def test_linear_model_time_series(data):
mod = TradedFactorModel(data.portfolios, data.factors)
mod.fit()
res = mod.fit()
get_all(res)
all_params = []
all_tstats = []
nobs, nport = data.portfolios.shape
nf = data.factors.shape[1]
e = np.zeros((nobs, (nport * (nf + 1))))
x = np.zeros((nobs, (nport * (nf + 1))))
factors = sm.add_constant(data.factors)
loc = 0
for i in range(data.portfolios.shape[1]):
if isinstance(data.portfolios, pd.DataFrame):
p = data.portfolios.iloc[:, i:(i + 1)]
else:
p = data.portfolios[:, i:(i + 1)]
ols_res = _OLS(p, factors).fit(cov_type='robust', debiased=True)
all_params.extend(list(ols_res.params))
all_tstats.extend(list(ols_res.tstats))
x[:, loc:(loc + nf + 1)] = factors
e[:, loc:(loc + nf + 1)] = ols_res.resids.values[:, None]
loc += nf + 1
cov = res.cov.values[(nf + 1) * i:(nf + 1) * (i + 1), (nf + 1) * i:(nf + 1) * (i + 1)]
ols_cov = ols_res.cov.values
assert_allclose(cov, ols_cov)
assert_allclose(res.params.values.ravel(), np.array(all_params))
assert_allclose(res.tstats.values.ravel(), np.array(all_tstats))
assert_allclose(res.risk_premia, np.asarray(factors).mean(0)[1:])
xpxi_direct = np.eye((nf + 1) * nport + nf)
f = np.asarray(factors)
fpfi = np.linalg.inv(f.T @ f / nobs)
nfp1 = nf + 1
for i in range(nport):
st, en = i * nfp1, (i + 1) * nfp1
xpxi_direct[st:en, st:en] = fpfi
f = np.asarray(factors)[:, 1:]
xe = np.c_[x * e, f - f.mean(0)[None, :]]
xeex_direct = xe.T @ xe / nobs
cov = xpxi_direct @ xeex_direct @ xpxi_direct / (nobs - nfp1)
assert_allclose(cov, res.cov.values)
alphas = np.array(all_params)[0::nfp1][:, None]
alpha_cov = cov[0:(nfp1 * nport):nfp1, 0:(nfp1 * nport):nfp1]
stat_direct = float(alphas.T @ np.linalg.inv(alpha_cov) @ alphas)
assert_allclose(res.j_statistic.stat, stat_direct)
assert_allclose(1.0 - stats.chi2.cdf(stat_direct, nport), res.j_statistic.pval)
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