/statsmodels/tsa/seasonal.py

"""
Seasonal Decomposition by Moving Averages
"""
from statsmodels.compat.python import lmap, range, iteritems
import numpy as np
from pandas.core.nanops import nanmean as pd_nanmean
from .filters._utils import _maybe_get_pandas_wrapper_freq
from .filters.filtertools import convolution_filter
from statsmodels.tsa.tsatools import freq_to_period


def seasonal_mean(x, freq):
    """
    Return means for each period in x. freq 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::freq]) for i in range(freq)])


def seasonal_decompose(x, model="additive", filt=None, freq=None):
    """
    Parameters
    ----------
    x : array-like
        Time series
    model : str {"additive", "multiplicative"}
        Type of seasonal component. Abbreviations are accepted.
    filt : array-like
        The filter coefficients for filtering out the seasonal component.
        The default is a symmetric moving average.
    freq : int, optional
        Frequency of the series. Must be used if x is not a pandas
        object with a timeseries index.

    Returns
    -------
    results : obj
        A object with seasonal, trend, and resid attributes.

    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.

    See Also
    --------
    statsmodels.tsa.filters.convolution_filter
    """
    _pandas_wrapper, pfreq = _maybe_get_pandas_wrapper_freq(x)
    x = np.asanyarray(x).squeeze()
    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 pfreq is not None:
        pfreq = freq_to_period(pfreq)
        if freq and pfreq != freq:
            raise ValueError("Inferred frequency of index and frequency "
                             "don't match. This function does not re-sample")
        else:
            freq = pfreq

    elif freq is None:
        raise ValueError("You must specify a freq or x must be a "
                         "pandas object with a timeseries index")


    if filt is None:
        if freq % 2 == 0:  # split weights at ends
            filt = np.array([.5] + [1] * (freq - 1) + [.5]) / freq
        else:
            filt = np.repeat(1./freq, freq)

    trend = convolution_filter(x, filt)

    # nan pad for conformability - convolve doesn't do it
    if model.startswith('m'):
        detrended = x / trend
    else:
        detrended = x - trend

    period_averages = seasonal_mean(detrended, freq)

    if model.startswith('m'):
        period_averages /= np.mean(period_averages)
    else:
        period_averages -= np.mean(period_averages)

    seasonal = np.tile(period_averages, nobs // freq + 1)[:nobs]

    if model.startswith('m'):
        resid = x / seasonal / trend
    else:
        resid = detrended - seasonal

    results = lmap(_pandas_wrapper, [seasonal, trend, resid, x])
    return DecomposeResult(seasonal=results[0], trend=results[1],
                           resid=results[2], observed=results[3])


class DecomposeResult(object):
    def __init__(self, **kwargs):
        for key, value in iteritems(kwargs):
            setattr(self, key, value)
        self.nobs = len(self.observed)

    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


if __name__ == "__main__":
    x = np.array([-50, 175, 149, 214, 247, 237, 225, 329, 729, 809,
                  530, 489, 540, 457, 195, 176, 337, 239, 128, 102,
                  232, 429, 3, 98, 43, -141, -77, -13, 125, 361, -45, 184])
    results = seasonal_decompose(x, freq=4)

    from pandas import DataFrame, DatetimeIndex
    data = DataFrame(x, DatetimeIndex(start='1/1/1951',
                                      periods=len(x),
                                      freq='Q'))

    res = seasonal_decompose(data)