Source code for statsmodels.tsa.filters.hp_filter
from __future__ import absolute_import
from scipy import sparse
from scipy.sparse import dia_matrix, eye as speye
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
>>> dates = sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3')
>>> index = pd.DatetimeIndex(dates)
>>> dta.set_index(index, inplace=True)
>>> cycle, trend = sm.tsa.filters.hpfilter(dta.realgdp, 1600)
>>> dta["cycle"] = cycle
>>> dta["trend"] = trend
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> dta.ix["2003-03-31":, ["realgdp", "trend"]].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
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 = speye(nobs,nobs)
offsets = np.array([0,1,2])
data = np.repeat([[1.],[-2.],[1.]], nobs, axis=1)
K = dia_matrix((data, offsets), shape=(nobs-2,nobs))
import scipy
if (X.dtype != np.dtype('<f8') and
int(scipy.__version__[:3].split('.')[1]) < 11):
#scipy umfpack bug on Big Endian machines, will be fixed in 0.11
use_umfpack = False
else:
use_umfpack = True
if scipy.__version__[:3] == '0.7':
#doesn't have use_umfpack option
#will be broken on big-endian machines with scipy 0.7 and umfpack
trend = spsolve(I+lamb*K.T.dot(K), X)
else:
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