Source code for statsmodels.tsa.filters.hp_filter

from __future__ import absolute_import

from scipy import sparse
from scipy.sparse.linalg import spsolve
import numpy as np
from ._utils import _maybe_get_pandas_wrapper


[docs]def hpfilter(X, lamb=1600): """ Hodrick-Prescott filter Parameters ---------- X : array-like The 1d ndarray timeseries to filter of length (nobs,) or (nobs,1) lamb : float The Hodrick-Prescott smoothing parameter. A value of 1600 is suggested for quarterly data. Ravn and Uhlig suggest using a value of 6.25 (1600/4**4) for annual data and 129600 (1600*3**4) for monthly data. Returns ------- cycle : array The estimated cycle in the data given lamb. trend : array The estimated trend in the data given lamb. Examples --------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.macrodata.load_pandas().data >>> index = pd.DatetimeIndex(start='1959Q1', end='2009Q4', freq='Q') >>> dta.set_index(index, inplace=True) >>> cycle, trend = sm.tsa.filters.hpfilter(dta.realgdp, 1600) >>> gdp_decomp = dta[['realgdp']] >>> gdp_decomp["cycle"] = cycle >>> gdp_decomp["trend"] = trend >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> gdp_decomp[["realgdp", "trend"]]["2000-03-31":].plot(ax=ax, ... fontsize=16); >>> plt.show() .. plot:: plots/hpf_plot.py Notes ----- The HP filter removes a smooth trend, `T`, from the data `X`. by solving min sum((X[t] - T[t])**2 + lamb*((T[t+1] - T[t]) - (T[t] - T[t-1]))**2) T t Here we implemented the HP filter as a ridge-regression rule using scipy.sparse. In this sense, the solution can be written as T = inv(I - lamb*K'K)X where I is a nobs x nobs identity matrix, and K is a (nobs-2) x nobs matrix such that K[i,j] = 1 if i == j or i == j + 2 K[i,j] = -2 if i == j + 1 K[i,j] = 0 otherwise See Also -------- statsmodels.tsa.filters.bk_filter.bkfilter statsmodels.tsa.filters.cf_filter.cffilter statsmodels.tsa.seasonal.seasonal_decompose References ---------- Hodrick, R.J, and E. C. Prescott. 1980. "Postwar U.S. Business Cycles: An Empricial Investigation." `Carnegie Mellon University discussion paper no. 451`. Ravn, M.O and H. Uhlig. 2002. "Notes On Adjusted the Hodrick-Prescott Filter for the Frequency of Observations." `The Review of Economics and Statistics`, 84(2), 371-80. """ _pandas_wrapper = _maybe_get_pandas_wrapper(X) X = np.asarray(X, float) if X.ndim > 1: X = X.squeeze() nobs = len(X) I = sparse.eye(nobs,nobs) offsets = np.array([0,1,2]) data = np.repeat([[1.],[-2.],[1.]], nobs, axis=1) K = sparse.dia_matrix((data, offsets), shape=(nobs-2,nobs)) use_umfpack = True trend = spsolve(I+lamb*K.T.dot(K), X, use_umfpack=use_umfpack) cycle = X-trend if _pandas_wrapper is not None: return _pandas_wrapper(cycle), _pandas_wrapper(trend) return cycle, trend