%d' % exponent
data[key] = x**exponent
keys.append(key)
result2 = pandas.ols(y=data['y'], x=data[keys])
keys.reverse()
keys += ['intercept']
p = [result2.beta[s] for s in keys]
labelstr = 'y= '
for i, pv in enumerate(p):
pw = len(p) - i - 1
if pw == 1:
labelstr += '%.4e x + ' % (pv)
elif pw == 0:
labelstr += '%.4e + ' % (pv)
else:
labelstr += '%.4e x^%d + ' % (pv, pw)
labelstr = labelstr[:-3] # take off the last +
result = Struct()
result.params = p
result.type = 'power'
result.label = labelstr
result.pandas_result = result2
else:
raise ValueError('Unknown fit name %s' % funcstr)
return result
def test_window_ols_full(ols_data):
y, x = ols_data['y'], ols_data['x']
res1 = _window_ols(y, x, window_type='full_sample')
res2 = _window_ols(y, x)
res3 = pd.ols(y=y, x=x, window_type='full_sample')
assert_ols_equal(res1, res2)
assert_ols_equal(res1, res3)
def pandas_rolling_ols(single_id_dataframe,
date_column="AdjDate"):
"""
Perform rolling ols and return the columns of date-based coefficients,
t-stats, idiosyncratic vol, etc.
"""
df = (
single_id_dataframe
.sort(date_column, ascending=True)
.set_index(date_column)
)
try:
ols_result = pandas.ols(
y=df["TotalReturnMonthly"] - df["RiskFreeRate"],
x=df["ExcessMarket"],
window=60,
min_periods=12,
intercept=True
)
beta = ols_result.beta['x']
beta.name = "Beta"
beta_tstat = ols_result.t_stat['x']
beta_tstat.name = "Beta_tstat"
df = df.join(beta).join(beta_tstat)
except:
df["Beta"] = np.NaN
df["Beta_tstat"] = np.NaN
return df
def calculate_spread_zscore(pairs, symbols, lookback=100):
"""Creates a hedge ratio between the two symbols by calculating
a rolling linear regression with a defined lookback period. This
is then used to create a z-score of the 'spread' between the two
symbols based on a linear combination of the two."""
# Use the pandas Ordinary Least Squares method to fit a rolling
# linear regression between the two closing price time series
#print "Fitting the rolling Linear Regression..."
model = pd.ols(y=pairs['%s_close' % symbols[0].lower()],
x=pairs['%s_close' % symbols[1].lower()],
window=lookback)
# Construct the hedge ratio and eliminate the first
# lookback-length empty/NaN period
pairs['hedge_ratio'] = model.beta['x']
#pairs = pairs.dropna()
# Create the spread and then a z-score of the spread
#print "Creating the spread/zscore columns..."
pairs['spread'] = pairs['%s_close' % symbols[0].lower()] - pairs['hedge_ratio']*pairs['%s_close' % symbols[1].lower()]
pairs['zscore'] = (pairs['spread'] - np.mean(pairs['spread']))/np.std(pairs['spread'])
return pairs
def calculate_spread_zscore(pairs, symbols, lookback=100):
"""Creates a hedge ratio between the two symbols by calculating
a rolling linear regression with a defined lookback period. This
is then used to create a z-score of the 'spread' between the two
symbols based on a linear combination of the two."""
# Use the pandas Ordinary Least Squares method to fit a rolling
# linear regression between the two closing price time series
print "Fitting the rolling Linear Regression..."
model = pd.ols(y=pairs['%s_close' % symbols[0].lower()],
x=pairs['%s_close' % symbols[1].lower()],
window=100)
# Construct the hedge ratio and eliminate the first
# lookback-length empty/NaN period
pairs['hedge_ratio'] = model.beta['x']
pairs = pairs.dropna()
# Create the spread and then a z-score of the spread
print "Creating the spread/zscore columns..."
pairs['spread'] = pairs[
'spy_close'] - pairs['hedge_ratio'] * pairs['iwm_close']
# ********** this is biased! **********
pairs['zscore'] = (pairs['spread'] - np.mean(pairs['spread'])) / np.std(
pairs['spread'])
return pairs
def ar_periodogram(x, window='hanning', window_len=7):
"""
Compute periodogram from data x, using prewhitening, smoothing and
recoloring. The data is fitted to an AR(1) model for prewhitening,
and the residuals are used to compute a first-pass periodogram with
smoothing. The fitted coefficients are then used for recoloring.
Parameters:
* x is a NumPy array containing time series data
* window is a string indicating window type
* window_len is an odd integer
See the periodogram function documentation for more details on the window
arguments.
"""
# === run regression === #
x_current, x_lagged = x[1:], x[:-1] # x_t and x_{t-1}
x_current, x_lagged = Series(x_current), Series(x_lagged) # pandas series
results = ols(y=x_current, x=x_lagged, intercept=True, nw_lags=1)
e_hat = results.resid.values
phi = results.beta['x']
# === compute periodogram on residuals === #
w, I_w = periodogram(e_hat, window=window, window_len=window_len)
# === recolor and return === #
I_w = I_w / np.abs(1 - phi * np.exp(1j * w))**2
return w, I_w
def plot(request, c="population density"):
indicator = VARIABLES_DICT[c]
filename = join(settings.STATIC_ROOT, 'myapp/merged.csv')
df = pd.read_csv(filename)
plt.figure() # needed, to avoid adding curves in plot
lm = pd.ols(x=df[indicator], y=df['life expectancy'])
plt.plot(df[indicator], df["life expectancy"], 'ro', color="blue")
plt.plot(df[indicator], lm.y_fitted, 'r', linewidth=2)
plt.tight_layout()
plt.ylabel('life expectancy')
plt.xlabel(indicator)
plt.title('Regression between ' + 'life expectancy and ' + indicator,
fontsize=15)
# write bytes instead of file.
from io import BytesIO
figfile = BytesIO()
# this is where the color is used.
try:
plt.savefig(figfile, format='png')
except ValueError:
raise Http404("No such color")
figfile.seek(0) # rewind to beginning of file
return HttpResponse(figfile.read(), content_type="image/png")
def compute_hedge_ratios(self, **kwargs):
fd = self.settings['fd']
rolling_beta_com = kwargs.get('rolling_beta_com', 21)
# Trailing betas
y = self.strat_data['cm_vol_fut_prices'][fd].diff(1)
# Predict volatility move as a function of stuff
x = pd.DataFrame(index=self.strat_data['index_fut_returns'].index)
x['index_return'] = self.strat_data['index_fut_returns'][
self.settings['index_fut_ticker']]
x['vol_level'] = self.strat_data['cm_vol_fut_prices'][fd].shift(1)
x['interaction'] = x['index_return'] * x['vol_level']
exog_vars = ['index_return', 'vol_level', 'interaction']
r1 = pd.ols(y=y, x=x)
r2 = pd.ols(y=np.log(r1.resid**2), x=x[exog_vars])
pred_sq_err = np.exp(r2.y_fitted)
weights = 1. / pred_sq_err
reg_data = x
reg_data['endog'] = y
reg_data['weights'] = weights
reg_data = reg_data[np.isfinite(reg_data).all(axis=1)]
reg_data = sm.add_constant(reg_data)
r3 = sm.WLS(endog=reg_data['endog'],
exog=reg_data[['const'] + exog_vars],
weights=reg_data['weights']).fit()
vol_level_grid = np.arange(10, 51)
beta_df = pd.DataFrame(index=vol_level_grid, columns=['beta'])
for i in range(0, len(vol_level_grid)):
beta_df.loc[vol_level_grid[i], 'beta'] \
= (1.0 / 100.0) * (r3.params.index_return +
vol_level_grid[i] * r3.params.interaction)
# Historical spot-vol betas (vol points per 1%)
self.calc['spot_vol_beta'] = (r3.params.index_return + x['vol_level'] *
r3.params.interaction) / 100.0
self.calc['rolling_spot_vol_beta'] = \
y.ewm(com=rolling_beta_com).cov(x['index_return']
.ewm(com=rolling_beta_com)) \
/ x['index_return'].ewm(com=rolling_beta_com).var()
def sig_veh_buy(data):
"""
Extract the MMR columns that are valuable when compared to the
VehBCost (i.e. what someone paid at the auction)
ARGS:
data: :class:`pandas.DataFrame` of the lemon training data
RETURNS:
:class:`pandas.DataFrame` of the significant MMR pairings
divided by the 'VehBCost' or Vehicle Buy Cost
"""
cols = [
'MMRAcquisitionAuctionAveragePrice', 'MMRAcquisitionAuctionCleanPrice',
'MMRAcquisitionRetailAveragePrice', 'MMRAcquisitonRetailCleanPrice',
'MMRCurrentAuctionAveragePrice', 'MMRCurrentAuctionCleanPrice',
'MMRCurrentRetailAveragePrice', 'MMRCurrentRetailCleanPrice'
]
to_use = {}
# go through and construct a rough cut based on .95 p-value
for col in cols:
xs = data['VehBCost'].div(data[col])
is_inf = numpy.isinf(xs)
xs[is_inf] = numpy.nan
ols = pandas.ols(x=xs, y=data['IsBadBuy'])
if ols.p_value['x'] < .05:
to_use[col] = xs
is_sig = 1e-3
not_parsimonious = True
while not_parsimonious:
#now trim down to the most parsimonious model
buy_df = pandas.DataFrame(to_use)
ols = pandas.ols(x=buy_df, y=data['IsBadBuy'])
if any(ols.p_value > is_sig):
for val in ols.p_value[ols.p_value > is_sig].index:
try:
to_use.pop(val)
except:
print "Intercept not significant"
else:
not_parsimonious = False
return buy_df
def geneticAlgo(mutation_rate, pop_size):
baseball = pd.read_table(
"/Users/Ahmet/Box Sync/Classes/Vanderbilt/AdvancedStatisticalComputing/Bios8366/data/textbook/baseball.dat",
sep='\s+')
predictors = baseball.copy()
logsalary = predictors.pop('salary').apply(np.log)
nrows, ncols = predictors.shape
iterations = 100
aic_best = []
best_solution = []
aic_history = []
# Initialize genotype
current_gen = np.random.binomial(1, 0.5, pop_size * ncols).reshape(
(pop_size, ncols))
for i in range(iterations):
# Get phenotype
current_phe = [
predictors[predictors.columns[g.astype(bool)]] for g in current_gen
]
# Calculate AIC
current_aic = np.array(
[aic(pd.ols(y=logsalary, x=x)) for x in current_phe])
# Get lowest AIC
aic_best.append(current_aic[np.argmin(current_aic)])
best_solution.append(current_gen[np.argmin(current_aic)])
# Calculate fitness according to AIC rank
fitness = calculate_fitness(current_aic)
# Choose first parents according to fitness
moms = np.random.choice(range(pop_size),
size=int(pop_size / 2),
p=fitness)
# Choose second parents randomly
dads = np.random.choice(range(pop_size), size=int(pop_size / 2))
next_gen = []
for x, y in zip(current_gen[moms], current_gen[dads]):
# Crossover
cross = np.random.randint(0, ncols)
child1 = np.r_[x[:cross], y[cross:]]
child2 = np.r_[y[:cross], x[cross:]]
# Mutate
m1 = np.random.binomial(1, mutation_rate, size=ncols).astype(bool)
child1[m1] = abs(child1[m1] - 1)
m2 = np.random.binomial(1, mutation_rate, size=ncols)
child2[m2] = abs(child1[m2] - 1)
next_gen += [child1, child2]
# Increment generation
current_gen = np.array(next_gen)
# Store AIC values
aic_history.append(current_aic)
return aic_best
def annualBeta():
'''
exercise.
This function was in the handouts and looked very interesting.
So I implemented it to see the inner workings.
Purpose of this function is to calculate beta of a stock.
:return:
'''
def ret_f(ticker, startDate, endDate):
p = finance.quotes_historical_yahoo(ticker,
startDate,
endDate,
asobject=True,
adjusted=True)
return ((p.aclose[1:] - p.aclose[0:-1]) / p.aclose[:-1])
startDate = (1990, 1, 1)
endDate = (2014, 12, 31)
# Pandas Series for Oracle's Data
y0 = pd.Series(ret_f('ORCL', startDate, endDate))
# Pandas Series for S&P500 Data
x0 = pd.Series(ret_f('^GSPC', startDate, endDate))
# Historical Date values of S&P500
dateVal = finance.quotes_historical_yahoo('^GSPC',
startDate,
endDate,
asobject=True,
adjusted=True).date[0:-1]
lag_year = dateVal[0].strftime("%Y")
y1, x1, beta, index0 = [], [], [], []
# Calculate Beta for each year
for i in range(1, len(dateVal)):
year = dateVal[i].strftime("%Y")
if (year == lag_year):
x1.append(x0[i])
y1.append(y0[i])
else:
model = pd.ols(y=pd.Series(y1), x=pd.Series(x1))
print(lag_year, round(model.beta[0], 4))
beta.append(model.beta[0])
index0.append(lag_year)
x1 = []
y1 = []
lag_year = year
# Plot the main graph
plt.plot(beta, c='firebrick', label='ORCL Beta w.r.t S&P500')
plt.hlines(y=1,
xmin=0,
xmax=25,
label='Perfect Correlation',
lw=2,
color='steelblue')
plt.legend()
plt.show()
def linearfunction(x,y,name='linear rating'):
datadf = pd.DataFrame.from_dict({'x':x,'y':y}).dropna() ## put x and y in a dataframe so you can drop ones that don't match up
datadf = datadf[datadf>=0].dropna() ##verify data is valid (not inf)
regression = pd.ols(y=datadf['y'],x=datadf['x'])
pearson = pearson_r(datadf['x'],datadf['y'])[0]
spearman = spearman_r(datadf['x'],datadf['y'])[0]
coeffdf = pd.DataFrame({'a':[regression.beta[1]],'b':[regression.beta[0]],'r2':[regression.r2],'rmse':[regression.rmse],'pearson':[pearson],'spearman':[spearman]},index=[name])
return coeffdf
def regress(df, index=pd.Index((u'slope', u'intercept'))):
xcol = u'seed_cell_number_ml'
ycol = u'signal'
subdf = df.sort(columns=[xcol], axis=0)
# ols = "ordinary least squares"
ret = pd.ols(x=subdf[xcol][2:], y=subdf[ycol][2:]).beta
ret.index = index
return ret
def test_solve_rect(self):
if not _have_statsmodels:
raise nose.SkipTest("no statsmodels")
b = Series(np.random.randn(N), self.frame.index)
result = pmath.solve(self.frame, b)
expected = ols(y=b, x=self.frame, intercept=False).beta
self.assert_(np.allclose(result, expected))
def find_trend(series):
import numpy as np
ln = len(series)
x = pd.Series(np.arange(ln))
regression = pd.ols(y=series, x=x)
return regression.beta[0]
def calc_port_beta(port, mkt, window=20, min_periods=15):
'''
Given a Series of portfolio returns and a Series of market returns,
compute the beta of the portfolio against the market,
using the windowed approach.
'''
model = pd.ols(y=port, x=mkt, window_type='rolling', window=window, min_periods=min_periods, intercept=True)
return model.beta.intercept, model.beta.x
def sig_MMR(data):
"""
Extract the MMR columns that are valuable based on the multivariate
regression run by statsmodels
ARGS:
data: :class:`pandas.DataFrame` of the lemon training data
RETURNS:
:class:`pandas.DataFrame` of the significant MMR pairings
"""
cols = [
'MMRAcquisitionAuctionAveragePrice', 'MMRAcquisitionAuctionCleanPrice',
'MMRAcquisitionRetailAveragePrice', 'MMRAcquisitonRetailCleanPrice',
'MMRCurrentAuctionAveragePrice', 'MMRCurrentAuctionCleanPrice',
'MMRCurrentRetailAveragePrice', 'MMRCurrentRetailCleanPrice'
]
to_use = {}
pairs = itertools.combinations(range(len(cols)), 2)
# go through and construct a rough cut based on .95 p-value
for x, y in pairs:
xs = data[cols[x]].div(data[cols[y]])
is_inf = numpy.isinf(xs)
xs[is_inf] = numpy.nan
ols = pandas.ols(x=xs, y=data['IsBadBuy'])
if ols.p_value['x'] < .05:
to_use[str(x) + ',' + str(y)] = xs
is_sig = 1e-3
not_parsimonious = True
while not_parsimonious:
#now trim down to the most parsimonious model
mmr_df = pandas.DataFrame(to_use)
ols = pandas.ols(x=mmr_df, y=data['IsBadBuy'])
if any(ols.p_value > is_sig):
for val in ols.p_value[ols.p_value > is_sig].index:
try:
to_use.pop(val)
except:
print "Intercept not significant"
else:
not_parsimonious = False
return mmr_df
def reg(df, index=pd.Index(('coeff', 'intercept'))):
xcol = 'seed_cell_number_ml'
ycol = 'signal'
sdf = df.sort(columns=[xcol], axis=0)
ls = pd.ols(x=sdf[xcol][2:], y=sdf[ycol][2:])
ret = ls.beta
ret.index = index
return ret
def find_trend(series):
import numpy as np
ln = len(series)
x = pd.Series(np.arange(ln))
regression = pd.ols(y=series, x=x)
return regression.beta[0]
def test_solve_rect(self):
if not _have_statsmodels:
raise nose.SkipTest
b = Series(np.random.randn(N), self.frame.index)
result = pmath.solve(self.frame, b)
expected = ols(y=b, x=self.frame, intercept=False).beta
self.assert_(np.allclose(result, expected))
def sig_veh_buy(data):
"""
Extract the MMR columns that are valuable when compared to the
VehBCost (i.e. what someone paid at the auction)
ARGS:
data: :class:`pandas.DataFrame` of the lemon training data
RETURNS:
:class:`pandas.DataFrame` of the significant MMR pairings
divided by the 'VehBCost' or Vehicle Buy Cost
"""
cols = ['MMRAcquisitionAuctionAveragePrice','MMRAcquisitionAuctionCleanPrice',
'MMRAcquisitionRetailAveragePrice','MMRAcquisitonRetailCleanPrice',
'MMRCurrentAuctionAveragePrice', 'MMRCurrentAuctionCleanPrice',
'MMRCurrentRetailAveragePrice','MMRCurrentRetailCleanPrice']
to_use = {}
# go through and construct a rough cut based on .95 p-value
for col in cols:
xs = data['VehBCost'].div(data[col])
is_inf = numpy.isinf(xs)
xs[is_inf] = numpy.nan
ols = pandas.ols(x = xs, y = data['IsBadBuy'])
if ols.p_value['x'] < .05:
to_use[col] = xs
is_sig = 1e-3
not_parsimonious = True
while not_parsimonious:
#now trim down to the most parsimonious model
buy_df = pandas.DataFrame(to_use)
ols = pandas.ols(x = buy_df, y = data['IsBadBuy'])
if any(ols.p_value > is_sig):
for val in ols.p_value[ols.p_value > is_sig].index:
try:
to_use.pop(val)
except:
print "Intercept not significant"
else:
not_parsimonious = False
return buy_df
def test_r2_adj(man_calcs, prices):
log_rets = analyze.log_returns(prices).dropna()
pandas_rsq = pandas.ols(x = log_rets['S&P 500'],
y = log_rets['VGTSX']).r2_adj
analyze_rsq = analyze.r2_adj(benchmark = log_rets['S&P 500'],
series = log_rets['VGTSX'])
testing.assert_almost_equal(pandas_rsq, analyze_rsq)
def test_solve_rect(self):
if not _have_statsmodels:
raise nose.SkipTest("no statsmodels")
b = Series(np.random.randn(N), self.frame.index)
result = pmath.solve(self.frame, b)
with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
expected = ols(y=b, x=self.frame, intercept=False).beta
self.assertTrue(np.allclose(result, expected))
def get_rolling_beta(my_y, my_x, my_window=252):
"""
given x,y, runs ols regression on rolling window, outputs the beta coefficient series
y -- your portfolio or asset
x -- SPX
window -- # days rolling period
"""
model = pd.ols(y=my_y, x=my_x, window=my_window)
return model.beta.x
def regression_line():
'''Fit a line, using the powerful "ordinary least square" method of pandas'''
# Get the data
data = getData('altman_11_6.txt')
df = pd.DataFrame(data, columns=['glucose', 'Vcf'])
model = pd.ols(y=df['Vcf'], x=df['glucose'])
print model.summary
def cv_ols(y, x, k=10):
kfold = cross_validation.KFold(len(y), k)
rmse = []
for trIdx, teIdx in kfold:
result = pd.ols(y=y[trIdx], x=x.loc[trIdx])
predictions = result.predict(result.beta, x.loc[teIdx])
error = sqrt(mean_squared_error(y[teIdx], predictions))
rmse.append(error)
return rmse.mean()
def test_solve_rect(self):
if not _have_statsmodels:
raise nose.SkipTest("no statsmodels")
b = Series(np.random.randn(N), self.frame.index)
result = pmath.solve(self.frame, b)
with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
expected = ols(y=b, x=self.frame, intercept=False).beta
self.assertTrue(np.allclose(result, expected))
def degree_day_regression(df, x_opt='both'):
'''
Function that runs the weather normalization regression on energy use data
df: dataframe that includes
use per day (upd)
heating degree days per day (hddpd)
cooling degree days per day (cddpd)
x_opt: options for the regression function
'hdd': run regression with just heating degree days
'cdd': run regression with just cooling degree days
'both' (default):
'''
if x_opt == 'hdd':
covar = {'HDD': df.hdd_per_day}
results = pd.ols(y=df.use_per_day, x = covar)
return pd.DataFrame([[results.beta[1], results.std_err[1],
results.beta[0], results.std_err[0],
results.r2, results.r2_adj, results.nobs ]],
columns = ['intercept', 'intercept_std_err',
'HDD', 'HDD_std_err',
'R2', 'R2_adj','N_reads'])
elif x_opt == 'cdd':
covar = {'CDD': df.cdd_per_day}
results = pd.ols(y=df.use_per_day, x = covar)
return pd.DataFrame([[results.beta[1], results.std_err[1],
results.beta[0], results.std_err[0],
results.r2, results.r2_adj, results.nobs]],
columns = ['intercept', 'intercept_std_err',
'CDD', 'CDD_std_err',
'R2', 'R2_adj','N_reads'])
elif x_opt == 'both':
covar = {'CDD': df.cdd_per_day, 'HDD': df.hdd_per_day}
results = pd.ols(y=df.use_per_day, x = covar)
return pd.DataFrame([[results.beta[2], results.std_err[2],
results.beta[0], results.std_err[0],
results.beta[1], results.std_err[1],
results.r2, results.r2_adj, results.nobs]],
columns = ['intercept', 'intercept_std_err',
'CDD', 'CDD_std_err',
'HDD','HDD_std_err',
'R2', 'R2_adj','N_reads'])
def sig_MMR(data):
"""
Extract the MMR columns that are valuable based on the multivariate
regression run by statsmodels
ARGS:
data: :class:`pandas.DataFrame` of the lemon training data
RETURNS:
:class:`pandas.DataFrame` of the significant MMR pairings
"""
cols = ['MMRAcquisitionAuctionAveragePrice','MMRAcquisitionAuctionCleanPrice',
'MMRAcquisitionRetailAveragePrice','MMRAcquisitonRetailCleanPrice',
'MMRCurrentAuctionAveragePrice', 'MMRCurrentAuctionCleanPrice',
'MMRCurrentRetailAveragePrice','MMRCurrentRetailCleanPrice']
to_use = {}
pairs = itertools.combinations(range(len(cols)), 2)
# go through and construct a rough cut based on .95 p-value
for x, y in pairs:
xs = data[cols[x]].div(data[cols[y]])
is_inf = numpy.isinf(xs)
xs[is_inf] = numpy.nan
ols = pandas.ols(x = xs, y = data['IsBadBuy'])
if ols.p_value['x'] < .05:
to_use[str(x) + ',' + str(y)] = xs
is_sig = 1e-3
not_parsimonious = True
while not_parsimonious:
#now trim down to the most parsimonious model
mmr_df = pandas.DataFrame(to_use)
ols = pandas.ols(x = mmr_df, y = data['IsBadBuy'])
if any(ols.p_value > is_sig):
for val in ols.p_value[ols.p_value > is_sig].index:
try:
to_use.pop(val)
except:
print "Intercept not significant"
else:
not_parsimonious = False
return mmr_df
def plots(self, temp, city_code, business_class, per_meter):
'''
Regress measured usage to temperatures in cold and hot months and
generate x- and y-vectors for plotting this data set
:param temp: temperature time series to regress to
:param city_code: 'PRINCETON TWP' or 'PRINCETON BORO'
:param business_class: a single business_class or a collection thereof
- if a collection is given, the values are summed up
:param per_meter: True for consumption per meter, False for aggregate
:return: frame containing scatterplot and regression lines to temperature
'''
data = self.select(city_code, business_class, per_meter)
#
# split monthly average temperature series into two:
# cool => samples when temps are cool basetemp
# warm => samples when temps are warm basetemp
# use the full time period over which any usage data exists
#
temp = temp.ix[self.usage.index]['temp']
cool = temp[temp < self.basetemp]
warm = temp[temp >= self.basetemp]
#
# regress separately for cool and warm months
#
model = ps.ols(x=cool, y=data[cool.index])
m_cool, c_cool = model.beta.x, model.beta.intercept
model = ps.ols(x=warm, y=data[warm.index])
m_warm, c_warm = model.beta.x, model.beta.intercept
vs_temp = ps.DataFrame(
{'temp': temp, 'scatter': data[temp.index]}
).merge(
ps.DataFrame(
{'temp': cool, 'heating regression': line(cool, m_cool, c_cool)}),
on='temp', how='outer', suffixes=('', '')
).merge(
ps.DataFrame(
{'temp': warm, 'cooling regression': line(warm, m_warm, c_warm)}),
on='temp', how='outer', suffixes=('', ''))
vs_time = data
return vs_temp.set_index('temp'), vs_time
def equations(self):
eqs = {}
for col, ts in self.y.iteritems():
model = pn.ols(y=ts, x=self.x, window=self._window,
window_type=self._window_type,
min_periods=self._min_periods)
eqs[col] = model
return eqs
def cointegration_test(self):
"""协整检验，主要通过ADF检验的方式进行检验"""
#协整检验，主要通过ADF检验的方式进行检验
if len(self.contract1_Close) != 0 and len(self.contract2_Close) != 0:
model=pd.ols(y=self.contract1_Close,x=self.contract2_Close,intercept=True)
spread=self.contract1_Close-self.contract2_Close*model.beta["x"] #得出价差序列
spread=spread.dropna() #去除缺失数据
sta=sts.adfuller(spread,1) #进行ADF检验
result=sta[0]
print(sta)
def year_based_significance_regression(file_path):
"""
Run a year-based multivariate regression that uses only the
significant variables as well as Random Forest Regression Trees to
estimate the parameters
Args:
------
- file_path: string of the location of `baseball.csv`
Returns:
---------
- pandas.DataFrame of the in-sample and out-of-sample salary estimates
"""
data = pandas.DataFrame.from_csv(file_path, index_col = None)
data['age'] = data['yearID'] - data['birthYear']
cols = ['G_batting', 'AB', 'R', 'H', 'X2B', 'X3B', 'HR', 'RBI','SB',
'CS', 'BB', 'SO', 'IBB', 'HBP', 'SH', 'SF', 'GIDP', 'teamID',
'salary', 'yearID', 'age']
all_data = data[cols].copy()
all_data.dropna(inplace = True)
teams = pandas.get_dummies(all_data['teamID'])
x_cols = all_data.columns[map(lambda x: x not in ['teamID', 'salary'],
all_data.columns)]
xs = all_data[x_cols].join(teams)
ys = all_data['salary']
N = xs.shape[0]
isi, in_sample, osi, out_sample = create_in_out_samples(xs, N/2)
d = {}
for year in all_data['yearID'].unique():
no_yr = in_sample.columns.drop('yearID')
d_too = {}
is_yr = in_sample['yearID'] == year
os_yr = out_sample['yearID'] == year
ols = pandas.ols(x = in_sample.loc[is_yr, no_yr], y = ys[isi][is_yr])
df = ols.summary_as_matrix
is_sig = df.loc['p-value', df.loc['p-value', :] < .01].index
if 'intercept' in is_sig:
is_sig = is_sig.drop('intercept')
clf = ensemble.RandomForestRegressor(n_estimators = 15)
clf.fit(in_sample.loc[is_yr, is_sig], ys[isi][is_yr])
is_score = clf.score(in_sample.loc[is_yr, is_sig], ys[isi][is_yr])
d_too['is-r2'] = is_score
os_score = clf.score(out_sample.loc[os_yr, is_sig], ys[osi][os_yr])
d_too['os-r2'] = os_score
eps = ys[osi][os_yr].sub(clf.predict(out_sample.loc[os_yr, is_sig]))
d_too['mae'] = eps.abs().sum()/(len(ys[osi][os_yr]) - 2.)
d[year] = pandas.Series(d_too)
return pandas.DataFrame(d).transpose()
def simAnnealing(periods,cooling,tau_start,numChangeNeigh):
baseball = pd.read_table("/Users/Ahmet/Box Sync/Classes/Vanderbilt/AdvancedStatisticalComputing/Bios8366/data/textbook/baseball.dat", sep='\s+')
predictors = baseball.copy()
logsalary = predictors.pop('salary').apply(np.log)
nrows, ncols = predictors.shape
aic_values = []
solution_current = solution_best = np.random.binomial(1, 0.5, ncols).astype(bool)
solution_vars = predictors[predictors.columns[solution_current]]
g = pd.ols(y=logsalary, x=solution_vars)
aic_best = aic(g)
aic_values.append(aic_best)
# Cooling schedule
tau = [tau_start * 0.9**i for i in range(periods)]
for j in range(periods):
for i in range(cooling[j]):
# Random change n-neighborhood
flip = np.random.choice(ncols,numChangeNeigh,replace = False)
for i in range(numChangeNeigh):
solution_current[flip[i]] = not solution_current[flip[i]]
solution_vars = predictors[predictors.columns[solution_current]]
g = pd.ols(y=logsalary, x=solution_vars)
aic_step = aic(g)
alpha = min(1, np.exp((aic_values[-1] - aic_step)/tau[j]))
if ((aic_step < aic_values[-1]) or (np.random.uniform() < alpha)):
# Accept proposed solution
aic_values.append(aic_step)
if aic_step < aic_best:
# Replace previous best with this one
aic_best = aic_step
solution_best = solution_current.copy()
else:
# Revert solution
for i in range(numChangeNeigh):
solution_current[flip[i]] = not solution_current[flip[i]]
aic_values.append(aic_values[-1])
return aic_values,aic_best,solution_best
def regression_line():
"""Fit a line, using the powerful "ordinary least square" method of pandas"""
# Get the data
data = getData("altman_11_6.txt", subDir=r"..\Data\data_altman")
df = pd.DataFrame(data, columns=["glucose", "Vcf"])
model = pd.ols(y=df["Vcf"], x=df["glucose"])
print(model.summary)
return model.f_stat["f-stat"] # should be 4.4140184331462571
def equations(self):
eqs = {}
for col, ts in iteritems(self.y):
# TODO: Remove in favor of statsmodels implemetation
model = pd.ols(y=ts, x=self.x, window=self._window,
window_type=self._window_type,
min_periods=self._min_periods)
eqs[col] = model
return eqs