# Source code for quantecon.filter

"""

function for filtering

"""
import numpy as np

[docs]def hamilton_filter(data, h, *args):
r"""
This function applies "Hamilton filter" to the data

http://econweb.ucsd.edu/~jhamilto/hp.pdf

Parameters
----------
data : array or dataframe
h : integer
Time horizon that we are likely to predict incorrectly.
Original paper recommends 2 for annual data, 8 for quarterly data,
24 for monthly data.
*args : integer
If supplied, it is p in the paper. Number of lags in regression.
Must be greater than h.
If not supplied, random walk process is assumed.

Note: For seasonal data, it's desirable for p and h to be integer multiples
of the number of obsevations in a year.
e.g. For quarterly data, h = 8 and p = 4 are recommended.

Returns
-------
cycle : array of cyclical component
trend : trend component

"""
# transform data to array
y = np.asarray(data, float)
# sample size
T = len(y)

if len(args) == 1: # if p is supplied
p = args
# construct X matrix of lags
X = np.ones((T-p-h+1, p+1))
for j in range(1, p+1):
X[:, j] = y[p-j:T-h-j+1:1]

# do OLS regression
b = np.linalg.solve(X.transpose()@X, X.transpose()@y[p+h-1:T])
# trend component (nan for the first p+h-1 period)
trend = np.append(np.zeros(p+h-1)+np.nan, X@b)
# cyclical component
cycle = y - trend

elif len(args) == 0: # if p is not supplied (random walk)
cycle = np.append(np.zeros(h)+np.nan, y[h:T] - y[0:T-h])
trend = y - cycle

return cycle, trend