Leader follower hypothesis testing

leader_test.py

# First get distributions of lagged dot products in both directions
c1_leading_c2_dps = get_lag_dot_products(c1, c2, lagged_timesteps)
c2_leading_c1_dps = get_lag_dot_products(c2, c1, lagged_timesteps)

# Check whether distributions are the same using paired t-test
t_score, pval = scipy.stats.ttest_rel(c1_leading_c2_dps, c2_leading_c1_dps)

if pval < PVAL_THRESH:
    # Choose direction with larger mean
    if numpy.mean(c1_leading_c2_dps) > numpy.mean(c2_leading_c1_dps):
        leader, follower, dot_products = c1, c2, c1_leading_c2_dps
    else:
        leader, follower, dot_products = c2, c1, c2_leading_c1_dps

    # Make sure mean of dot products (our measure of correlation) differs from zero
    tscore, nonzero_pval = stats.ttest_1samp(dot_products, 0.) # get two-sided pval score
    nonzero_pval = nonzero_pval / 2. # convert to 1-sided score because we know apriori that we'll accept only a positive correlation
    if (nonzero_pval < pval_thresh):
        correlation = numpy.mean(dot_products)
        if correlation > 0.:
            record_relationship(c1, c2, correlation)