def plot_loadings(self, loading_pairs=None, plot_prerotated=False):
"""
Plot factor loadings in 2-d plots
Parameters
----------
loading_pairs : None or a list of tuples
Specify plots. Each tuple (i, j) represent one figure, i and j is
the loading number for x-axis and y-axis, respectively. If `None`,
all combinations of the loadings will be plotted.
plot_prerotated : True or False
If True, the loadings before rotation applied will be plotted. If
False, rotated loadings will be plotted.
Returns
-------
figs : a list of figure handles
"""
_import_mpl()
from .plots import plot_loadings
if self.rotation_method is None:
plot_prerotated = True
loadings = self.loadings_no_rot if plot_prerotated else self.loadings
if plot_prerotated:
title = 'Prerotated Factor Pattern'
else:
title = '%s Rotated Factor Pattern' % (self.rotation_method)
var_explained = self.eigenvals / self.n_comp * 100
return plot_loadings(loadings,
loading_pairs=loading_pairs,
title=title,
row_names=self.endog_names,
percent_variance=var_explained)
def plot_partial(self,
smooth_index,
plot_se=True,
cpr=False,
include_constant=True,
ax=None):
"""plot the contribution of a smooth term to the linear prediction
Parameters
----------
smooth_index : int
index of the smooth term within list of smooth terms
plot_se : book
If plot_se is true, then the confidence interval for the linear
prediction will be added to the plot.
cpr : bool
If cpr (component plus residual) is true, the a scatter plot of
the partial working residuals will be added to the plot.
include_constant : bool
If true, then the estimated intercept is added to the prediction
and its standard errors. This avoids that the confidence interval
has zero width at the imposed identification constraint, e.g.
either at a reference point or at the mean.
ax : None or matplotlib axis instance
If ax is not None, then the plot will be added to it.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the Figure to which
`ax` is connected.
"""
from statsmodels.graphics.utils import _import_mpl, create_mpl_ax
_import_mpl()
variable = smooth_index
y_est, se = self.partial_values(variable,
include_constant=include_constant)
smoother = self.model.smoother
x = smoother.smoothers[variable].x
sort_index = np.argsort(x)
x = x[sort_index]
y_est = y_est[sort_index]
se = se[sort_index]
fig, ax = create_mpl_ax(ax)
ax.plot(x, y_est, c='blue', lw=2)
if plot_se:
ax.plot(x, y_est + 1.96 * se, '-', c='blue')
ax.plot(x, y_est - 1.96 * se, '-', c='blue')
if cpr:
# TODO: resid_response does not make sense with nonlinear link
# use resid_working ?
cpr_ = y_est + self.resid_working
ax.plot(x, cpr_, '.', lw=2)
ax.set_xlabel(smoother.smoothers[variable].variable_name)
return fig
def plot_cusum(self, alpha=0.05, legend_loc='upper left',
fig=None, figsize=None):
r"""
Plot the CUSUM statistic and significance bounds.
Parameters
----------
alpha : float, optional
The plotted significance bounds are alpha %.
legend_loc : string, optional
The location of the legend in the plot. Default is upper left.
fig : Matplotlib Figure instance, optional
If given, subplots are created in this figure instead of in a new
figure. Note that the grid will be created in the provided
figure using `fig.add_subplot()`.
figsize : tuple, optional
If a figure is created, this argument allows specifying a size.
The tuple is (width, height).
Notes
-----
Evidence of parameter instability may be found if the CUSUM statistic
moves out of the significance bounds.
References
----------
.. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975.
"Techniques for Testing the Constancy of
Regression Relationships over Time."
Journal of the Royal Statistical Society.
Series B (Methodological) 37 (2): 149-92.
"""
# Create the plot
from statsmodels.graphics.utils import _import_mpl, create_mpl_fig
_import_mpl()
fig = create_mpl_fig(fig, figsize)
ax = fig.add_subplot(1, 1, 1)
# Get dates, if applicable
if hasattr(self.data, 'dates') and self.data.dates is not None:
dates = self.data.dates._mpl_repr()
else:
dates = np.arange(self.nobs)
d = max(self.nobs_diffuse, self.loglikelihood_burn)
# Plot cusum series and reference line
ax.plot(dates[d:], self.cusum, label='CUSUM')
ax.hlines(0, dates[d], dates[-1], color='k', alpha=0.3)
# Plot significance bounds
lower_line, upper_line = self._cusum_significance_bounds(alpha)
ax.plot([dates[d], dates[-1]], upper_line, 'k--',
label='%d%% significance' % (alpha * 100))
ax.plot([dates[d], dates[-1]], lower_line, 'k--')
ax.legend(loc=legend_loc)
return fig
def plot_cusum(self, alpha=0.05, legend_loc='upper left',
fig=None, figsize=None):
r"""
Plot the CUSUM statistic and significance bounds.
Parameters
----------
alpha : float, optional
The plotted significance bounds are alpha %.
legend_loc : string, optional
The location of the legend in the plot. Default is upper left.
fig : Matplotlib Figure instance, optional
If given, subplots are created in this figure instead of in a new
figure. Note that the grid will be created in the provided
figure using `fig.add_subplot()`.
figsize : tuple, optional
If a figure is created, this argument allows specifying a size.
The tuple is (width, height).
Notes
-----
Evidence of parameter instability may be found if the CUSUM statistic
moves out of the significance bounds.
References
----------
.. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975.
"Techniques for Testing the Constancy of
Regression Relationships over Time."
Journal of the Royal Statistical Society.
Series B (Methodological) 37 (2): 149-92.
"""
# Create the plot
from statsmodels.graphics.utils import _import_mpl, create_mpl_fig
_import_mpl()
fig = create_mpl_fig(fig, figsize)
ax = fig.add_subplot(1, 1, 1)
# Get dates, if applicable
if hasattr(self.data, 'dates') and self.data.dates is not None:
dates = self.data.dates._mpl_repr()
else:
dates = np.arange(self.nobs)
d = max(self.nobs_diffuse, self.loglikelihood_burn)
# Plot cusum series and reference line
ax.plot(dates[d:], self.cusum, label='CUSUM')
ax.hlines(0, dates[d], dates[-1], color='k', alpha=0.3)
# Plot significance bounds
lower_line, upper_line = self._cusum_significance_bounds(alpha)
ax.plot([dates[d], dates[-1]], upper_line, 'k--',
label='%d%% significance' % (alpha * 100))
ax.plot([dates[d], dates[-1]], lower_line, 'k--')
ax.legend(loc=legend_loc)
return fig
def plot_partial(self, smooth_index, plot_se=True, cpr=False,
include_constant=True, ax=None):
"""plot the contribution of a smooth term to the linear prediction
Parameters
----------
smooth_index : int
index of the smooth term within list of smooth terms
plot_se : book
If plot_se is true, then the confidence interval for the linear
prediction will be added to the plot.
cpr : bool
If cpr (component plus residual) is true, the a scatter plot of
the partial working residuals will be added to the plot.
include_constant : bool
If true, then the estimated intercept is added to the prediction
and its standard errors. This avoids that the confidence interval
has zero width at the imposed identification constraint, e.g.
either at a reference point or at the mean.
ax : None or matplotlib axis instance
If ax is not None, then the plot will be added to it.
Returns
-------
fig : matplotlib Figure instance
"""
from statsmodels.graphics.utils import _import_mpl, create_mpl_ax
_import_mpl()
variable = smooth_index
y_est, se = self.partial_values(variable,
include_constant=include_constant)
smoother = self.model.smoother
x = smoother.smoothers[variable].x
sort_index = np.argsort(x)
x = x[sort_index]
y_est = y_est[sort_index]
se = se[sort_index]
fig, ax = create_mpl_ax(ax)
ax.plot(x, y_est, c='blue', lw=2)
if plot_se:
ax.plot(x, y_est + 1.96 * se, '-', c='blue')
ax.plot(x, y_est - 1.96 * se, '-', c='blue')
if cpr:
# TODO: resid_response doesn't make sense with nonlinear link
# use resid_working ?
cpr_ = y_est + self.resid_working
ax.plot(x, cpr_, '.', lw=2)
ax.set_xlabel(smoother.smoothers[variable].variable_name)
return fig
def plot(self):
from statsmodels.graphics.utils import _import_mpl
plt = _import_mpl()
fig, axes = plt.subplots(4, 1, sharex=True)
if hasattr(self.observed, 'plot'): # got pandas use it
self.observed.plot(ax=axes[0], legend=False)
axes[0].set_ylabel('Observed')
self.trend.plot(ax=axes[1], legend=False)
axes[1].set_ylabel('Trend')
self.seasonal.plot(ax=axes[2], legend=False)
axes[2].set_ylabel('Seasonal')
self.resid.plot(ax=axes[3], legend=False)
axes[3].set_ylabel('Residual')
else:
axes[0].plot(self.observed)
axes[0].set_ylabel('Observed')
axes[1].plot(self.trend)
axes[1].set_ylabel('Trend')
axes[2].plot(self.seasonal)
axes[2].set_ylabel('Seasonal')
axes[3].plot(self.resid)
axes[3].set_ylabel('Residual')
axes[3].set_xlabel('Time')
axes[3].set_xlim(0, self.nobs)
fig.tight_layout()
return fig
def plot(self):
from statsmodels.graphics.utils import _import_mpl
plt = _import_mpl()
fig, axes = plt.subplots(4, 1, sharex=True)
if hasattr(self.observed, 'plot'): # got pandas use it
self.observed.plot(ax=axes[0], legend=False)
axes[0].set_ylabel('Observed')
self.trend.plot(ax=axes[1], legend=False)
axes[1].set_ylabel('Trend')
self.seasonal.plot(ax=axes[2], legend=False)
axes[2].set_ylabel('Seasonal')
self.resid.plot(ax=axes[3], legend=False)
axes[3].set_ylabel('Residual')
else:
axes[0].plot(self.observed)
axes[0].set_ylabel('Observed')
axes[1].plot(self.trend)
axes[1].set_ylabel('Trend')
axes[2].plot(self.seasonal)
axes[2].set_ylabel('Seasonal')
axes[3].plot(self.resid)
axes[3].set_ylabel('Residual')
axes[3].set_xlabel('Time')
axes[3].set_xlim(0, self.nobs)
fig.tight_layout()
return fig
def test_baseline(self, close_figures):
plt = _import_mpl()
fig, ax = gofplots._do_plot(self.x, self.y)
assert isinstance(fig, plt.Figure)
assert isinstance(ax, plt.Axes)
assert self.fig is not fig
assert self.ax is not ax
def test_with_ax(self, close_figures):
plt = _import_mpl()
fig, ax = gofplots._do_plot(self.x, self.y, ax=self.ax)
assert isinstance(fig, plt.Figure)
assert isinstance(ax, plt.Axes)
assert self.fig is fig
assert self.ax is ax
def plot(self,
observed=True,
seasonal=True,
trend=True,
resid=True,
weights=False):
"""
Plot estimated components
Parameters
----------
observed : bool
Include the observed series in the plot
seasonal : bool
Include the seasonal component in the plot
trend : bool
Include the trend component in the plot
resid : bool
Include the residual in the plot
weights : bool
Include the weights in the plot (if any)
Returns
-------
matplotlib.figure.Figure
The figure instance that containing the plot.
"""
from statsmodels.graphics.utils import _import_mpl
from pandas.plotting import register_matplotlib_converters
plt = _import_mpl()
register_matplotlib_converters()
series = [(self._observed, 'Observed')] if observed else []
series += [(self.trend, 'trend')] if trend else []
series += [(self.seasonal, 'seasonal')] if seasonal else []
series += [(self.resid, 'residual')] if resid else []
series += [(self.weights, 'weights')] if weights else []
if isinstance(self._observed, (pd.DataFrame, pd.Series)):
nobs = self._observed.shape[0]
xlim = self._observed.index[0], self._observed.index[nobs - 1]
else:
xlim = (0, self._observed.shape[0] - 1)
fig, axs = plt.subplots(len(series), 1)
for i, (ax, (series, def_name)) in enumerate(zip(axs, series)):
if def_name != 'residual':
ax.plot(series)
else:
ax.plot(series, marker='o', linestyle='none')
ax.plot(xlim, (0, 0), color='#000000', zorder=-3)
name = getattr(series, 'name', def_name)
if def_name != 'Observed':
name = name.capitalize()
title = ax.set_title if i == 0 and observed else ax.set_ylabel
title(name)
ax.set_xlim(xlim)
fig.tight_layout()
return fig
def plot_scree(self, ncomp=None):
"""
Plot of the ordered eigenvalues and variance explained for the loadings
Parameters
----------
ncomp : int, optional
Number of loadings to include in the plot. If None, will
included the same as the number of maximum possible loadings
Returns
-------
Figure
Handle to the figure.
"""
_import_mpl()
from .plots import plot_scree
return plot_scree(self.eigenvals, self.n_comp, ncomp)
def plot(self):
from statsmodels.graphics.utils import _import_mpl
plt = _import_mpl()
fig, axes = plt.subplots(4, 1, sharex=True)
self.observed.plot(ax=axes[0], legend=False)
axes[0].set_ylabel('Observed')
self.seasadj.plot(ax=axes[1], legend=False)
axes[1].set_ylabel('Seas. Adjusted')
self.trend.plot(ax=axes[2], legend=False)
axes[2].set_ylabel('Trend')
self.irregular.plot(ax=axes[3], legend=False)
axes[3].set_ylabel('Irregular')
fig.tight_layout()
return fig
def plot(self):
from statsmodels.graphics.utils import _import_mpl
plt = _import_mpl()
fig, axes = plt.subplots(4, 1, sharex=True)
self.observed.plot(ax=axes[0], legend=False)
axes[0].set_ylabel('Observed')
self.seasadj.plot(ax=axes[1], legend=False)
axes[1].set_ylabel('Seas. Adjusted')
self.trend.plot(ax=axes[2], legend=False)
axes[2].set_ylabel('Trend')
self.irregular.plot(ax=axes[3], legend=False)
axes[3].set_ylabel('Irregular')
fig.tight_layout()
return fig
def plot_path(self):
from statsmodels.graphics.utils import _import_mpl
plt = _import_mpl()
plt.plot(self.alphas, self.cv_error, c='black')
plt.plot(self.alphas, self.cv_error + 1.96 * self.cv_std,
c='blue')
plt.plot(self.alphas, self.cv_error - 1.96 * self.cv_std,
c='blue')
plt.plot(self.alphas, self.cv_error, 'o', c='black')
plt.plot(self.alphas, self.cv_error + 1.96 * self.cv_std, 'o',
c='blue')
plt.plot(self.alphas, self.cv_error - 1.96 * self.cv_std, 'o',
c='blue')
return
def plot_cusum_squares(self, alpha=0.05, legend_loc='upper left',
fig=None, figsize=None):
r"""
Plot the CUSUM of squares statistic and significance bounds.
Parameters
----------
alpha : float, optional
The plotted significance bounds are alpha %.
legend_loc : string, optional
The location of the legend in the plot. Default is upper left.
fig : Matplotlib Figure instance, optional
If given, subplots are created in this figure instead of in a new
figure. Note that the grid will be created in the provided
figure using `fig.add_subplot()`.
figsize : tuple, optional
If a figure is created, this argument allows specifying a size.
The tuple is (width, height).
Notes
-----
Evidence of parameter instability may be found if the CUSUM of squares
statistic moves out of the significance bounds.
Critical values used in creating the significance bounds are computed
using the approximate formula of [2]_.
References
----------
.. [1] Brown, R. L., J. Durbin, and J. M. Evans. 1975.
"Techniques for Testing the Constancy of
Regression Relationships over Time."
Journal of the Royal Statistical Society.
Series B (Methodological) 37 (2): 149-92.
.. [2] Edgerton, David, and Curt Wells. 1994.
"Critical Values for the Cusumsq Statistic
in Medium and Large Sized Samples."
Oxford Bulletin of Economics and Statistics 56 (3): 355-65.
"""
# Create the plot
from statsmodels.graphics.utils import _import_mpl, create_mpl_fig
plt = _import_mpl()
fig = create_mpl_fig(fig, figsize)
ax = fig.add_subplot(1, 1, 1)
# Get dates, if applicable
if hasattr(self.data, 'dates') and self.data.dates is not None:
dates = self.data.dates._mpl_repr()
else:
dates = np.arange(self.nobs)
llb = self.loglikelihood_burn
# Plot cusum series and reference line
ax.plot(dates[llb:], self.cusum_squares, label='CUSUM of squares')
ref_line = (np.arange(llb, self.nobs) - llb) / (self.nobs - llb)
ax.plot(dates[llb:], ref_line, 'k', alpha=0.3)
# Plot significance bounds
lower_line, upper_line = self._cusum_squares_significance_bounds(alpha)
ax.plot([dates[llb], dates[-1]], upper_line, 'k--',
label='%d%% significance' % (alpha * 100))
ax.plot([dates[llb], dates[-1]], lower_line, 'k--')
ax.legend(loc=legend_loc)
return fig
def plot_recursive_coefficient(
self,
variables=None,
alpha=0.05,
legend_loc="upper left",
fig=None,
figsize=None,
):
r"""
Plot the recursively estimated coefficients on a given variable
Parameters
----------
variables : {int, str, Iterable[int], Iterable[str], None}, optional
Integer index or string name of the variables whose coefficients
to plot. Can also be an iterable of integers or strings. Default
plots all coefficients.
alpha : float, optional
The confidence intervals for the coefficient are (1 - alpha)%. Set
to None to exclude confidence intervals.
legend_loc : str, optional
The location of the legend in the plot. Default is upper left.
fig : Figure, optional
If given, subplots are created in this figure instead of in a new
figure. Note that the grid will be created in the provided
figure using `fig.add_subplot()`.
figsize : tuple, optional
If a figure is created, this argument allows specifying a size.
The tuple is (width, height).
Returns
-------
Figure
The matplotlib Figure object.
"""
from statsmodels.graphics.utils import _import_mpl, create_mpl_fig
if alpha is not None:
ci = self._conf_int(alpha, None)
row_labels = self.model.data.row_labels
if row_labels is None:
row_labels = np.arange(self._params.shape[0])
k_variables = self._params.shape[1]
param_names = self.model.data.param_names
if variables is None:
variable_idx = list(range(k_variables))
else:
if isinstance(variables, (int, str)):
variables = [variables]
variable_idx = []
for i in range(len(variables)):
variable = variables[i]
if variable in param_names:
variable_idx.append(param_names.index(variable))
elif isinstance(variable, int):
variable_idx.append(variable)
else:
msg = ("variable {0} is not an integer and was not found "
"in the list of variable "
"names: {1}".format(variables[i],
", ".join(param_names)))
raise ValueError(msg)
_import_mpl()
fig = create_mpl_fig(fig, figsize)
loc = 0
import pandas as pd
if isinstance(row_labels, pd.PeriodIndex):
row_labels = row_labels.to_timestamp()
row_labels = np.asarray(row_labels)
for i in variable_idx:
ax = fig.add_subplot(len(variable_idx), 1, loc + 1)
params = self._params[:, i]
valid = ~np.isnan(self._params[:, i])
row_lbl = row_labels[valid]
ax.plot(row_lbl, params[valid])
if alpha is not None:
this_ci = np.reshape(ci[:, :, i], (-1, 2))
if not np.all(np.isnan(this_ci)):
ax.plot(row_lbl,
this_ci[:, 0][valid],
"k:",
label="Lower CI")
ax.plot(row_lbl,
this_ci[:, 1][valid],
"k:",
label="Upper CI")
if loc == 0:
ax.legend(loc=legend_loc)
ax.set_xlim(row_lbl[0], row_lbl[-1])
ax.set_title(param_names[i])
loc += 1
fig.tight_layout()
return fig
def plot(
self,
observed=True,
seasonal=True,
trend=True,
resid=True,
weights=False,
):
"""
Plot estimated components
Parameters
----------
observed : bool
Include the observed series in the plot
seasonal : bool
Include the seasonal component in the plot
trend : bool
Include the trend component in the plot
resid : bool
Include the residual in the plot
weights : bool
Include the weights in the plot (if any)
Returns
-------
matplotlib.figure.Figure
The figure instance that containing the plot.
"""
from pandas.plotting import register_matplotlib_converters
from statsmodels.graphics.utils import _import_mpl
plt = _import_mpl()
register_matplotlib_converters()
series = [(self._observed, "Observed")] if observed else []
series += [(self.trend, "trend")] if trend else []
if self.seasonal.ndim == 1:
series += [(self.seasonal, "seasonal")] if seasonal else []
elif self.seasonal.ndim > 1:
if isinstance(self.seasonal, pd.DataFrame):
for col in self.seasonal.columns:
series += ([(self.seasonal[col],
"seasonal")] if seasonal else [])
else:
for i in range(self.seasonal.shape[1]):
series += ([(self.seasonal[:, i],
"seasonal")] if seasonal else [])
series += [(self.resid, "residual")] if resid else []
series += [(self.weights, "weights")] if weights else []
if isinstance(self._observed, (pd.DataFrame, pd.Series)):
nobs = self._observed.shape[0]
xlim = self._observed.index[0], self._observed.index[nobs - 1]
else:
xlim = (0, self._observed.shape[0] - 1)
fig, axs = plt.subplots(len(series), 1)
for i, (ax, (series, def_name)) in enumerate(zip(axs, series)):
if def_name != "residual":
ax.plot(series)
else:
ax.plot(series, marker="o", linestyle="none")
ax.plot(xlim, (0, 0), color="#000000", zorder=-3)
name = getattr(series, "name", def_name)
if def_name != "Observed":
name = name.capitalize()
title = ax.set_title if i == 0 and observed else ax.set_ylabel
title(name)
ax.set_xlim(xlim)
fig.tight_layout()
return fig
def plot_recursive_coefficient(self, variables=0, alpha=0.05,
legend_loc='upper left', fig=None,
figsize=None):
r"""
Plot the recursively estimated coefficients on a given variable
Parameters
----------
variables : int or str or iterable of int or string, optional
Integer index or string name of the variable whose coefficient will
be plotted. Can also be an iterable of integers or strings. Default
is the first variable.
alpha : float, optional
The confidence intervals for the coefficient are (1 - alpha) %
legend_loc : string, optional
The location of the legend in the plot. Default is upper left.
fig : Matplotlib Figure instance, optional
If given, subplots are created in this figure instead of in a new
figure. Note that the grid will be created in the provided
figure using `fig.add_subplot()`.
figsize : tuple, optional
If a figure is created, this argument allows specifying a size.
The tuple is (width, height).
Notes
-----
All plots contain (1 - `alpha`) % confidence intervals.
"""
# Get variables
if isinstance(variables, (int, str)):
variables = [variables]
k_variables = len(variables)
# If a string was given for `variable`, try to get it from exog names
exog_names = self.model.exog_names
for i in range(k_variables):
variable = variables[i]
if isinstance(variable, str):
variables[i] = exog_names.index(variable)
# Create the plot
from scipy.stats import norm
from statsmodels.graphics.utils import _import_mpl, create_mpl_fig
plt = _import_mpl()
fig = create_mpl_fig(fig, figsize)
for i in range(k_variables):
variable = variables[i]
ax = fig.add_subplot(k_variables, 1, i + 1)
# Get dates, if applicable
if hasattr(self.data, 'dates') and self.data.dates is not None:
dates = self.data.dates._mpl_repr()
else:
dates = np.arange(self.nobs)
d = max(self.nobs_diffuse, self.loglikelihood_burn)
# Plot the coefficient
coef = self.recursive_coefficients
ax.plot(dates[d:], coef.filtered[variable, d:],
label='Recursive estimates: %s' % exog_names[variable])
# Legend
handles, labels = ax.get_legend_handles_labels()
# Get the critical value for confidence intervals
if alpha is not None:
critical_value = norm.ppf(1 - alpha / 2.)
# Plot confidence intervals
std_errors = np.sqrt(coef.filtered_cov[variable, variable, :])
ci_lower = (
coef.filtered[variable] - critical_value * std_errors)
ci_upper = (
coef.filtered[variable] + critical_value * std_errors)
ci_poly = ax.fill_between(
dates[d:], ci_lower[d:], ci_upper[d:], alpha=0.2
)
ci_label = ('$%.3g \\%%$ confidence interval'
% ((1 - alpha)*100))
# Only add CI to legend for the first plot
if i == 0:
# Proxy artist for fill_between legend entry
# See https://matplotlib.org/1.3.1/users/legend_guide.html
p = plt.Rectangle((0, 0), 1, 1,
fc=ci_poly.get_facecolor()[0])
handles.append(p)
labels.append(ci_label)
ax.legend(handles, labels, loc=legend_loc)
# Remove xticks for all but the last plot
if i < k_variables - 1:
ax.xaxis.set_ticklabels([])
fig.tight_layout()
return fig
def hdrboxplot(data,
ncomp=2,
alpha=None,
threshold=0.95,
bw=None,
xdata=None,
labels=None,
ax=None,
use_brute=False,
seed=None):
"""
High Density Region boxplot
Parameters
----------
data : sequence of ndarrays or 2-D ndarray
The vectors of functions to create a functional boxplot from. If a
sequence of 1-D arrays, these should all be the same size.
The first axis is the function index, the second axis the one along
which the function is defined. So ``data[0, :]`` is the first
functional curve.
ncomp : int, optional
Number of components to use. If None, returns the as many as the
smaller of the number of rows or columns in data.
alpha : list of floats between 0 and 1, optional
Extra quantile values to compute. Default is None
threshold : float between 0 and 1, optional
Percentile threshold value for outliers detection. High value means
a lower sensitivity to outliers. Default is `0.95`.
bw: array_like or str, optional
If an array, it is a fixed user-specified bandwidth. If `None`, set to
`normal_reference`. If a string, should be one of:
- normal_reference: normal reference rule of thumb (default)
- cv_ml: cross validation maximum likelihood
- cv_ls: cross validation least squares
xdata : ndarray, optional
The independent variable for the data. If not given, it is assumed to
be an array of integers 0..N-1 with N the length of the vectors in
`data`.
labels : sequence of scalar or str, optional
The labels or identifiers of the curves in `data`. If not given,
outliers are labeled in the plot with array indices.
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
use_brute : bool
Use the brute force optimizer instead of the default differential
evolution to find the curves. Default is False.
seed : {None, int, np.random.RandomState}
Seed value to pass to scipy.optimize.differential_evolution. Can be an
integer or RandomState instance. If None, then the default RandomState
provided by np.random is used.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
hdr_res : HdrResults instance
An `HdrResults` instance with the following attributes:
- 'median', array. Median curve.
- 'hdr_50', array. 50% quantile band. [sup, inf] curves
- 'hdr_90', list of array. 90% quantile band. [sup, inf]
curves.
- 'extra_quantiles', list of array. Extra quantile band.
[sup, inf] curves.
- 'outliers', ndarray. Outlier curves.
Notes
-----
The median curve is the curve with the highest probability on the reduced
space of a Principal Component Analysis (PCA).
Outliers are defined as curves that fall outside the band corresponding
to the quantile given by `threshold`.
The non-outlying region is defined as the band made up of all the
non-outlying curves.
Behind the scene, the dataset is represented as a matrix. Each line
corresponding to a 1D curve. This matrix is then decomposed using Principal
Components Analysis (PCA). This allows to represent the data using a finite
number of modes, or components. This compression process allows to turn the
functional representation into a scalar representation of the matrix. In
other words, you can visualize each curve from its components. Each curve
is thus a point in this reduced space. With 2 components, this is called a
bivariate plot (2D plot).
In this plot, if some points are adjacent (similar components), it means
that back in the original space, the curves are similar. Then, finding the
median curve means finding the higher density region (HDR) in the reduced
space. Moreover, the more you get away from this HDR, the more the curve is
unlikely to be similar to the other curves.
Using a kernel smoothing technique, the probability density function (PDF)
of the multivariate space can be recovered. From this PDF, it is possible
to compute the density probability linked to the cluster of points and plot
its contours.
Finally, using these contours, the different quantiles can be extracted
along with the median curve and the outliers.
Steps to produce the HDR boxplot include:
1. Compute a multivariate kernel density estimation
2. Compute contour lines for quantiles 90%, 50% and `alpha` %
3. Plot the bivariate plot
4. Compute median curve along with quantiles and outliers curves.
References
----------
[1] R.J. Hyndman and H.L. Shang, "Rainbow Plots, Bagplots, and Boxplots for
Functional Data", vol. 19, pp. 29-45, 2010.
Examples
--------
Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea
surface temperature data.
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> data = sm.datasets.elnino.load(as_pandas=False)
Create a functional boxplot. We see that the years 1982-83 and 1997-98 are
outliers; these are the years where El Nino (a climate pattern
characterized by warming up of the sea surface and higher air pressures)
occurred with unusual intensity.
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> res = sm.graphics.hdrboxplot(data.raw_data[:, 1:],
... labels=data.raw_data[:, 0].astype(int),
... ax=ax)
>>> ax.set_xlabel("Month of the year")
>>> ax.set_ylabel("Sea surface temperature (C)")
>>> ax.set_xticks(np.arange(13, step=3) - 1)
>>> ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"])
>>> ax.set_xlim([-0.2, 11.2])
>>> plt.show()
.. plot:: plots/graphics_functional_hdrboxplot.py
See Also
--------
banddepth, rainbowplot, fboxplot
"""
fig, ax = utils.create_mpl_ax(ax)
if labels is None:
# For use with pandas, get the labels
if hasattr(data, 'index'):
labels = data.index
else:
labels = np.arange(len(data))
data = np.asarray(data)
if xdata is None:
xdata = np.arange(data.shape[1])
n_samples, dim = data.shape
# PCA and bivariate plot
pca = PCA(data, ncomp=ncomp)
data_r = pca.factors
# Create gaussian kernel
ks_gaussian = KDEMultivariate(data_r,
bw=bw,
var_type='c' * data_r.shape[1])
# Boundaries of the n-variate space
bounds = np.array([data_r.min(axis=0), data_r.max(axis=0)]).T
# Compute contour line of pvalue linked to a given probability level
if alpha is None:
alpha = [threshold, 0.9, 0.5]
else:
alpha.extend([threshold, 0.9, 0.5])
alpha = list(set(alpha))
alpha.sort(reverse=True)
n_quantiles = len(alpha)
pdf_r = ks_gaussian.pdf(data_r).flatten()
pvalues = [
np.percentile(pdf_r, (1 - alpha[i]) * 100, interpolation='linear')
for i in range(n_quantiles)
]
# Find mean, outliers curves
if have_de_optim and not use_brute:
median = differential_evolution(lambda x: -ks_gaussian.pdf(x),
bounds=bounds,
maxiter=5,
seed=seed).x
else:
median = brute(lambda x: -ks_gaussian.pdf(x),
ranges=bounds,
finish=fmin)
outliers_idx = np.where(pdf_r < pvalues[alpha.index(threshold)])[0]
labels_outlier = [labels[i] for i in outliers_idx]
outliers = data[outliers_idx]
# Find HDR given some quantiles
def _band_quantiles(band, use_brute=use_brute, seed=seed):
"""
Find extreme curves for a quantile band.
From the `band` of quantiles, the associated PDF extrema values
are computed. If `min_alpha` is not provided (single quantile value),
`max_pdf` is set to `1E6` in order not to constrain the problem on high
values.
An optimization is performed per component in order to find the min and
max curves. This is done by comparing the PDF value of a given curve
with the band PDF.
Parameters
----------
band : array_like
alpha values ``(max_alpha, min_alpha)`` ex: ``[0.9, 0.5]``
use_brute : bool
Use the brute force optimizer instead of the default differential
evolution to find the curves. Default is False.
seed : {None, int, np.random.RandomState}
Seed value to pass to scipy.optimize.differential_evolution. Can
be an integer or RandomState instance. If None, then the default
RandomState provided by np.random is used.
Returns
-------
band_quantiles : list of 1-D array
``(max_quantile, min_quantile)`` (2, n_features)
"""
min_pdf = pvalues[alpha.index(band[0])]
try:
max_pdf = pvalues[alpha.index(band[1])]
except IndexError:
max_pdf = 1E6
band = [min_pdf, max_pdf]
pool = Pool()
data = zip(
range(dim),
itertools.repeat(
(band, pca, bounds, ks_gaussian, seed, use_brute)))
band_quantiles = pool.map(_min_max_band, data)
pool.terminate()
pool.close()
band_quantiles = list(zip(*band_quantiles))
return band_quantiles
extra_alpha = [
i for i in alpha if 0.5 != i and 0.9 != i and threshold != i
]
if len(extra_alpha) > 0:
extra_quantiles = []
for x in extra_alpha:
for y in _band_quantiles([x], use_brute=use_brute, seed=seed):
extra_quantiles.append(y)
else:
extra_quantiles = []
# Inverse transform from n-variate plot to dataset dataset's shape
median = _inverse_transform(pca, median)[0]
hdr_90 = _band_quantiles([0.9, 0.5], use_brute=use_brute, seed=seed)
hdr_50 = _band_quantiles([0.5], use_brute=use_brute, seed=seed)
hdr_res = HdrResults({
"median": median,
"hdr_50": hdr_50,
"hdr_90": hdr_90,
"extra_quantiles": extra_quantiles,
"outliers": outliers,
"outliers_idx": outliers_idx
})
# Plots
ax.plot(np.array([xdata] * n_samples).T,
data.T,
c='c',
alpha=.1,
label=None)
ax.plot(xdata, median, c='k', label='Median')
fill_betweens = []
fill_betweens.append(
ax.fill_between(xdata,
*hdr_50,
color='gray',
alpha=.4,
label='50% HDR'))
fill_betweens.append(
ax.fill_between(xdata,
*hdr_90,
color='gray',
alpha=.3,
label='90% HDR'))
if len(extra_quantiles) != 0:
ax.plot(np.array([xdata] * len(extra_quantiles)).T,
np.array(extra_quantiles).T,
c='y',
ls='-.',
alpha=.4,
label='Extra quantiles')
if len(outliers) != 0:
for ii, outlier in enumerate(outliers):
if labels_outlier is None:
label = 'Outliers'
else:
label = str(labels_outlier[ii])
ax.plot(xdata, outlier, ls='--', alpha=0.7, label=label)
handles, labels = ax.get_legend_handles_labels()
# Proxy artist for fill_between legend entry
# See https://matplotlib.org/1.3.1/users/legend_guide.html
plt = _import_mpl()
for label, fill_between in zip(['50% HDR', '90% HDR'], fill_betweens):
p = plt.Rectangle((0, 0), 1, 1, fc=fill_between.get_facecolor()[0])
handles.append(p)
labels.append(label)
by_label = OrderedDict(zip(labels, handles))
if len(outliers) != 0:
by_label.pop('Median')
by_label.pop('50% HDR')
by_label.pop('90% HDR')
ax.legend(by_label.values(), by_label.keys(), loc='best')
return fig, hdr_res
def plot_predict(
result,
start=None,
end=None,
dynamic=False,
alpha=0.05,
ax=None,
**predict_kwargs,
):
"""
Parameters
----------
result : Result
Any model result supporting ``get_prediction``.
start : int, str, or datetime, optional
Zero-indexed observation number at which to start forecasting,
i.e., the first forecast is start. Can also be a date string to
parse or a datetime type. Default is the the zeroth observation.
end : int, str, or datetime, optional
Zero-indexed observation number at which to end forecasting, i.e.,
the last forecast is end. Can also be a date string to
parse or a datetime type. However, if the dates index does not
have a fixed frequency, end must be an integer index if you
want out of sample prediction. Default is the last observation in
the sample.
dynamic : bool, int, str, or datetime, optional
Integer offset relative to `start` at which to begin dynamic
prediction. Can also be an absolute date string to parse or a
datetime type (these are not interpreted as offsets).
Prior to this observation, true endogenous values will be used for
prediction; starting with this observation and continuing through
the end of prediction, forecasted endogenous values will be used
instead.
alpha : {float, None}
The tail probability not covered by the confidence interval. Must
be in (0, 1). Confidence interval is constructed assuming normally
distributed shocks. If None, figure will not show the confidence
interval.
ax : AxesSubplot
matplotlib Axes instance to use
**predict_kwargs
Any additional keyword arguments to pass to ``result.get_prediction``.
Returns
-------
Figure
matplotlib Figure containing the prediction plot
"""
from statsmodels.graphics.utils import _import_mpl, create_mpl_ax
_ = _import_mpl()
fig, ax = create_mpl_ax(ax)
from statsmodels.tsa.base.prediction import PredictionResults
# use predict so you set dates
pred: PredictionResults = result.get_prediction(start=start,
end=end,
dynamic=dynamic,
**predict_kwargs)
mean = pred.predicted_mean
if isinstance(mean, (pd.Series, pd.DataFrame)):
x = mean.index
mean.plot(ax=ax, label="forecast")
else:
x = np.arange(mean.shape[0])
ax.plot(x, mean)
if alpha is not None:
label = f"{1-alpha:.0%} confidence interval"
ci = pred.conf_int(alpha)
conf_int = np.asarray(ci)
ax.fill_between(
x,
conf_int[:, 0],
conf_int[:, 1],
color="gray",
alpha=0.5,
label=label,
)
ax.legend(loc="best")
return fig
def hdrboxplot(data, ncomp=2, alpha=None, threshold=0.95, bw=None,
xdata=None, labels=None, ax=None):
"""
High Density Region boxplot
Parameters
----------
data : sequence of ndarrays or 2-D ndarray
The vectors of functions to create a functional boxplot from. If a
sequence of 1-D arrays, these should all be the same size.
The first axis is the function index, the second axis the one along
which the function is defined. So ``data[0, :]`` is the first
functional curve.
ncomp : int, optional
Number of components to use. If None, returns the as many as the
smaller of the number of rows or columns in data.
alpha : list of floats between 0 and 1, optional
Extra quantile values to compute. Default is None
threshold : float between 0 and 1, optional
Percentile threshold value for outliers detection. High value means
a lower sensitivity to outliers. Default is `0.95`.
bw: array_like or str, optional
If an array, it is a fixed user-specified bandwidth. If `None`, set to
`normal_reference`. If a string, should be one of:
- normal_reference: normal reference rule of thumb (default)
- cv_ml: cross validation maximum likelihood
- cv_ls: cross validation least squares
xdata : ndarray, optional
The independent variable for the data. If not given, it is assumed to
be an array of integers 0..N-1 with N the length of the vectors in
`data`.
labels : sequence of scalar or str, optional
The labels or identifiers of the curves in `data`. If not given,
outliers are labeled in the plot with array indices.
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
hdr_res : HdrResults instance
An `HdrResults` instance with the following attributes:
- 'median', array. Median curve.
- 'hdr_50', array. 50% quantile band. [sup, inf] curves
- 'hdr_90', list of array. 90% quantile band. [sup, inf]
curves.
- 'extra_quantiles', list of array. Extra quantile band.
[sup, inf] curves.
- 'outliers', ndarray. Outlier curves.
Notes
-----
The median curve is the curve with the highest probability on the reduced
space of a Principal Component Analysis (PCA).
Outliers are defined as curves that fall outside the band corresponding
to the quantile given by `threshold`.
The non-outlying region is defined as the band made up of all the
non-outlying curves.
Behind the scene, the dataset is represented as a matrix. Each line
corresponding to a 1D curve. This matrix is then decomposed using Principal
Components Analysis (PCA). This allows to represent the data using a finite
number of modes, or components. This compression process allows to turn the
functional representation into a scalar representation of the matrix. In
other words, you can visualize each curve from its components. Each curve
is thus a point in this reduced space. With 2 components, this is called a
bivariate plot (2D plot).
In this plot, if some points are adjacent (similar components), it means
that back in the original space, the curves are similar. Then, finding the
median curve means finding the higher density region (HDR) in the reduced
space. Moreover, the more you get away from this HDR, the more the curve is
unlikely to be similar to the other curves.
Using a kernel smoothing technique, the probability density function (PDF)
of the multivariate space can be recovered. From this PDF, it is possible to
compute the density probability linked to the cluster of points and plot
its contours.
Finally, using these contours, the different quantiles can be extracted
along with the median curve and the outliers.
Steps to produce the HDR boxplot include:
1. Compute a multivariate kernel density estimation
2. Compute contour lines for quantiles 90%, 50% and `alpha` %
3. Plot the bivariate plot
4. Compute median curve along with quantiles and outliers curves.
References
----------
[1] R.J. Hyndman and H.L. Shang, "Rainbow Plots, Bagplots, and Boxplots for
Functional Data", vol. 19, pp. 29-45, 2010.
Examples
--------
Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea
surface temperature data.
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> data = sm.datasets.elnino.load(as_pandas=False)
Create a functional boxplot. We see that the years 1982-83 and 1997-98 are
outliers; these are the years where El Nino (a climate pattern
characterized by warming up of the sea surface and higher air pressures)
occurred with unusual intensity.
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> res = sm.graphics.hdrboxplot(data.raw_data[:, 1:],
... labels=data.raw_data[:, 0].astype(int),
... ax=ax)
>>> ax.set_xlabel("Month of the year")
>>> ax.set_ylabel("Sea surface temperature (C)")
>>> ax.set_xticks(np.arange(13, step=3) - 1)
>>> ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"])
>>> ax.set_xlim([-0.2, 11.2])
>>> plt.show()
.. plot:: plots/graphics_functional_hdrboxplot.py
See Also
--------
banddepth, rainbowplot, fboxplot
"""
fig, ax = utils.create_mpl_ax(ax)
if labels is None:
# For use with pandas, get the labels
if hasattr(data, 'index'):
labels = data.index
else:
labels = np.arange(len(data))
data = np.asarray(data)
if xdata is None:
xdata = np.arange(data.shape[1])
n_samples, dim = data.shape
# PCA and bivariate plot
pca = PCA(data, ncomp=ncomp)
data_r = pca.factors
# Create gaussian kernel
ks_gaussian = KDEMultivariate(data_r, bw=bw,
var_type='c' * data_r.shape[1])
# Boundaries of the n-variate space
bounds = np.array([data_r.min(axis=0), data_r.max(axis=0)]).T
# Compute contour line of pvalue linked to a given probability level
if alpha is None:
alpha = [threshold, 0.9, 0.5]
else:
alpha.extend([threshold, 0.9, 0.5])
alpha = list(set(alpha))
alpha.sort(reverse=True)
n_quantiles = len(alpha)
pdf_r = ks_gaussian.pdf(data_r).flatten()
pvalues = [np.percentile(pdf_r, (1 - alpha[i]) * 100,
interpolation='linear')
for i in range(n_quantiles)]
# Find mean, outliers curves
if have_de_optim:
median = differential_evolution(lambda x: - ks_gaussian.pdf(x),
bounds=bounds, maxiter=5).x
else:
median = brute(lambda x: - ks_gaussian.pdf(x),
ranges=bounds, finish=fmin)
outliers_idx = np.where(pdf_r < pvalues[alpha.index(threshold)])[0]
labels_outlier = [labels[i] for i in outliers_idx]
outliers = data[outliers_idx]
# Find HDR given some quantiles
def _band_quantiles(band):
"""Find extreme curves for a quantile band.
From the `band` of quantiles, the associated PDF extrema values
are computed. If `min_alpha` is not provided (single quantile value),
`max_pdf` is set to `1E6` in order not to constrain the problem on high
values.
An optimization is performed per component in order to find the min and
max curves. This is done by comparing the PDF value of a given curve
with the band PDF.
Parameters
----------
band : array_like
alpha values ``(max_alpha, min_alpha)`` ex: ``[0.9, 0.5]``
Returns
-------
band_quantiles : list of 1-D array
``(max_quantile, min_quantile)`` (2, n_features)
"""
min_pdf = pvalues[alpha.index(band[0])]
try:
max_pdf = pvalues[alpha.index(band[1])]
except IndexError:
max_pdf = 1E6
band = [min_pdf, max_pdf]
pool = Pool()
data = zip(range(dim), itertools.repeat((band, pca,
bounds, ks_gaussian)))
band_quantiles = pool.map(_min_max_band, data)
pool.terminate()
pool.close()
band_quantiles = list(zip(*band_quantiles))
return band_quantiles
extra_alpha = [i for i in alpha
if 0.5 != i and 0.9 != i and threshold != i]
if extra_alpha != []:
extra_quantiles = [y for x in extra_alpha
for y in _band_quantiles([x])]
else:
extra_quantiles = []
# Inverse transform from n-variate plot to dataset dataset's shape
median = _inverse_transform(pca, median)[0]
hdr_90 = _band_quantiles([0.9, 0.5])
hdr_50 = _band_quantiles([0.5])
hdr_res = HdrResults({
"median": median,
"hdr_50": hdr_50,
"hdr_90": hdr_90,
"extra_quantiles": extra_quantiles,
"outliers": outliers,
"outliers_idx": outliers_idx
})
# Plots
ax.plot(np.array([xdata] * n_samples).T, data.T,
c='c', alpha=.1, label=None)
ax.plot(xdata, median, c='k', label='Median')
fill_betweens = []
fill_betweens.append(ax.fill_between(xdata, *hdr_50, color='gray',
alpha=.4, label='50% HDR'))
fill_betweens.append(ax.fill_between(xdata, *hdr_90, color='gray',
alpha=.3, label='90% HDR'))
if len(extra_quantiles) != 0:
ax.plot(np.array([xdata] * len(extra_quantiles)).T,
np.array(extra_quantiles).T,
c='y', ls='-.', alpha=.4, label='Extra quantiles')
if len(outliers) != 0:
for ii, outlier in enumerate(outliers):
label = str(labels_outlier[ii]) if labels_outlier is not None else 'Outliers'
ax.plot(xdata, outlier,
ls='--', alpha=0.7, label=label)
handles, labels = ax.get_legend_handles_labels()
# Proxy artist for fill_between legend entry
# See http://matplotlib.org/1.3.1/users/legend_guide.html
plt = _import_mpl()
for label, fill_between in zip(['50% HDR', '90% HDR'], fill_betweens):
p = plt.Rectangle((0, 0), 1, 1,
fc=fill_between.get_facecolor()[0])
handles.append(p)
labels.append(label)
by_label = OrderedDict(zip(labels, handles))
if len(outliers) != 0:
by_label.pop('Median')
by_label.pop('50% HDR')
by_label.pop('90% HDR')
ax.legend(by_label.values(), by_label.keys(), loc='best')
return fig, hdr_res
def plot_predict(
self,
steps: int = 1,
theta: float = 2,
alpha: Optional[float] = 0.05,
in_sample: bool = False,
fig: Optional["matplotlib.figure.Figure"] = None,
figsize: Tuple[float, float] = None,
) -> "matplotlib.figure.Figure":
r"""
Plot forecasts, prediction intervals and in-sample values
Parameters
----------
steps : int, default 1
The number of steps ahead to compute the forecast components.
theta : float, default 2
The theta value to use when computing the weight to combine
the trend and the SES forecasts.
alpha : {float, None}, default 0.05
The tail probability not covered by the confidence interval. Must
be in (0, 1). Confidence interval is constructed assuming normally
distributed shocks. If None, figure will not show the confidence
interval.
in_sample : bool, default False
Flag indicating whether to include the in-sample period in the
plot.
fig : Figure, default None
An existing figure handle. If not provided, a new figure is
created.
figsize: tuple[float, float], default None
Tuple containing the figure size.
Returns
-------
Figure
Figure handle containing the plot.
Notes
-----
The variance of the h-step forecast is assumed to follow from the
integrated Moving Average structure of the Theta model, and so is
:math:`\sigma^2(\alpha^2 + (h-1))`. The prediction interval assumes
that innovations are normally distributed.
"""
from statsmodels.graphics.utils import _import_mpl, create_mpl_fig
_import_mpl()
fig = create_mpl_fig(fig, figsize)
assert fig is not None
predictions = self.forecast(steps, theta)
pred_index = predictions.index
ax = fig.add_subplot(111)
nobs = self.model.endog_orig.shape[0]
index = NumericIndex(np.arange(nobs))
if in_sample:
if isinstance(self.model.endog_orig, pd.Series):
index = self.model.endog_orig.index
ax.plot(index, self.model.endog_orig)
ax.plot(pred_index, predictions)
if alpha is not None:
pi = self.prediction_intervals(steps, theta, alpha)
label = "{0:.0%} confidence interval".format(1 - alpha)
ax.fill_between(
pred_index,
pi["lower"],
pi["upper"],
color="gray",
alpha=0.5,
label=label,
)
ax.legend(loc="best", frameon=False)
fig.tight_layout(pad=1.0)
return fig
def plot_cusum_squares(self,
alpha=0.05,
legend_loc='upper left',
fig=None,
figsize=None):
r"""
Plot the CUSUM of squares statistic and significance bounds.
Parameters
----------
alpha : float, optional
The plotted significance bounds are alpha %.
legend_loc : string, optional
The location of the legend in the plot. Default is upper left.
fig : Matplotlib Figure instance, optional
If given, subplots are created in this figure instead of in a new
figure. Note that the grid will be created in the provided
figure using `fig.add_subplot()`.
figsize : tuple, optional
If a figure is created, this argument allows specifying a size.
The tuple is (width, height).
Notes
-----
Evidence of parameter instability may be found if the CUSUM of squares
statistic moves out of the significance bounds.
Critical values used in creating the significance bounds are computed
using the approximate formula of [2]_.
References
----------
.. [1] Brown, R. L., J. Durbin, and J. M. Evans. 1975.
"Techniques for Testing the Constancy of
Regression Relationships over Time."
Journal of the Royal Statistical Society.
Series B (Methodological) 37 (2): 149-92.
.. [2] Edgerton, David, and Curt Wells. 1994.
"Critical Values for the Cusumsq Statistic
in Medium and Large Sized Samples."
Oxford Bulletin of Economics and Statistics 56 (3): 355-65.
"""
# Create the plot
from statsmodels.graphics.utils import _import_mpl, create_mpl_fig
plt = _import_mpl()
fig = create_mpl_fig(fig, figsize)
ax = fig.add_subplot(1, 1, 1)
# Get dates, if applicable
if hasattr(self.data, 'dates') and self.data.dates is not None:
dates = self.data.dates._mpl_repr()
else:
dates = np.arange(self.nobs)
llb = self.loglikelihood_burn
# Plot cusum series and reference line
ax.plot(dates[llb:], self.cusum_squares, label='CUSUM of squares')
ref_line = (np.arange(llb, self.nobs) - llb) / (self.nobs - llb)
ax.plot(dates[llb:], ref_line, 'k', alpha=0.3)
# Plot significance bounds
lower_line, upper_line = self._cusum_squares_significance_bounds(alpha)
ax.plot([dates[llb], dates[-1]],
upper_line,
'k--',
label='%d%% significance' % (alpha * 100))
ax.plot([dates[llb], dates[-1]], lower_line, 'k--')
ax.legend(loc=legend_loc)
return fig
def plot_diagnostics(residuals,
variable=0,
lags=40,
fig=None,
figsize=(15, 7),
savefig=False,
path=None):
_import_mpl()
fig = create_mpl_fig(fig, figsize)
# # Eliminate residuals associated with burned or diffuse likelihoods
# d = np.maximum(self.loglikelihood_burn, self.nobs_diffuse)
# resid = self.filter_results.standardized_forecasts_error[variable, d:]
# loglikelihood_burn: the number of observations during which the likelihood is not evaluated.
# Standardize residual
# Source: https://alkaline-ml.com/pmdarima/1.1.1/_modules/pmdarima/arima/arima.html
resid = residuals
resid = (resid - np.nanmean(resid)) / np.nanstd(resid)
# Top-left: residuals vs time
ax = fig.add_subplot(221)
# if hasattr(self.data, 'dates') and self.data.dates is not None:
# x = self.data.dates[d:]._mpl_repr()
# else:
# x = np.arange(len(resid))
x = np.arange(len(resid))
ax.plot(x, resid)
ax.hlines(0, x[0], x[-1], alpha=0.5)
ax.set_xlim(x[0], x[-1])
ax.set_title('Standardized residual')
# Top-right: histogram, Gaussian kernel density, Normal density
# Can only do histogram and Gaussian kernel density on the non-null
# elements
resid_nonmissing = resid[~(np.isnan(resid))]
ax = fig.add_subplot(222)
# gh5792: Remove except after support for matplotlib>2.1 required
try:
ax.hist(resid_nonmissing, density=True, label='Hist')
except AttributeError:
ax.hist(resid_nonmissing, normed=True, label='Hist')
from scipy.stats import gaussian_kde, norm
kde = gaussian_kde(resid_nonmissing)
xlim = (-1.96 * 2, 1.96 * 2)
x = np.linspace(xlim[0], xlim[1])
ax.plot(x, kde(x), label='KDE')
ax.plot(x, norm.pdf(x), label='N(0,1)')
ax.set_xlim(xlim)
ax.legend()
ax.set_title('Histogram plus estimated density')
# Bottom-left: QQ plot
ax = fig.add_subplot(223)
from statsmodels.graphics.gofplots import qqplot
qqplot(resid_nonmissing, line='s', ax=ax)
ax.set_title('Normal Q-Q')
# Bottom-right: Correlogram
ax = fig.add_subplot(224)
from statsmodels.graphics.tsaplots import plot_pacf
plot_pacf(resid, ax=ax, lags=lags)
ax.set_title('Partial Autocorrelation function')
ax.set_ylim(-0.1, 0.1)
if savefig == True:
fig.suptitle('Residual diagnostic', fontsize=20)
fig.savefig(path, dpi=500)
fig.show()
return fig
def plot_recursive_coefficient(self, variables=0, alpha=0.05,
legend_loc='upper left', fig=None,
figsize=None):
r"""
Plot the recursively estimated coefficients on a given variable
Parameters
----------
variables : int or str or iterable of int or string, optional
Integer index or string name of the variable whose coefficient will
be plotted. Can also be an iterable of integers or strings. Default
is the first variable.
alpha : float, optional
The confidence intervals for the coefficient are (1 - alpha) %
legend_loc : string, optional
The location of the legend in the plot. Default is upper left.
fig : Matplotlib Figure instance, optional
If given, subplots are created in this figure instead of in a new
figure. Note that the grid will be created in the provided
figure using `fig.add_subplot()`.
figsize : tuple, optional
If a figure is created, this argument allows specifying a size.
The tuple is (width, height).
Notes
-----
All plots contain (1 - `alpha`) % confidence intervals.
"""
# Get variables
if isinstance(variables, (int, str)):
variables = [variables]
k_variables = len(variables)
# If a string was given for `variable`, try to get it from exog names
exog_names = self.model.exog_names
for i in range(k_variables):
variable = variables[i]
if isinstance(variable, str):
variables[i] = exog_names.index(variable)
# Create the plot
from scipy.stats import norm
from statsmodels.graphics.utils import _import_mpl, create_mpl_fig
plt = _import_mpl()
fig = create_mpl_fig(fig, figsize)
for i in range(k_variables):
variable = variables[i]
ax = fig.add_subplot(k_variables, 1, i + 1)
# Get dates, if applicable
if hasattr(self.data, 'dates') and self.data.dates is not None:
dates = self.data.dates._mpl_repr()
else:
dates = np.arange(self.nobs)
d = max(self.nobs_diffuse, self.loglikelihood_burn)
# Plot the coefficient
coef = self.recursive_coefficients
ax.plot(dates[d:], coef.filtered[variable, d:],
label='Recursive estimates: %s' % exog_names[variable])
# Legend
handles, labels = ax.get_legend_handles_labels()
# Get the critical value for confidence intervals
if alpha is not None:
critical_value = norm.ppf(1 - alpha / 2.)
# Plot confidence intervals
std_errors = np.sqrt(coef.filtered_cov[variable, variable, :])
ci_lower = (
coef.filtered[variable] - critical_value * std_errors)
ci_upper = (
coef.filtered[variable] + critical_value * std_errors)
ci_poly = ax.fill_between(
dates[d:], ci_lower[d:], ci_upper[d:], alpha=0.2
)
ci_label = ('$%.3g \\%%$ confidence interval'
% ((1 - alpha)*100))
# Only add CI to legend for the first plot
if i == 0:
# Proxy artist for fill_between legend entry
# See http://matplotlib.org/1.3.1/users/legend_guide.html
p = plt.Rectangle((0, 0), 1, 1,
fc=ci_poly.get_facecolor()[0])
handles.append(p)
labels.append(ci_label)
ax.legend(handles, labels, loc=legend_loc)
# Remove xticks for all but the last plot
if i < k_variables - 1:
ax.xaxis.set_ticklabels([])
fig.tight_layout()
return fig
