Source code for statsmodels.tsa.seasonal

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)])

[docs]def seasonal_decompose(x, model="additive", filt=None, freq=None, two_sided=True): """ Seasonal decomposition using moving averages 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 concrete moving average method used in filtering is determined by two_sided. freq : int, optional Frequency of the series. Must be used if x is not a pandas object. Overrides default periodicity of x if x is a pandas object with a timeseries index. two_sided : bool 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. 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.bk_filter.bkfilter statsmodels.tsa.filters.cf_filter.xffilter statsmodels.tsa.filters.hp_filter.hpfilter 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 freq is None: if pfreq is not None: pfreq = freq_to_period(pfreq) freq = pfreq else: raise ValueError("You must specify a freq or x must be a " "pandas object with a timeseries index with" "a freq not set to None") 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) nsides = int(two_sided) + 1 trend = convolution_filter(x, filt, nsides) # 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 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)