def grangerMatrix(matrix, mem=5):
# pass a spike train matrix
n = np.shape(matrix)[1]
gMat = np.zeros((n, n))
for i in range(n):
for j in range(n):
if i != j:
f = []
c = matrix[:, (i, j)]
g = granger(c, maxlag=mem, verbose=False)
for k in g.keys():
f.append(g[k][0]['ssr_ftest'][0])
gMat[i, j] = max(f)
return (gMat)
def grangertests(v1, v2, maxlag=3):
g = granger([*zip(*[v1, v2] / mV)], maxlag, verbose=True)
print(g)
return g
def plot_correlations(nc,
src,
target,
s,
compare_test='correlation',
connectivity=None):
a, b = src, target
all_vals = np.concatenate((a.flatten(), b.flatten()))
lims = [np.min(all_vals), np.max(all_vals)]
lim_diff = lims[1] - lims[0]
lim_prct = 0.07
lim_delta = lim_prct * lim_diff
lims = [lims[0] - lim_delta, lims[1] + lim_delta]
fig = plt.figure(figsize=(10, 10))
gs_factor = 3
gs = plt.GridSpec(nc * gs_factor + 1,
nc * gs_factor + 1,
figure=fig,
wspace=0,
hspace=0)
normed_map2 = mpl.cm.ScalarMappable(norm=mpl.colors.Normalize(vmin=-1,
vmax=1),
cmap=mpl.cm.RdBu)
normed_map1 = mpl.cm.ScalarMappable(norm=mpl.colors.Normalize(vmin=-1,
vmax=1),
cmap=mpl.cm.RdBu)
for i in range(nc + 1):
for j in range(nc + 1):
if i == nc * gs_factor / 2 or j == nc * gs_factor / 2:
ax = plt.subplot(gs[i, j])
ax.set_axis_off()
match_count = 0
n = 0
for i, i_row in enumerate(reversed(range(nc))):
for j in range(nc):
n += 1
print('%s Calculator Cycle # %d / %d' % (compare_test, n, nc**2))
if i_row >= nc / 2:
ax_row_idx = 1
else:
ax_row_idx = 0
if j >= nc / 2:
ax_col_idx = 1
else:
ax_col_idx = 0
ax = plt.subplot(
gs[(i_row * gs_factor + ax_row_idx):((i_row + 1) * gs_factor +
ax_row_idx),
(j * gs_factor + ax_col_idx):((j + 1) * gs_factor +
ax_col_idx)])
try:
w = float(s.w[np.logical_and(s.i == j, s.j == i)]) / 3
except TypeError:
w = 0
if compare_test == 'correlation':
R = np.corrcoef(a[j].flatten(), b[i].flatten())[1, 0]
metric = (R, R)
text2_args = ['\\textbf{R = %.2f}' % metric[1]]
if (metric[0]**2 > 0.75 and w > 0.1) or (metric[0]**2 < 0.75
and w < 0.1):
match_count += 1
elif compare_test == 'granger':
gg = np.stack((b[i], a[j]), 1).T / mV
G = granger(gg.T, maxlag=20, verbose=False)
all_ps = []
for k_gr, v_gr in G.items():
all_ps.append(v_gr[0]['ssr_ftest'][0])
all_ps = np.array(all_ps)
metric = (np.max(all_ps) / 300, np.max(all_ps))
text2_args = ['\\textbf{F = %.1f}' % metric[1]]
if (metric[0] > 0.035
and np.abs(w) > 0.1) or (metric[0] < 0.035
and np.abs(w) < 0.1):
match_count += 1
scatter_kwargs = dict(x=a[j],
y=b[i],
s=3,
facecolors='none',
edgecolors=(0, 0, 0, 0.2),
marker='o',
linewidths=0.5)
text1_args = ['\\textbf{w = %.2f}' % w]
text1_kwargs = dict(
loc='lower right',
frameon=False,
pad=0.09,
prop=dict(color='k', fontsize='xx-small'),
)
text2_kwargs = dict(text1_kwargs)
text2_kwargs['loc'] = 'upper left'
pt1 = mpl.patches.Polygon(np.array([[1, 1], [0, 0], [1, 0]]),
transform=ax.transAxes,
facecolor=normed_map1.to_rgba(w),
edgecolor='none',
alpha=0.6,
zorder=0.5)
pt2 = mpl.patches.Polygon(np.array([[1, 1], [0, 0], [0, 1]]),
transform=ax.transAxes,
facecolor=normed_map2.to_rgba(metric[0]),
edgecolor='none',
alpha=0.6,
zorder=0.4)
ax.add_artist(pt1)
ax.add_artist(pt2)
if compare_test == 'correlation':
ax.scatter(**scatter_kwargs)
ax.add_artist(AnchoredText(*text1_args, **text1_kwargs))
ax.add_artist(AnchoredText(*text2_args, **text2_kwargs))
ax.set_xticklabels([])
ax.set_yticklabels([])
ax.set_xlim(*lims)
ax.set_ylim(*lims)
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
ax = fig.add_subplot(gs[:, :])
ax.patch.set_alpha(0)
despine_all(ax)
ax.set_xticks([])
ax.set_yticks([])
ax.set_xlabel('Source Neuron', fontsize='large', labelpad=30)
ax.set_ylabel('Target Neuron', fontsize='large', labelpad=30)
gap_size = 1 / (gs_factor * nc + 1)
low_middle = 0.5 - gap_size / 2
high_middle = 0.5 + gap_size / 2
thickness = -0.03
cset1 = ('xkcd:golden yellow', 'k')
cset2 = ('k', 'w')
if connectivity in ('e_to_e', 'e_to_i', 'all'):
color = cset1
else:
color = cset2
pt = mpl.patches.Rectangle((0, -0.01),
width=low_middle,
height=thickness,
transform=ax.transAxes,
facecolor=color[0],
edgecolor='k',
clip_path=None,
clip_on=False)
ax.text(low_middle / 2,
-0.01 + thickness / 2,
'$E$',
color=color[1],
fontsize='large',
verticalalignment='center',
horizontalalignment='center')
ax.add_artist(pt)
if connectivity in ('i_to_e', 'i_to_i', 'all'):
color = cset1
else:
color = cset2
pt = mpl.patches.Rectangle((high_middle, -0.01),
width=low_middle,
height=thickness,
transform=ax.transAxes,
facecolor=color[0],
edgecolor='k',
clip_path=None,
clip_on=False)
ax.text(low_middle / 2 + high_middle,
-0.01 + thickness / 2,
'$I$',
color=color[1],
fontsize='large',
verticalalignment='center',
horizontalalignment='center')
ax.add_artist(pt)
if connectivity in ('i_to_e', 'e_to_e', 'all'):
color = cset1
else:
color = cset2
pt = mpl.patches.Rectangle((-0.01, 0),
width=thickness,
height=low_middle,
transform=ax.transAxes,
facecolor=color[0],
edgecolor='k',
clip_path=None,
clip_on=False)
ax.text(-0.01 + thickness / 2,
low_middle / 2,
'$E$',
color=color[1],
fontsize='large',
verticalalignment='center',
horizontalalignment='center')
ax.add_artist(pt)
if connectivity in ('i_to_i', 'e_to_i', 'all'):
color = cset1
else:
color = cset2
pt = mpl.patches.Rectangle((-0.01, high_middle),
width=thickness,
height=low_middle,
transform=ax.transAxes,
facecolor=color[0],
edgecolor='k',
clip_path=None,
clip_on=False)
ax.text(-0.01 + thickness / 2,
low_middle / 2 + high_middle,
'$I$',
color=color[1],
fontsize='large',
verticalalignment='center',
horizontalalignment='center')
ax.add_artist(pt)
return match_count
else:
for date_range in date_range_tags:
start_end_date_pair = date_range.split("-")
start_date = datetime.strptime(start_end_date_pair[0], "%Y%m%d")
end_date = datetime.strptime(start_end_date_pair[1], "%Y%m%d")
date_ranges.append((start_date, end_date))
# slicing by date range
for date_range in date_ranges:
start_date = date_range[0]
end_date = date_range[1]
partial_df = total_df[start_date:end_date]
mdata = partial_df[["ret_y", "ret_x"]]
results = granger(mdata, maxlag=lag)
print("\n")
print("\n")
print("Date Range: ", start_date, " - ", end_date)
print("###########################################################")
for index in range(1, lag + 1):
print("parameters ftest: ", results[index][0]["params_ftest"])
print("ssr chi2test: ", results[index][0]["ssr_chi2test"])
print("likelihood ratio test:", results[index][0]["lrtest"])
print("ssr ftest: ", results[index][0]["ssr_ftest"])
print("--------------------------------------------------------------")
print("restricted model:")
reg = results[index][1][0]
slopes = reg.params[1:]
print('AR:', p, 'MA:', q, 'AIC:', NHS_arima_model.aic)
# for first differenced NHS models searched, AR p=2 MA q=2 is best
NHS_arima_model_selected = ARIMA(NHS_data['NHS'], order = (2,1,2)).fit()
# fitted parameters of the selected model
print(NHS_arima_model_selected.params)
# look-ahead forecasts needed
# Which regressors have potential as leading indicators?
# look for relationships across three of the time series
# using the period of overlap for those series
# does time series in second column "cause" time series in first column
print('Granger Tests')
# R form of test: grangertest(ICS~ER, order = 3, data=modeling.mts)
ICS_from_ER = pd.DataFrame(modeling_mts, columns = ['ICS','ER'])
test = granger(ICS_from_ER, maxlag = 3, addconst=True, verbose=False)
print('ICS_from_ER:',test[3][0]['params_ftest'])
# R form of test: grangertest(ICS~DGO, order = 3, data=modeling.mts)
ICS_from_DGO = pd.DataFrame(modeling_mts, columns = ['ICS','DGO'])
test = granger(ICS_from_DGO, maxlag = 3, addconst=True, verbose=False)
print('ICS_from_DGO:',test[3][0]['params_ftest'])
# R form of test: grangertest(DGO~ER, order = 3, data=modeling.mts)
DGO_from_ER = pd.DataFrame(modeling_mts, columns = ['DGO','ER'])
test = granger(DGO_from_ER, maxlag = 3, addconst=True, verbose=False)
print('DGO_from_ER:',test[3][0]['params_ftest'])
# R form of test: grangertest(DGO~ICS, order = 3, data=modeling.mts)
DGO_from_ICS = pd.DataFrame(modeling_mts, columns = ['DGO','ICS'])
test = granger(DGO_from_ICS, maxlag = 3, addconst=True, verbose=False)
print('AR:', p, 'MA:', q, 'AIC:', NHS_arima_model.aic)
# for first differenced NHS models searched, AR p=2 MA q=2 is best
NHS_arima_model_selected = ARIMA(NHS_data['NHS'], order=(2, 1, 2)).fit()
# fitted parameters of the selected model
print(NHS_arima_model_selected.params)
# look-ahead forecasts needed
# Which regressors have potential as leading indicators?
# look for relationships across three of the time series
# using the period of overlap for those series
# does time series in second column "cause" time series in first column
print('Granger Tests')
# R form of test: grangertest(ICS~ER, order = 3, data=modeling.mts)
ICS_from_ER = pd.DataFrame(modeling_mts, columns=['ICS', 'ER'])
test = granger(ICS_from_ER, maxlag=3, addconst=True, verbose=False)
print('ICS_from_ER:', test[3][0]['params_ftest'])
# R form of test: grangertest(ICS~DGO, order = 3, data=modeling.mts)
ICS_from_DGO = pd.DataFrame(modeling_mts, columns=['ICS', 'DGO'])
test = granger(ICS_from_DGO, maxlag=3, addconst=True, verbose=False)
print('ICS_from_DGO:', test[3][0]['params_ftest'])
# R form of test: grangertest(DGO~ER, order = 3, data=modeling.mts)
DGO_from_ER = pd.DataFrame(modeling_mts, columns=['DGO', 'ER'])
test = granger(DGO_from_ER, maxlag=3, addconst=True, verbose=False)
print('DGO_from_ER:', test[3][0]['params_ftest'])
# R form of test: grangertest(DGO~ICS, order = 3, data=modeling.mts)
DGO_from_ICS = pd.DataFrame(modeling_mts, columns=['DGO', 'ICS'])
test = granger(DGO_from_ICS, maxlag=3, addconst=True, verbose=False)
else:
for date_range in date_range_tags:
start_end_date_pair = date_range.split("-")
start_date = datetime.strptime(start_end_date_pair[0], '%Y%m%d')
end_date = datetime.strptime(start_end_date_pair[1], '%Y%m%d')
date_ranges.append((start_date, end_date))
# slicing by date range
for date_range in date_ranges:
start_date = date_range[0]
end_date = date_range[1]
partial_df = total_df[start_date:end_date]
mdata = partial_df[['ret_y', 'ret_x']]
results = granger(mdata, maxlag=lag)
print("\n")
print("\n")
print("Date Range: ", start_date, " - ", end_date)
print("###########################################################")
for index in range(1, lag+1):
print("parameters ftest: ", results[index][0]["params_ftest"])
print("ssr chi2test: ", results[index][0]["ssr_chi2test"])
print("likelihood ratio test:", results[index][0]["lrtest"])
print("ssr ftest: ", results[index][0]["ssr_ftest"])
print("--------------------------------------------------------------")
print("restricted model:")
reg = results[index][1][0]
slopes = reg.params[1:]
