def cm_test(X):
"""
Conditional moment test. X is a flat numpy array.
"""
betahat, alphahat, shat = ar1_functions.fit(X)
n = len(X)
xL = X[:(n-1)] # All but the last one
xF = X[1:] # All but the first one
Z = (xF - betahat - alphahat * xL)**2
XX = sm.add_constant(xL)
out = sm.OLS(Z, XX).fit()
return np.abs(out.tvalues[0]) > 1.96
def compute_power(alt_mod=None, ts_length=500, replications=1000, cv_reps=1000):
"""
Computes the rejection frequency for a given null and alternative.
"""
outcomes = []
for m in range(replications):
# Generate time series from alternative
X = alt_mod.ts(ts_length)
# Estimate parameters under the null
betahat, alphahat, shat = ar1_functions.fit(X)
cvs = v_test.compute_critical(betahat, alphahat, shat,
num_reps=cv_reps, ts_length=ts_length)
T = v_test.test_stat(betahat, alphahat, shat, X)
outcomes.append(T > cvs)
return sum(outcomes) / replications
def compute_critical(self, beta, alpha, s, ep=True, num_reps=500, ts_length=264):
"""
Compute the critical value of the test stat associated with parameters
(beta, alpha, s) and AR1 null by Monte Carlo. The flag ep determines
whether or not the test is with estimated parameters. (Note that the
test statistic has a different asymptotic distribution when parameters
are estimated---see the paper.)
"""
# Step 1: Compute num_reps observations of the test statistic
T = np.empty(num_reps)
a1 = ar1_functions.AR1(beta=beta, alpha=alpha, s=s)
data = a1.sim_data(num_reps, ts_length) # Simulate under null
for k in range(num_reps):
if ep:
betahat, alphahat, shat = ar1_functions.fit(data[k,:])
T[k] = self.test_stat(betahat, alphahat, shat, data[k,:])
else:
T[k] = self.test_stat(beta, alpha, s, data[k,:])
# Step 2: Compute and return (1 - size) quantile of test stat observations
T.sort()
return T[int((1 - self.test_size) * num_reps)]