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MFE Computational Assignment 4 FAQ

Using AutoReg to generate out-of-sample predictions

AutoReg can be used twice to produce out-of-sample predictions. The first uses the data that is used to estimate parameters. The second uses all of the data and then calls predict using the parameters estimated on the in-sample data.

import numpy as np
from statsmodels.tsa.api import AutoReg

# Simulate some data
tau = 100
y = np.random.standard_normal(tau)

# Fit using first half, tau//2
mod = AutoReg(y[:tau//2], lags=1, trend="c", old_names=False)
res =

# Full-sample model
oos_mod = AutoReg(y, lags=1, trend="c", old_names=False)
# One-step predictions
oos_1step = oos_mod.predict(res.params)
# OOS Random Walk predictions
oos_rw = oos_mod.predict([0, 1])

# Get second half of both
# Use -tau//2: to get second half
oos_1step = oos_1step[-tau//2:]
oos_rw = oos_rw[-tau//2:]

Out-of-sample forecasts from arch models

Out-of-sample forecasting is simpler in models from the arch package since you can use the argument last_obs in a call to fit to set the final observation.

from import sp500
from arch import arch_model

rets = 100 * sp500.load()["Adj Close"].pct_change().dropna()
mod = arch_model(rets)
tau = rets.shape[0]
res =

oos = res.forecast()
onestep_variance = oos.variance.dropna()["h.1"]

which produces

2009-01-02    7.752248
2009-01-05    7.178808
2009-01-06    6.672307
2009-01-07    6.830862
2009-01-08    6.317631
Name: h.1, dtype: float64