Source code for statsmodels.tsa.seasonal

"""
Seasonal Decomposition by Moving Averages
"""
from statsmodels.compat.pandas import deprecate_kwarg

import numpy as np
import pandas as pd
from pandas.core.nanops import nanmean as pd_nanmean

from statsmodels.tools.validation import PandasWrapper, array_like
from statsmodels.tsa._stl import STL
from statsmodels.tsa.filters.filtertools import convolution_filter
from statsmodels.tsa.tsatools import freq_to_period

__all__ = ['STL', 'seasonal_decompose', 'seasonal_mean', 'DecomposeResult']


def _extrapolate_trend(trend, npoints):
    """
    Replace nan values on trend's end-points with least-squares extrapolated
    values with regression considering npoints closest defined points.
    """
    front = next(i for i, vals in enumerate(trend)
                 if not np.any(np.isnan(vals)))
    back = trend.shape[0] - 1 - next(i for i, vals in enumerate(trend[::-1])
                                     if not np.any(np.isnan(vals)))
    front_last = min(front + npoints, back)
    back_first = max(front, back - npoints)

    k, n = np.linalg.lstsq(
        np.c_[np.arange(front, front_last), np.ones(front_last - front)],
        trend[front:front_last], rcond=-1)[0]
    extra = (np.arange(0, front) * np.c_[k] + np.c_[n]).T
    if trend.ndim == 1:
        extra = extra.squeeze()
    trend[:front] = extra

    k, n = np.linalg.lstsq(
        np.c_[np.arange(back_first, back), np.ones(back - back_first)],
        trend[back_first:back], rcond=-1)[0]
    extra = (np.arange(back + 1, trend.shape[0]) * np.c_[k] + np.c_[n]).T
    if trend.ndim == 1:
        extra = extra.squeeze()
    trend[back + 1:] = extra

    return trend


@deprecate_kwarg('freq', 'period')
def seasonal_mean(x, period):
    """
    Return means for each period in x. period is an int that gives the
    number of periods per cycle. E.g., 12 for monthly. NaNs are ignored
    in the mean.
    """
    return np.array([pd_nanmean(x[i::period], axis=0) for i in range(period)])


[docs]@deprecate_kwarg('freq', 'period') def seasonal_decompose(x, model="additive", filt=None, period=None, two_sided=True, extrapolate_trend=0): """ Seasonal decomposition using moving averages. Parameters ---------- x : array_like Time series. If 2d, individual series are in columns. x must contain 2 complete cycles. model : {"additive", "multiplicative"}, optional Type of seasonal component. Abbreviations are accepted. filt : array_like, optional The filter coefficients for filtering out the seasonal component. The concrete moving average method used in filtering is determined by two_sided. period : int, optional Period of the series. Must be used if x is not a pandas object or if the index of x does not have a frequency. Overrides default periodicity of x if x is a pandas object with a timeseries index. two_sided : bool, optional The moving average method used in filtering. If True (default), a centered moving average is computed using the filt. If False, the filter coefficients are for past values only. extrapolate_trend : int or 'freq', optional If set to > 0, the trend resulting from the convolution is linear least-squares extrapolated on both ends (or the single one if two_sided is False) considering this many (+1) closest points. If set to 'freq', use `freq` closest points. Setting this parameter results in no NaN values in trend or resid components. Returns ------- DecomposeResult A object with seasonal, trend, and resid attributes. See Also -------- statsmodels.tsa.filters.bk_filter.bkfilter Baxter-King filter. statsmodels.tsa.filters.cf_filter.cffilter Christiano-Fitzgerald asymmetric, random walk filter. statsmodels.tsa.filters.hp_filter.hpfilter Hodrick-Prescott filter. statsmodels.tsa.filters.convolution_filter Linear filtering via convolution. statsmodels.tsa.seasonal.STL Season-Trend decomposition using LOESS. Notes ----- This is a naive decomposition. More sophisticated methods should be preferred. The additive model is Y[t] = T[t] + S[t] + e[t] The multiplicative model is Y[t] = T[t] * S[t] * e[t] The seasonal component is first removed by applying a convolution filter to the data. The average of this smoothed series for each period is the returned seasonal component. """ pfreq = period pw = PandasWrapper(x) if period is None: pfreq = getattr(getattr(x, 'index', None), 'inferred_freq', None) x = array_like(x, 'x', maxdim=2) nobs = len(x) if not np.all(np.isfinite(x)): raise ValueError("This function does not handle missing values") if model.startswith('m'): if np.any(x <= 0): raise ValueError("Multiplicative seasonality is not appropriate " "for zero and negative values") if period is None: if pfreq is not None: pfreq = freq_to_period(pfreq) period = pfreq else: raise ValueError("You must specify a period or x must be a " "pandas object with a DatetimeIndex with " "a freq not set to None") if x.shape[0] < 2 * pfreq: raise ValueError('x must have 2 complete cycles requires {0} ' 'observations. x only has {1} ' 'observation(s)'.format(2 * pfreq, x.shape[0])) if filt is None: if period % 2 == 0: # split weights at ends filt = np.array([.5] + [1] * (period - 1) + [.5]) / period else: filt = np.repeat(1. / period, period) nsides = int(two_sided) + 1 trend = convolution_filter(x, filt, nsides) if extrapolate_trend == 'freq': extrapolate_trend = period - 1 if extrapolate_trend > 0: trend = _extrapolate_trend(trend, extrapolate_trend + 1) if model.startswith('m'): detrended = x / trend else: detrended = x - trend period_averages = seasonal_mean(detrended, period) if model.startswith('m'): period_averages /= np.mean(period_averages, axis=0) else: period_averages -= np.mean(period_averages, axis=0) seasonal = np.tile(period_averages.T, nobs // period + 1).T[:nobs] if model.startswith('m'): resid = x / seasonal / trend else: resid = detrended - seasonal results = [] for s, name in zip((seasonal, trend, resid, x), ('seasonal', 'trend', 'resid', None)): results.append(pw.wrap(s.squeeze(), columns=name)) return DecomposeResult(seasonal=results[0], trend=results[1], resid=results[2], observed=results[3])
[docs]class DecomposeResult(object): """ Results class for seasonal decompositions Parameters ---------- observed : array_like The data series that has been decomposed. seasonal : array_like The seasonal component of the data series. trend : array_like The trend component of the data series. resid : array_like The residual component of the data series. weights : array_like, optional The weights used to reduce outlier influence. """ def __init__(self, observed, seasonal, trend, resid, weights=None): self._seasonal = seasonal self._trend = trend if weights is None: weights = np.ones_like(observed) if isinstance(observed, pd.Series): weights = pd.Series(weights, index=observed.index, name='weights') self._weights = weights self._resid = resid self._observed = observed @property def observed(self): """Observed data""" return self._observed @property def seasonal(self): """The estimated seasonal component""" return self._seasonal @property def trend(self): """The estimated trend component""" return self._trend @property def resid(self): """The estimated residuals""" return self._resid @property def weights(self): """The weights used in the robust estimation""" return self._weights @property def nobs(self): """Number of observations""" return self._observed.shape
[docs] 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