def display_qqplot(name: str, df: pd.DataFrame, target: str):
"""Show QQ plot for data against normal quantiles
Parameters
----------
name : str
Stock ticker
df : pd.DataFrame
Dataframe
target : str
Column in data to look at
"""
# Statsmodels has a UserWarning for marker kwarg-- which we dont use
warnings.filterwarnings(category=UserWarning, action="ignore")
data = df[target]
fig, ax = plt.subplots(figsize=plot_autoscale(), dpi=PLOT_DPI)
qqplot(data, stats.distributions.norm, fit=True, line="45", ax=ax)
ax.set_title(f"Q-Q plot for {name} {target}")
ax.set_ylabel("Sample quantiles")
ax.set_xlabel("Theoretical quantiles")
ax.grid(True)
if gtff.USE_ION:
plt.ion()
fig.tight_layout(pad=1)
plt.show()
print("")
def _plotQQPlotOtherBars(self, saveDirectory='', showIt=False):
# Plot the quantile plot of each asset in the portfolio:
for eachAssetName, eachAssetDataFrame in self.ALTERNATIVE_BARS.items():
logger.warning(f'[{self._plotQQPlotOtherBars.__name__}] - Looping for asset <{eachAssetName}>...')
# Plot the QQplot:
qqplot(eachAssetDataFrame.Returns.values, line='s')
# Add more variables:
plt.grid(linestyle='dotted')
plt.xlabel('Theoretical Quantiles', horizontalalignment='center', verticalalignment='center', fontsize=14, labelpad=20)
plt.ylabel('Sample Quantiles', horizontalalignment='center', verticalalignment='center', fontsize=14, labelpad=20)
plt.title(f'Asset: {eachAssetName} -- Quantile-Quantile (QQ) Plot')
plt.subplots_adjust(left=0.09, bottom=0.20, right=0.94, top=0.90, wspace=0.2, hspace=0)
# In PNG:
plt.savefig(saveDirectory + f'/QQPlot_{eachAssetName}.png')
# Show it:
if showIt:
plt.show()
######################### PLOTS #########################
def normal(x):
print('Shapiro-Wilk p =', stats.shapiro(x)[1])
print('Jarque-Bera p =', stats.jarque_bera(x)[1])
print('QQ plot')
qqplot(x, line='s')
pyplot.show()
return 0
def test_distribution(dataframe, t=None):
def print_res(p, alpha):
print('p = ', p)
if np.isnan(p):
print('p is null')
elif p < alpha:
print(
"The null hypothesis of normality can be rejected --> NOT NORMAL"
)
else:
print(
"The null hypothesis of normality cannot be rejected --> LIKELY NORMAL"
)
alpha = 0.05
global arr
arr = dataframe.values.flatten()
arr = arr[~np.isnan(arr)]
corrected = (arr - np.mean(arr)) / np.std(arr)
plt.hist(corrected, bins=15)
plt.suptitle(t)
plt.show()
qqplot(corrected)
plt.show()
# test raw values
print("Raw Data:")
k2, p = normaltest(corrected)
print_res(p, alpha)
def plot(data):
n, bins, patches = plt.hist(np.array(data), 50)
mu = np.mean(data)
sigma = np.std(data)
print("Mean: {}, std: {}".format(mu, sigma))
# Shapiro test
stat, p = shapiro(np.array(data))
if p > 0.05:
print("Shapiro: Data is normally distributed")
else:
print("Shapiro: Data is NOT normally distributed, p-value: {}".format(p))
stat, p = normaltest(np.array(data))
if p > 0.05:
print("D'Agostino: Data is normally distributed")
else:
print("D'Agostino: Data is NOT normally distributed, p-value: {}".format(p))
result = anderson(np.array(data))
p = 0
for i in range(len(result.critical_values)):
sl, cv = result.significance_level[i], result.critical_values[i]
if result.statistic < result.critical_values[i]:
print('Anderson: %.3f: %.3f, data looks normal (fail to reject H0)' % (sl, cv))
else:
print('Anderson: %.3f: %.3f, data does not look normal (reject H0)' % (sl, cv))
plt.plot(bins, norm.pdf(bins, mu, sigma))
qqplot(np.array(data), line='s')
plt.show()
def _plot_data(self):
for plot in ["MA", "STD"]:
plt.figure()
col_temp = [
col1 for col1 in self.data.columns if str(plot) in col1
]
for col in col_temp:
plt.plot(self.data['DateTime_Stamp'], self.data[col])
plt.title(plot)
plt.xticks(rotation=90)
plt.subplots_adjust(bottom=0.2)
plt.show()
plt.figure()
plt.hist(self.data['Y_label'], bins=np.arange(0.00, 1.01, 0.05))
qqplot(self.data['Y_label'], line='s')
plt.figure()
plt.plot(self.data['DateTime_Stamp'], self.data["OPEN_Bid"])
col_temp = [col1 for col1 in self.data.columns if "Band" in col1]
for col in col_temp:
plt.plot(self.data['DateTime_Stamp'], self.data[col])
return self
def qq_plot(self, column=None):
if column:
series = self.data[column]
else:
column = self.data_column
series = self.data[self.data_column]
qqplot(series, line='r')
plt.show()
def qq_plot(data):
#convert data (python list) to a numpy array
data = np.array(data)
#plot the data
qqplot(data, line='s')
pyplot.show()
def plot(label):
QQdata = pd.read_csv(
f"~/Dropbox/Fundamental Market Research/QQPlots/{label}.csv")
numpyQQdata = QQdata.values
newdata = numpy.array(
[numpyQQdata[k, 0] for k in range(numpy.size(numpyQQdata))])
qqplot(newdata, line='s')
pyplot.show()
def qq_plot():
# seed the random number generator
seed(1)
# generate univariate observations
data = 5 * randn(100) + 50
# q-q plot
qqplot(data, line='s')
pyplot.show()
def AR_model(X, data_in, lag, i):
model = AR(data_in)
results_AR = model.fit(maxlag=lag, disp=0)
AR_data = results_AR.fittedvalues
act = data_in[3:]
print("Parameters of Autoregressive Model AR(%d) are:" % lag)
print(results_AR.params)
plt.figure()
plt.plot(act, color='blue', label='Actual Value')
plt.plot(results_AR.fittedvalues, color='red', label="Predicted Value")
plt.legend(loc='best')
plt.xlabel("Time")
plt.ylabel("Time series values")
plt.title('AR(' + str(lag) + ")" + "Model with RMSE:" +
str(np.sqrt((np.sum(np.square(AR_data - act))) / len(act))))
plt.title("AR Fit (not scaled)")
plt.savefig("AR fit not scaled" + str(i))
#plt.show()
inverted_in = [
inverse_difference(X[i], data_in[i]) for i in range(len(AR_data))
]
inverted_AR = [
inverse_difference(X[i], AR_data[i]) for i in range(len(AR_data))
]
plt.figure()
plt.plot(inverted_in, color='red', label="actual value")
plt.plot(inverted_AR, color='blue', label="predicted value")
plt.legend(loc='upper left')
plt.title(
"Comparison of predicted and actual values for Autoregression model, lag"
+ str(lag))
plt.savefig(" AR Fit Final" + str(i))
print("RMSE on the Data is:" +
str(np.sqrt((np.sum(np.square(AR_data - act))) / len(act))))
residuals = results_AR.resid
plt.figure()
plt.title("Residual Scatter Plot")
plt.scatter(AR_data, residuals)
plt.savefig("residuals" + str(i))
#plt.show()
plt.figure()
qqplot(residuals)
plt.title("Residual Q-Q Plot")
plt.savefig("QQ" + str(i))
plt.figure()
plt.hist(residuals)
plt.title("Residual Histogram")
plt.savefig("Hist" + str(i))
k2, p = stats.normaltest(residuals)
alpha = 0.001
print("Chi-Square Test : k2 = %.4f p = %.4f" % (k2, p))
print("two sided chi squared probability :" + str(p))
def newDeath(request):
plt.clf()
boxPlot('new_deaths')
uri = renderMatplotlib(plt)
describe = df['new_deaths'].describe()
describes = {
"count": describe['count'],
"mean": describe['mean'],
"std": describe['std'],
"min": describe['min'],
"haiNam": describe['25%'],
"namMuoi": describe['50%'],
"bayNam": describe['75%'],
"max": describe['max'],
"median": df['new_deaths'].median(),
"mode": df['new_deaths'].mode()
}
doPhanTan = {
"IQR": interquartile_range('new_deaths'),
"var": df['new_deaths'].var(),
"std": df['new_deaths'].std(),
}
mucDo = {
"knewness": df['new_deaths'].skew(),
"kurtosis": df['new_deaths'].kurtosis()
}
plt.clf()
fig, ax = plt.subplots()
df['new_deaths'].plot.kde(ax=ax,
legend=False,
title='Histogram new_deaths')
df['new_deaths'].plot.hist(density=True, ax=ax, color='red')
ax.set_ylabel('new_deaths')
ax.grid(axis='y')
ax.set_facecolor('#d8dcd0')
hist = renderMatplotlib(plt)
plt.clf()
x = df['new_deaths']
data = randn(len(x))
qqplot(data, line='s')
plt.title('Biểu đồ phân phối chuẩn của new_deaths')
kiemDinh = renderMatplotlib(plt)
data = {
"uri": uri,
"describe": describes,
"doPhanTan": doPhanTan,
"mucDo": mucDo,
"hist": hist,
"kiemDinh": kiemDinh
}
return render(request, 'components/newDead.html', {"data": data})
def normality_test(ts): # Completed
"""
Performs a series of hypothesis tests about normality
on the time series data distribution. Besides
the result of the statistical test, this also includes
a quantile plot of the data (qqplot).
Note: Shapiro & Kolmogorov-Smirnov Tests can still produce
inconsistencies if the data set (size) is to small to detect
non-normality.
"""
ts = ts_to_list(ts)
data = np.array(ts)
# Shapiro-Wilk test: Detects all departures from normality.
# Rejects the hypothesis of normality when the p-value is <= to 0.05.
# i.e not from a normal distribution.
stat_sw, p_sw = shapiro(data) # (1) Normality test
# Kolmogorov-Smirnov: Tests the sample data against
# another sample, to compare their distributions for
# similarities, not just for normal distributions.
# If p < .05 we can reject the null, meaning our sample
# distribution is not identical to a normal distribution.
stat_ks, p_ks = normaltest(data) # (2) Normality test
# Anderson-Darling: Test is the data comes from a particular
# distribution (one of many). Modified version of the
# Kolmogorov-Smirnov to check for normality. However, rather
# Than a p-value, we're given an array of critical values
# where the hypothesis can be rejected.
stat_ad = anderson(data) # (3) Normality test
# Print results of all 3 tests
print(f'\nShapiro-Wilk Statistic Test Result: {stat_sw:.3f}')
print(f'P-value: {p_sw}: ', end='')
# Check if (SW) from normal distribution or not.
if p_sw < 0.05:
print("Null Hypothesis Rejected. Not from normal distribution.\n")
else:
print("Accepted Null Hypothesis.\n")
print(f'Kolmogorov-Smirnov Statistic Test Result: {stat_ks:.3f}')
print(f'P-value: {p_ks}', end='')
# Check if (KS) from normal distribution or not.
if p_ks < 0.05:
print("Null Hypothesis Rejected. Not from normal distribution.\n")
else:
print("Accepted Null Hypothesis. Can occurs if data set is too small.")
print(f'Anderson-Darling Statistic Test Result: {stat_ad.statistic}')
# Check if (AD) from normal distribution or not.
for i in range(len(stat_ad.critical_values)):
st, cv = stat_ad.significance_level[i], stat_ad.critical_values[i]
if stat_ad.statistic < stat_ad.critical_values[i]:
print(f'{st:.3f}: {cv:.3f}: Accepted. From normal distribution')
else:
print(f'{st:.3f}: {cv:.3f}: Rejected. Data not normal')
# Plots a standardized line, scaled by the SD of the time series.
qqplot(data, line='s')
plt.show()
ts = list_to_ts(ts)
return ts
def residooMultipleRegression(Y, A, B1, B2, B3, B4, x1, x2, x3, x4): # Y is the ChangeNominal/Real, A is the intercept B1 - B4 are the corresponding coefficients of x1-x4
residual = numpy.empty_like(Y)
i = 0
while i < T-1:
PredicatedY = (B1 * x1[i]) + (B2 * x2[i]) + (B3 * x3[i]) + (B4 + x4[i])
residual[i] = Y[i] - PredicatedY
i += 1
qqplot(residual, line = 's')
plt.show()
def QQ_plot(data):
# QQ Plot
from numpy.random import seed
from numpy.random import randn
from statsmodels.graphics.gofplots import qqplot
from matplotlib import pyplot
# q-q plot
qqplot(data, line='s')
pyplot.show()
def spatial_QQ_plots(ALLdata, timestamps):
"""
INPUTS
stations - list of station objects
start - tuple or list in the form of (year,month,day)
end - tuple or list in the form of (year,month,day)
var - the variable to make the QQ plots for
"""
labels = ['temp', 'direction', 'speed', 'solar']
num_times = len(timestamps)
fig, axes = plt.subplots(num_times,
4,
figsize=(13, int(np.round(num_times * 13 / 4))),
dpi=80,
facecolor='w',
edgecolor='k')
for row, ts in enumerate(timestamps):
temp = []
wind_dir = []
wind_speed = []
solar = []
for station in ALLdata.WSdata:
df = station.data_binned.loc[ts]
temp.append(df['temp:'])
wind_dir.append(df['dir:'])
wind_speed.append(df['speed:'])
solar.append(df['solar:'])
lst = [
np.matrix(sorted(temp)).T,
np.matrix(sorted(wind_dir)).T,
np.matrix(sorted(wind_speed)).T,
np.matrix(sorted(solar)).T
]
for col, vals in enumerate(lst):
ax = axes[row, col]
qqplot(vals, line='s', ax=ax)
ax.set_xlabel('')
ax.set_ylabel('')
k2, p = sps.shapiro(vals)
p_str = '{:.2f}'.format(p)
print('timestamp:{}, var:{}, p: {}'.format(ts, labels[col], p_str))
ax.set_xlabel('Shap p:{}'.format(p_str))
#ax.annotate('Shap p:{}'.format(p_str),xy = (0.05,.9),xytext = (0.05,.9), textcoords='axes fraction',horizontalalignment='left', verticalalignment='top')
#ax.annotate('p'.format(p),xy = (0.05,.9),xytext = (0.05,.9), textcoords='axes fraction',horizontalalignment='left', verticalalignment='top')
if col == 0:
ax.set_ylabel(ts)
if row == 0:
ax.title.set_text(labels[col])
fig.tight_layout(pad=1.1)
def test_qqplot_pltkwargs(self, close_figures):
qqplot(
self.res,
line="r",
marker="d",
markerfacecolor="cornflowerblue",
markeredgecolor="white",
alpha=0.5,
)
def explore_series(df, columns_explore, plot_lags=20):
# Figure setup
fig_out = plt.figure(figsize=(22, 24))
plot_cols = len(columns_explore)
position = 0
# create lists for output values from adfuller tests
output_ADF = []
output_pval = []
output_crit1 = []
output_crit5 = []
output_crit10 = []
output_labels = []
# loop through the columns of interest
for column in df:
if column in columns_explore:
# time history plot
df[column].plot(ax=plt.subplot2grid((5, plot_cols), (0, position)),
title=column)
# histogram
df[column].hist(ax=plt.subplot2grid((5, plot_cols), (1, position)))
# qqplot to check normality
qqplot(df[column],
line='r',
ax=plt.subplot2grid((5, plot_cols), (2, position)))
# autocorrelation plot
plot_acf(df[column].dropna(),
lags=plot_lags,
ax=plt.subplot2grid((5, plot_cols), (3, position)))
# partial autocorrelation plot
plot_pacf(df[column].dropna(),
lags=plot_lags,
ax=plt.subplot2grid((5, plot_cols), (4, position)))
position += 1
# run adfuller test and append results to lists
result = adfuller(df[column].dropna())
output_ADF.append(result[0])
output_pval.append(result[1])
output_crit1.append(result[4]['1%'])
output_crit5.append(result[4]['5%'])
output_crit10.append(result[4]['10%'])
output_labels.append(column)
# create dataframe for the adfuller results
df_out = pd.DataFrame(columns=output_labels,
index=[
'ADF_Statistic', 'p-value', 'Critical_1percent',
'Critical_5_percent', 'Critical_10_percent'
])
df_out.iloc[0] = output_ADF
df_out.iloc[1] = output_pval
df_out.iloc[2] = output_crit1
df_out.iloc[3] = output_crit5
df_out.iloc[4] = output_crit10
return df_out, fig_out
def isGaussian(data):
# histogram plot --------------------------------------------------------------
print("Histogram plot -------------------------------------")
pyplot.hist(data)
pyplot.show()
#QQPlot ----------------------------------------------------------------------
print("QQ plot -------------------------------------")
from statsmodels.graphics.gofplots import qqplot
# q-q plot
qqplot(data, line='s')
pyplot.show()
#shapiro wilk-test -----------------------------------------------------------
print("Shapiro-Wilk test -------------------------------------")
from scipy.stats import shapiro
stat, p = shapiro(data)
print('Statistics=%.3f, p=%.3f' % (stat, p))
# interpret
alpha = 0.05
if p > alpha:
print('Sample looks Gaussian (fail to reject H0)')
else:
print('Sample does not look Gaussian (reject H0)')
#D'Agostino's K^2 Test --------------------------------------------------------
print("D'Agostino's K^2 test -------------------------------------")
from scipy.stats import normaltest
# normality test
stat, p = normaltest(data)
print('Statistics=%.3f, p=%.3f' % (stat, p))
# interpret
alpha = 0.05
if p > alpha:
print('Sample looks Gaussian (fail to reject H0)')
else:
print('Sample does not look Gaussian (reject H0)')
#Anderson-Darling Test --------------------------------------------------------
print("Anderson-Darling test -------------------------------------")
from scipy.stats import anderson
# normality test
result = anderson(data)
print('Statistic: %.3f' % result.statistic)
p = 0
for i in range(len(result.critical_values)):
sl, cv = result.significance_level[i], result.critical_values[i]
if result.statistic < result.critical_values[i]:
print('%.3f: %.3f, data looks normal (fail to reject H0)' % (sl, cv))
else:
print('%.3f: %.3f, data does not look normal (reject H0)' % (sl, cv))
def qq(a, logvalue, lognext, interval, NCHANGES):
V, A, r, sigma = regression(a, logvalue, lognext, interval, NCHANGES)
centralized = numpy.array([V[k] - r * A[k] for k in range(NCHANGES)])
s1 = stats.shapiro(centralized)[0]
s2 = stats.shapiro(centralized)[1]
qqplot(centralized, line='r')
# fig = plt.figure()
# fig.savefig(im + 'eco_'+ Ecoregions[eid] + '_Raw_Data_residuals.png')
pyplot.show()
return s1, s2
def plot_qqplot(
other_args: List[str],
ticker: str,
model_name: str,
residuals: List[float],
):
"""Qqplot time series against a standard normal curve
Parameters
----------
other_args : str
Command line arguments to be processed with argparse
ticker : str
Ticker of the stock
model_name : str
Model fitting name in use
residuals : List[float]
Residuals data
"""
parser = argparse.ArgumentParser(
add_help=False,
prog="qqplot",
description="""
Qqplot time series against a standard normal curve
""",
)
try:
ns_parser = parse_known_args_and_warn(parser, other_args)
if not ns_parser:
return
plt.figure(figsize=plot_autoscale(),
dpi=PLOT_DPI,
constrained_layout=True)
qqplot(residuals,
stats.distributions.norm,
fit=True,
line="45",
ax=plt.gca())
plt.title(f"Q-Q plot residuals from {model_name} on {ticker}")
plt.ylabel("Sample quantiles")
plt.xlabel("Theoretical quantiles")
plt.grid(True)
if gtff.USE_ION:
plt.ion()
plt.show()
print("")
except Exception as e:
print(e, "\n")
return
def display_qqplot(
name: str,
df: pd.DataFrame,
target: str,
external_axes: Optional[List[plt.Axes]] = None,
):
"""Show QQ plot for data against normal quantiles
Parameters
----------
name : str
Stock ticker
df : pd.DataFrame
Dataframe
target : str
Column in data to look at
external_axes : Optional[List[plt.Axes]], optional
External axes (1 axis is expected in the list), by default None
"""
# Statsmodels has a UserWarning for marker kwarg-- which we don't use
warnings.filterwarnings(category=UserWarning, action="ignore")
data = df[target]
# This plot has 1 axis
if external_axes is None:
_, ax = plt.subplots(
figsize=plot_autoscale(),
dpi=PLOT_DPI,
)
else:
if len(external_axes) != 1:
logger.error("Expected list of one axis item.")
console.print("[red]Expected list of 1 axis items./n[/red]")
return
(ax, ) = external_axes
qqplot(
data,
stats.distributions.norm,
fit=True,
line="45",
color=theme.down_color,
ax=ax,
)
ax.get_lines()[1].set_color(theme.up_color)
ax.set_title(f"Q-Q plot for {name} {target}")
ax.set_ylabel("Sample quantiles")
ax.set_xlabel("Theoretical quantiles")
theme.style_primary_axis(ax)
if external_axes is None:
theme.visualize_output()
def qqplots(self, epoch, sub=None):
assert 0 <= epoch <= self.epochs, 'epoch must be between 0 and %.0f, got %.0f' % (
self.epochs, epoch)
if not sub:
sub = range(self.masks)
for group in sub:
gofplots.qqplot(self.data[group, :, epoch], fit=True, line='45')
plt.suptitle("%s, %s, Epoch %.0f" %
(self.name, self.labels[group], epoch),
fontsize=18)
def plot_QQ_plot(self, series_values):
try:
from numpy.random import seed
from numpy.random import randn
from statsmodels.graphics.gofplots import qqplot
from matplotlib import pyplot
qqplot(series_values, line='s')
pyplot.show()
except Exception as exc:
raise exc
def residuals_eval(y_true, y_pred):
y_res = y_true - y_pred
df_res = DataFrame(y_res)
print(df_res.describe())
df_res.plot()#line
pyplot.show()
df_res.hist()#hist
pyplot.show()
df_res.plot(kind='kde')#density plot
pyplot.show()
qqplot(numpy.array(y_res), line='r')
pyplot.show()
def residuals_charts(test_dataset, test_output):
"""Build residuals charts for one experiment."""
prediction_series = test_output.mean(axis=0).reshape(test_output.shape[1])
residuals = prediction_series - test_dataset.y_data.reshape(
test_dataset.y_data.shape[0])
pd.Series(residuals).hist(bins=30)
print(stats.normaltest(residuals))
gofplots.qqplot(residuals)
xxx = np.linspace(-3.5, 3.5, 4)
pyplot.plot(xxx, xxx)
tsaplots.plot_acf(residuals, lags=30)
tsaplots.plot_pacf(residuals, lags=30)
def residual_plot(self):
'''
Plot the residual and save it to current directory
'''
import matplotlib.pyplot as plt
from scipy.stats import norm
from statsmodels.graphics.gofplots import qqplot
# set the size of the plot
plt.figure(figsize=(16, 9))
# plot the distribution
ax = plt.subplot(121)
# create bins and count the numbers
count = pd.DataFrame([0] * 24, index=np.arange(-5.75, 6, step=0.5))
for i in count.index:
for r in self._residual:
if r >= i - 0.25 and r < i + 0.25:
count.loc[i] += 1
# create a normal distribution reference
xx = np.linspace(-3, 3, 100)
normal = norm.pdf(xx, np.mean(self._residual), np.std(self._residual))
normalcdf = norm.cdf(xx, np.mean(self._residual),
np.std(self._residual))
low_flag = True
for i in range(xx.shape[0]):
if normalcdf[i] >= 0.025 and low_flag:
low = i
low_flag = False
if normalcdf[i] >= 0.975:
high = i
break
# plot the distribution
plt.plot(count.index, count, 'o', label="residual")
plt.plot(xx, normal * self._residual.shape[0], '--', label="normal")
plt.fill_between(xx[low:high],
0,
normal[low:high] * self._residual.shape[0],
alpha=.3,
facecolor="grey",
label="95% normal")
plt.xlim([-6, 6])
ax.set_ylim(bottom=5)
ax.legend()
plt.title("Distribution of the residual")
plt.yscale('log')
# plot the QQ plot
ax = plt.subplot(122)
qqplot(self._residual, line='s', ax=ax)
plt.xlim([-3.5, 3.5])
plt.ylim([-5, 5])
plt.title("residual QQ plot")
#plt.show()
plt.savefig("residual_plots.png")
def plot_Model_Identify(DataSet, frequency=1, acf_lag=12, pacf_lag=12):
"""
DataSet : dataframe with the type of first column either int()
or panda datetime
Frequency : int, Seasonal Component period (in time step)
"""
# Organize plot
fig, ax = plt.subplots(3, 4)
# Plot the Observed Data
DataSet.plot(ax=ax[0, 0])
ax[0, 0].set_title('Observed Value')
ax[0, 0].set_xlabel("")
# Plot the autocorrelation plot
autocorrelation_plot(DataSet.iloc[:, 0], ax=ax[1, 0])
ax[1, 0].set_title('Autocorrelation')
# Plot the QQ plot
qqplot(
DataSet.iloc[:, 0],
ax=ax[2, 0],
)
ax[2, 0].set_title('Q-Q Plot')
# Lag plot
lag_plot(DataSet.iloc[:, 0], ax=ax[0, 1])
ax[0, 1].set_title('Lag Plot')
ax[0, 1].set_ylabel("")
ax[0, 1].set_xlabel("")
# ACF Plot
tsa.plot_acf(DataSet.iloc[:, 0], ax=ax[1, 1], lags=acf_lag, alpha=0.05)
ax[1, 1].set_title('ACF')
# PACF Plot
tsa.plot_pacf(DataSet.iloc[:, 0], ax=ax[2, 1], lags=pacf_lag, alpha=0.05)
ax[2, 1].set_title('PACF')
# decomposition plot
decomposition = sm.tsa.seasonal_decompose(DataSet.iloc[:, 0],
freq=frequency)
decomposition.resid.plot(ax=ax[0, 2])
decomposition.resid.plot(ax=ax[0, 3], kind='kde')
decomposition.seasonal.plot(ax=ax[1, 2])
decomposition.trend.plot(ax=ax[2, 2])
ax[0, 2].set_title('Residual')
ax[1, 2].set_title('Seasonal')
ax[2, 2].set_title('Trend')
ax[0, 3].set_title('Residual Prob. Distrib')
plt.show()
def correctLin(x, y):
n = numpy.size(x)
r = stats.linregress(x, y)
s = r.slope
i = r.intercept
print(r)
residuals = numpy.array([y[k] - x[k] * s - i for k in range(n)])
stderr = math.sqrt((1 / (n - 2)) * numpy.dot(residuals, residuals))
qqplot(residuals, line='r')
pyplot.show()
print('Shapiro-Wilk p = ', stats.shapiro(residuals)[1])
print('Jarque-Bera p = ', stats.jarque_bera(residuals)[1])
return (residuals, s, i, stderr)
def simpleLin(x, y):
n = numpy.size(x)
x = numpy.array(x)
y = numpy.array(y)
k = numpy.dot(x, y) / numpy.dot(x, x)
residuals = y - k * x
stderr = numpy.std(residuals)
qqplot(residuals, line='r')
pyplot.show()
pyplot.plot(residuals)
pyplot.show()
print('normality', stats.shapiro(residuals))
return (k, stderr)
def plot_regress_analysis(model, influence=True, annotate=True):
plt.figure(figsize=(15, 16))
# Residuals vs Fitted
ax = plt.subplot2grid((3, 2), (0, 0))
ax.set_title("Residuals vs Fitted")
ax.set_xlabel('Fitted values')
ax.set_ylabel('Residuals')
fitted = model.predict()
residuals = model.resid
ax.plot(fitted, residuals, marker='.', linestyle='')
# Model non-linearity with quadratic
polyline = np.poly1d(np.polyfit(fitted, residuals, 2))
max_fitted = np.max(fitted)
xs = np.append(np.arange(np.min(fitted), max_fitted), max_fitted)
ax.plot(xs, polyline(xs), linewidth=2.5)
# Q-Q plot
ax = plt.subplot2grid((3, 2), (0, 1))
ax.set_title("Q-Q")
qqplot(model.resid_pearson, dist="norm", line='r', ax=ax)
# Scale-Location
ax = plt.subplot2grid((3, 2), (1, 0))
ax.set_title("Scale-Location")
ax.set_xlabel('Fitted values')
ax.set_ylabel('$|$Normalized residuals$|^{1/2}$')
std_residuals = np.sqrt(np.abs(model.resid_pearson))
ax.plot(fitted, std_residuals, linestyle='', marker='.')
# Model non-linearity with quadratic
polyline = np.poly1d(np.polyfit(fitted, std_residuals, 2))
ax.plot(xs, polyline(xs), linewidth=2.5)
# Residuals vs Leverage
ax = plt.subplot2grid((3, 2), (1, 1))
plot_leverage_resid2(model, ax, annotate=annotate)
# Influence plot
if influence:
ax = plt.subplot2grid((3, 2), (2, 0), colspan=2)
ax = influence_plot(model, ax=ax)
def env_corr(self, env_vars, coeff_plot=False, qq_plot=False):
"""
Determine correlations with environmental/non-discretionary variables
using a logit regression. Tobit will be implemented when available
upstream in statsmodels.
Takes:
env_vars: A pandas dataframe of environmental variables
Returns:
corr_mod: the statsmodels' model instance containing the inputs
and results from the logit model.
Note that there can be no spaces in the variables' names.
"""
import matplotlib.pyplot as plt
from statsmodels.regression.linear_model import OLS
from statsmodels.graphics.gofplots import qqplot
from seaborn import coefplot
env_data = _to_dataframe(env_vars)
corr_data = env_data.join(self['Efficiency'])
corr_mod = OLS.from_formula(
"Efficiency ~ " + " + ".join(env_vars.columns), corr_data)
corr_res = corr_mod.fit()
#plot coeffs
if coeff_plot:
coefplot("Efficiency ~ " + " + ".join(env_vars.columns),
data=corr_data)
plt.xticks(rotation=45, ha='right')
plt.title('Regression coefficients and standard errors')
#plot qq of residuals
if qq_plot:
qqplot(corr_res.resid, line='s')
plt.title('Distribution of residuals')
print(corr_res.summary())
return corr_res
def draw_figures():
bdims = pd.read_csv("bdims.csv")
fdims = bdims[ bdims["sex"] == 0]
fig, plots = plt.subplots(4, 2)
biidi = standardize(fdims["bii.di"])
elbdi = standardize(fdims["elb.di"])
age = standardize(bdims["age"])
chede = standardize(fdims["che.de"])
plots[0][0].hist(biidi, bins=range(-4,4))
plots[1][0].hist(elbdi, bins=range(-3,5))
plots[2][0].hist(age, bins=range(-2,5))
plots[3][0].hist(chede, bins=range(-2,6))
plots[0][0].set_title("Histogram of female biiliac diameter")
plots[1][0].set_title("Histogram of female elbow diameter")
plots[2][0].set_title("Histogram of general age")
plots[3][0].set_title("Histogram of female chest depth")
qqplot(biidi, ax=plots[1][1], line="q")
qqplot(elbdi, ax=plots[2][1], line="q")
qqplot(age, ax=plots[3][1], line="q")
qqplot(chede, ax=plots[0][1], line="q")
plots[0][1].set_title("Normal Q-Q Plot A")
plots[1][1].set_title("Normal Q-Q Plot B")
plots[2][1].set_title("Normal Q-Q Plot C")
plots[3][1].set_title("Normal Q-Q Plot D")
for i in range(0,4):
plots[i][0].set_xlabel("standarized data")
plots[i][0].set_ylabel("frequency")
fig.set_size_inches(12, 12)
plt.tight_layout()
return fig
print (final_test_loss)
for folder in folders:
print
print folder
for d in data[folder]:
breakeven_points = util.find_breakeven(d["curve"])
pr[folder].append(breakeven_points[-1])
print (breakeven_points[-1])
print ("Loss samples t test")
# Random samples from normal
s = np.random.normal(np.mean(lc[folders[0]]), np.std(lc[folders[1]]), 100)
print ("Random samples", scipy.stats.shapiro(s))
fig = qqplot(s, scipy.stats.norm, fit=True, line="45")
plt.show()
# First folder figures
fig = qqplot(np.array(lc[folders[0]]), scipy.stats.norm, fit=True, line="45")
plt.show()
print (folders[0], scipy.stats.shapiro(np.array(lc[folders[0]])))
# Second folder figures
fig = qqplot(np.array(lc[folders[1]]), scipy.stats.norm, fit=True, line="45")
plt.show()
print (folders[1], scipy.stats.shapiro(np.array(lc[folders[1]])))
tstat, pval = perform_welchs_test(lc[folders[0]], lc[folders[1]])
print ("t-statistics = {}".format(tstat))
print ("p-value = {}".format(pval))
irf.plot_cum_effects(orth=False)
plt.show()
fevd = results.fevd(1)
fevd.summary()
fevd.plot()
plt.show()
results.test_causality('DJIA', ['SP500'],kind='f')
results.test_causality('SP500', ['DJIA'],kind='f')
results.test_normality(signif=0.05,verbose=False)
resids = results.resid.sum(axis=1)
resids.plot()
plt.show()
from statsmodels.graphics.gofplots import qqplot, qqline
qqplot(data=resids,line='s')#, dist, distargs, a, loc, scale, fit, line, ax)
plt.show()
from statsmodels.sandbox.tsa.garch import Garch
rets1 = rets_bm.iloc[:,1]
Garch(rets1)
#Getting GARCH working -using RPY2
import rpy2
rpy2.__version__
t =datetime(2013,1,5)
from pandas.tseries.offsets import MonthEnd, BusinessMonthBegin
(t + 2*BusinessMonthBegin())> datetime(2013,1,1)
ma['teams'][0],
ma['teams'][1],
ma['score'][0],
ma['score'][1],
fitted[mai],
)
mfile.write(towrite)
mfile.write('\n')
print
print 'residual_std: %.10f' % (resid.std())
print
if PLOT_RESIDUAL_QQ:
import statsmodels.graphics.gofplots as sgg
sgg.qqplot(resid, fit=True)
if PLOT_RESIDUAL_HIST:
import pylab
import scipy.stats as ss
freqs, lefts = np.histogram(resid, bins = 'auto', density = True)
centers = (lefts[:-1] + lefts[1:]) / 2
pylab.bar(centers, freqs, width = centers[1] - centers[0])
empirical_dist = ss.norm(*(ss.norm.fit(resid)))
pylab.plot(centers, [empirical_dist.pdf(x) for x in centers], 'g-', linewidth = 5)
if PLOT_SCATTER_TOT_EXP_RESIDUALS:
import pylab
pylab.scatter(tot_exps, resid, marker = '.', s = 1)