Deprecated rolling window option in OLS from Pandas to Statsmodels
I created an ols
module designed to mimic pandas' deprecated MovingOLS
; it is here.
It has three core classes:
OLS
: static (single-window) ordinary least-squares regression. The output are NumPy arraysRollingOLS
: rolling (multi-window) ordinary least-squares regression. The output are higher-dimension NumPy arrays.PandasRollingOLS
: wraps the results ofRollingOLS
in pandas Series & DataFrames. Designed to mimic the look of the deprecated pandas module.
Note that the module is part of a package (which I'm currently in the process of uploading to PyPi) and it requires one inter-package import.
The first two classes above are implemented entirely in NumPy and primarily use matrix algebra. RollingOLS
takes advantage of broadcasting extensively also. Attributes largely mimic statsmodels' OLS RegressionResultsWrapper
.
An example:
import urllib.parse
import pandas as pd
from pyfinance.ols import PandasRollingOLS
# You can also do this with pandas-datareader; here's the hard way
url = "https://fred.stlouisfed.org/graph/fredgraph.csv"
syms = {
"TWEXBMTH" : "usd",
"T10Y2YM" : "term_spread",
"GOLDAMGBD228NLBM" : "gold",
}
params = {
"fq": "Monthly,Monthly,Monthly",
"id": ",".join(syms.keys()),
"cosd": "2000-01-01",
"coed": "2019-02-01",
}
data = pd.read_csv(
url + "?" + urllib.parse.urlencode(params, safe=","),
na_values={"."},
parse_dates=["DATE"],
index_col=0
).pct_change().dropna().rename(columns=syms)
print(data.head())
# usd term_spread gold
# DATE
# 2000-02-01 0.012580 -1.409091 0.057152
# 2000-03-01 -0.000113 2.000000 -0.047034
# 2000-04-01 0.005634 0.518519 -0.023520
# 2000-05-01 0.022017 -0.097561 -0.016675
# 2000-06-01 -0.010116 0.027027 0.036599
y = data.usd
x = data.drop('usd', axis=1)
window = 12 # months
model = PandasRollingOLS(y=y, x=x, window=window)
print(model.beta.head()) # Coefficients excluding the intercept
# term_spread gold
# DATE
# 2001-01-01 0.000033 -0.054261
# 2001-02-01 0.000277 -0.188556
# 2001-03-01 0.002432 -0.294865
# 2001-04-01 0.002796 -0.334880
# 2001-05-01 0.002448 -0.241902
print(model.fstat.head())
# DATE
# 2001-01-01 0.136991
# 2001-02-01 1.233794
# 2001-03-01 3.053000
# 2001-04-01 3.997486
# 2001-05-01 3.855118
# Name: fstat, dtype: float64
print(model.rsq.head()) # R-squared
# DATE
# 2001-01-01 0.029543
# 2001-02-01 0.215179
# 2001-03-01 0.404210
# 2001-04-01 0.470432
# 2001-05-01 0.461408
# Name: rsq, dtype: float64
Adding for completeness a speedier numpy
-only solution which limits calculations only to the regression coefficients and the final estimate
Numpy rolling regression function
import numpy as np
def rolling_regression(y, x, window=60):
"""
y and x must be pandas.Series
"""
# === Clean-up ============================================================
x = x.dropna()
y = y.dropna()
# === Trim acc to shortest ================================================
if x.index.size > y.index.size:
x = x[y.index]
else:
y = y[x.index]
# === Verify enough space =================================================
if x.index.size < window:
return None
else:
# === Add a constant if needed ========================================
X = x.to_frame()
X['c'] = 1
# === Loop... this can be improved ====================================
estimate_data = []
for i in range(window, x.index.size+1):
X_slice = X.values[i-window:i,:] # always index in np as opposed to pandas, much faster
y_slice = y.values[i-window:i]
coeff = np.dot(np.dot(np.linalg.inv(np.dot(X_slice.T, X_slice)), X_slice.T), y_slice)
estimate_data.append(coeff[0] * x.values[window-1] + coeff[1])
# === Assemble ========================================================
estimate = pandas.Series(data=estimate_data, index=x.index[window-1:])
return estimate
Notes
In some specific case uses, which only require the final estimate of the regression, x.rolling(window=60).apply(my_ols)
appears to be somewhat slow
As a reminder, the coefficients for a regression can be calculated as a matrix product, as you can read on wikipedia's least squares page. This approach via numpy
's matrix multiplication can speed up the process somewhat vs using the ols in statsmodels
. This product is expressed in the line starting as coeff = ...
Rolling beta with sklearn
import pandas as pd
from sklearn import linear_model
def rolling_beta(X, y, idx, window=255):
assert len(X)==len(y)
out_dates = []
out_beta = []
model_ols = linear_model.LinearRegression()
for iStart in range(0, len(X)-window):
iEnd = iStart+window
model_ols.fit(X[iStart:iEnd], y[iStart:iEnd])
#store output
out_dates.append(idx[iEnd])
out_beta.append(model_ols.coef_[0][0])
return pd.DataFrame({'beta':out_beta}, index=out_dates)
df_beta = rolling_beta(df_rtn_stocks['NDX'].values.reshape(-1, 1), df_rtn_stocks['CRM'].values.reshape(-1, 1), df_rtn_stocks.index.values, 255)