Source code for statsmodels.graphics.tsaplots

"""Correlation plot functions."""

from statsmodels.compat.pandas import deprecate_kwarg

import numpy as np
import pandas as pd

from statsmodels.graphics import utils
from statsmodels.tsa.stattools import acf, pacf


def _prepare_data_corr_plot(x, lags, zero):
    zero = bool(zero)
    irregular = False if zero else True
    if lags is None:
        # GH 4663 - use a sensible default value
        nobs = x.shape[0]
        lim = min(int(np.ceil(10 * np.log10(nobs))), nobs - 1)
        lags = np.arange(not zero, lim + 1)
    elif np.isscalar(lags):
        lags = np.arange(not zero, int(lags) + 1)  # +1 for zero lag
    else:
        irregular = True
        lags = np.asanyarray(lags).astype(int)
    nlags = lags.max(0)

    return lags, nlags, irregular


def _plot_corr(
    ax,
    title,
    acf_x,
    confint,
    lags,
    irregular,
    use_vlines,
    vlines_kwargs,
    auto_ylims=False,
    **kwargs,
):
    if irregular:
        acf_x = acf_x[lags]
        if confint is not None:
            confint = confint[lags]

    if use_vlines:
        ax.vlines(lags, [0], acf_x, **vlines_kwargs)
        ax.axhline(**kwargs)

    kwargs.setdefault("marker", "o")
    kwargs.setdefault("markersize", 5)
    if "ls" not in kwargs:
        # gh-2369
        kwargs.setdefault("linestyle", "None")
    ax.margins(0.05)
    ax.plot(lags, acf_x, **kwargs)
    ax.set_title(title)

    ax.set_ylim(-1, 1)
    if auto_ylims:
        ax.set_ylim(1.25*np.minimum(min(acf_x), min(confint[:, 0] - acf_x)),
                    1.25*np.maximum(max(acf_x), max(confint[:, 1] - acf_x)))

    if confint is not None:
        if lags[0] == 0:
            lags = lags[1:]
            confint = confint[1:]
            acf_x = acf_x[1:]
        lags = lags.astype(float)
        lags[0] -= 0.5
        lags[-1] += 0.5
        ax.fill_between(
            lags, confint[:, 0] - acf_x, confint[:, 1] - acf_x, alpha=0.25
        )


[docs]@deprecate_kwarg("unbiased", "adjusted") def plot_acf( x, ax=None, lags=None, *, alpha=0.05, use_vlines=True, adjusted=False, fft=False, missing="none", title="Autocorrelation", zero=True, auto_ylims=False, bartlett_confint=True, vlines_kwargs=None, **kwargs, ): """ Plot the autocorrelation function Plots lags on the horizontal and the correlations on vertical axis. Parameters ---------- x : array_like Array of time-series values ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. lags : {int, array_like}, optional An int or array of lag values, used on horizontal axis. Uses np.arange(lags) when lags is an int. If not provided, ``lags=np.arange(len(corr))`` is used. alpha : scalar, optional If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to Bartlett's formula. If None, no confidence intervals are plotted. use_vlines : bool, optional If True, vertical lines and markers are plotted. If False, only markers are plotted. The default marker is 'o'; it can be overridden with a ``marker`` kwarg. adjusted : bool If True, then denominators for autocovariance are n-k, otherwise n fft : bool, optional If True, computes the ACF via FFT. missing : str, optional A string in ['none', 'raise', 'conservative', 'drop'] specifying how the NaNs are to be treated. title : str, optional Title to place on plot. Default is 'Autocorrelation' zero : bool, optional Flag indicating whether to include the 0-lag autocorrelation. Default is True. auto_ylims : bool, optional If True, adjusts automatically the y-axis limits to ACF values. bartlett_confint : bool, default True Confidence intervals for ACF values are generally placed at 2 standard errors around r_k. The formula used for standard error depends upon the situation. If the autocorrelations are being used to test for randomness of residuals as part of the ARIMA routine, the standard errors are determined assuming the residuals are white noise. The approximate formula for any lag is that standard error of each r_k = 1/sqrt(N). See section 9.4 of [1] for more details on the 1/sqrt(N) result. For more elementary discussion, see section 5.3.2 in [2]. For the ACF of raw data, the standard error at a lag k is found as if the right model was an MA(k-1). This allows the possible interpretation that if all autocorrelations past a certain lag are within the limits, the model might be an MA of order defined by the last significant autocorrelation. In this case, a moving average model is assumed for the data and the standard errors for the confidence intervals should be generated using Bartlett's formula. For more details on Bartlett formula result, see section 7.2 in [1]. vlines_kwargs : dict, optional Optional dictionary of keyword arguments that are passed to vlines. **kwargs : kwargs, optional Optional keyword arguments that are directly passed on to the Matplotlib ``plot`` and ``axhline`` functions. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- matplotlib.pyplot.xcorr matplotlib.pyplot.acorr Notes ----- Adapted from matplotlib's `xcorr`. Data are plotted as ``plot(lags, corr, **kwargs)`` kwargs is used to pass matplotlib optional arguments to both the line tracing the autocorrelations and for the horizontal line at 0. These options must be valid for a Line2D object. vlines_kwargs is used to pass additional optional arguments to the vertical lines connecting each autocorrelation to the axis. These options must be valid for a LineCollection object. References ---------- [1] Brockwell and Davis, 1987. Time Series Theory and Methods [2] Brockwell and Davis, 2010. Introduction to Time Series and Forecasting, 2nd edition. Examples -------- >>> import pandas as pd >>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm >>> dta = sm.datasets.sunspots.load_pandas().data >>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008')) >>> del dta["YEAR"] >>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40) >>> plt.show() .. plot:: plots/graphics_tsa_plot_acf.py """ fig, ax = utils.create_mpl_ax(ax) lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero) vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs confint = None # acf has different return type based on alpha acf_x = acf( x, nlags=nlags, alpha=alpha, fft=fft, bartlett_confint=bartlett_confint, adjusted=adjusted, missing=missing, ) if alpha is not None: acf_x, confint = acf_x _plot_corr( ax, title, acf_x, confint, lags, irregular, use_vlines, vlines_kwargs, auto_ylims=auto_ylims, **kwargs, ) return fig
[docs]def plot_pacf( x, ax=None, lags=None, alpha=0.05, method="ywadjusted", use_vlines=True, title="Partial Autocorrelation", zero=True, vlines_kwargs=None, **kwargs, ): """ Plot the partial autocorrelation function Parameters ---------- x : array_like Array of time-series values ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. lags : {int, array_like}, optional An int or array of lag values, used on horizontal axis. Uses np.arange(lags) when lags is an int. If not provided, ``lags=np.arange(len(corr))`` is used. alpha : float, optional If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to 1/sqrt(len(x)) method : {'ywunbiased', 'ywmle', 'ols'} Specifies which method for the calculations to use: - yw or ywunbiased : yule walker with bias correction in denominator for acovf. Default. - ywm or ywmle : yule walker without bias correction - ols - regression of time series on lags of it and on constant - ld or ldunbiased : Levinson-Durbin recursion with bias correction - ldb or ldbiased : Levinson-Durbin recursion without bias correction use_vlines : bool, optional If True, vertical lines and markers are plotted. If False, only markers are plotted. The default marker is 'o'; it can be overridden with a ``marker`` kwarg. title : str, optional Title to place on plot. Default is 'Partial Autocorrelation' zero : bool, optional Flag indicating whether to include the 0-lag autocorrelation. Default is True. vlines_kwargs : dict, optional Optional dictionary of keyword arguments that are passed to vlines. **kwargs : kwargs, optional Optional keyword arguments that are directly passed on to the Matplotlib ``plot`` and ``axhline`` functions. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- matplotlib.pyplot.xcorr matplotlib.pyplot.acorr Notes ----- Plots lags on the horizontal and the correlations on vertical axis. Adapted from matplotlib's `xcorr`. Data are plotted as ``plot(lags, corr, **kwargs)`` kwargs is used to pass matplotlib optional arguments to both the line tracing the autocorrelations and for the horizontal line at 0. These options must be valid for a Line2D object. vlines_kwargs is used to pass additional optional arguments to the vertical lines connecting each autocorrelation to the axis. These options must be valid for a LineCollection object. Examples -------- >>> import pandas as pd >>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm >>> dta = sm.datasets.sunspots.load_pandas().data >>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008')) >>> del dta["YEAR"] >>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40) >>> plt.show() .. plot:: plots/graphics_tsa_plot_pacf.py """ fig, ax = utils.create_mpl_ax(ax) vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero) confint = None if alpha is None: acf_x = pacf(x, nlags=nlags, alpha=alpha, method=method) else: acf_x, confint = pacf(x, nlags=nlags, alpha=alpha, method=method) _plot_corr( ax, title, acf_x, confint, lags, irregular, use_vlines, vlines_kwargs, **kwargs, ) return fig
def seasonal_plot(grouped_x, xticklabels, ylabel=None, ax=None): """ Consider using one of month_plot or quarter_plot unless you need irregular plotting. Parameters ---------- grouped_x : iterable of DataFrames Should be a GroupBy object (or similar pair of group_names and groups as DataFrames) with a DatetimeIndex or PeriodIndex xticklabels : list of str List of season labels, one for each group. ylabel : str Lable for y axis ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. """ fig, ax = utils.create_mpl_ax(ax) start = 0 ticks = [] for season, df in grouped_x: df = df.copy() # or sort balks for series. may be better way df.sort_index() nobs = len(df) x_plot = np.arange(start, start + nobs) ticks.append(x_plot.mean()) ax.plot(x_plot, df.values, "k") ax.hlines( df.values.mean(), x_plot[0], x_plot[-1], colors="r", linewidth=3 ) start += nobs ax.set_xticks(ticks) ax.set_xticklabels(xticklabels) ax.set_ylabel(ylabel) ax.margins(0.1, 0.05) return fig
[docs]def month_plot(x, dates=None, ylabel=None, ax=None): """ Seasonal plot of monthly data. Parameters ---------- x : array_like Seasonal data to plot. If dates is None, x must be a pandas object with a PeriodIndex or DatetimeIndex with a monthly frequency. dates : array_like, optional If `x` is not a pandas object, then dates must be supplied. ylabel : str, optional The label for the y-axis. Will attempt to use the `name` attribute of the Series. ax : Axes, optional Existing axes instance. Returns ------- Figure If `ax` is provided, the Figure instance attached to `ax`. Otherwise a new Figure instance. Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.elnino.load_pandas().data >>> dta['YEAR'] = dta.YEAR.astype(int).astype(str) >>> dta = dta.set_index('YEAR').T.unstack() >>> dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1', ... dta.index.values))) >>> dta.index = pd.DatetimeIndex(dates, freq='MS') >>> fig = sm.graphics.tsa.month_plot(dta) .. plot:: plots/graphics_tsa_month_plot.py """ if dates is None: from statsmodels.tools.data import _check_period_index _check_period_index(x, freq="M") else: x = pd.Series(x, index=pd.PeriodIndex(dates, freq="M")) xticklabels = ["j", "f", "m", "a", "m", "j", "j", "a", "s", "o", "n", "d"] return seasonal_plot( x.groupby(lambda y: y.month), xticklabels, ylabel=ylabel, ax=ax )
[docs]def quarter_plot(x, dates=None, ylabel=None, ax=None): """ Seasonal plot of quarterly data Parameters ---------- x : array_like Seasonal data to plot. If dates is None, x must be a pandas object with a PeriodIndex or DatetimeIndex with a monthly frequency. dates : array_like, optional If `x` is not a pandas object, then dates must be supplied. ylabel : str, optional The label for the y-axis. Will attempt to use the `name` attribute of the Series. ax : matplotlib.axes, optional Existing axes instance. Returns ------- Figure If `ax` is provided, the Figure instance attached to `ax`. Otherwise a new Figure instance. Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.elnino.load_pandas().data >>> dta['YEAR'] = dta.YEAR.astype(int).astype(str) >>> dta = dta.set_index('YEAR').T.unstack() >>> dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1', ... dta.index.values))) >>> dta.index = dates.to_period('Q') >>> fig = sm.graphics.tsa.quarter_plot(dta) .. plot:: plots/graphics_tsa_quarter_plot.py """ if dates is None: from statsmodels.tools.data import _check_period_index _check_period_index(x, freq="Q") else: x = pd.Series(x, index=pd.PeriodIndex(dates, freq="Q")) xticklabels = ["q1", "q2", "q3", "q4"] return seasonal_plot( x.groupby(lambda y: y.quarter), xticklabels, ylabel=ylabel, ax=ax )
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