def test_variances_and_selection(self):
adj_models = self.models + linspace(-2, 0.5, self.k)
spa = SPA(self.benchmark, adj_models, block_size=10, reps=10)
spa.seed(23456)
spa.compute()
variances = spa._loss_diff_var
loss_diffs = spa._loss_diff
demeaned = spa._loss_diff - loss_diffs.mean(0)
t = loss_diffs.shape[0]
kernel_weights = np.zeros(t)
p = 1 / 10.0
for i in range(1, t):
kernel_weights[i] = ((1.0 - (i / t)) * ((1 - p) ** i)) + ((i / t) * ((1 - p) ** (t - i)))
direct_vars = (demeaned ** 2).sum(0) / t
for i in range(1, t):
direct_vars += 2 * kernel_weights[i] * (demeaned[:t - i, :] * demeaned[i:, :]).sum(0) / t
assert_allclose(direct_vars, variances)
selection_criteria = -1.0 * np.sqrt((direct_vars / t) * 2 * np.log(np.log(t)))
valid = loss_diffs.mean(0) >= selection_criteria
assert_equal(valid, spa._valid_columns)
# Bootstrap variances
spa = SPA(self.benchmark, self.models, block_size=10, reps=100, nested=True)
spa.seed(23456)
spa.compute()
spa.reset()
bs = spa.bootstrap.clone(demeaned)
variances = spa._loss_diff_var
bootstrap_variances = t * bs.var(lambda x: x.mean(0), reps=100, recenter=True)
assert_allclose(bootstrap_variances, variances)
def test_seed_reset(self):
spa = SPA(self.benchmark, self.models, reps=10)
spa.seed(23456)
initial_state = spa.bootstrap.random_state
assert_equal(spa.bootstrap._seed, 23456)
spa.compute()
spa.reset()
assert_equal(spa._pvalues, None)
assert_equal(spa.bootstrap.random_state, initial_state)
def test_seed_reset(self):
spa = SPA(self.benchmark, self.models, reps=10)
spa.seed(23456)
initial_state = spa.bootstrap.random_state
assert_equal(spa.bootstrap._seed, 23456)
spa.compute()
spa.reset()
assert_equal(spa._pvalues, None)
assert_equal(spa.bootstrap.random_state, initial_state)
def test_equivalence(self):
spa = SPA(self.benchmark, self.models, block_size=10, reps=100)
spa.seed(23456)
spa.compute()
numpy_pvalues = spa.pvalues
spa = SPA(self.benchmark_df, self.models_df, block_size=10, reps=100)
spa.seed(23456)
spa.compute()
pandas_pvalues = spa.pvalues
assert_series_equal(numpy_pvalues, pandas_pvalues)
def test_equivalence(self):
spa = SPA(self.benchmark, self.models, block_size=10, reps=100)
spa.seed(23456)
spa.compute()
numpy_pvalues = spa.pvalues
spa = SPA(self.benchmark_df, self.models_df, block_size=10, reps=100)
spa.seed(23456)
spa.compute()
pandas_pvalues = spa.pvalues
assert_series_equal(numpy_pvalues, pandas_pvalues)
def test_pvalues_and_critvals(self):
spa = SPA(self.benchmark, self.models, reps=100)
spa.compute()
spa.seed(23456)
simulated_vals = spa._simulated_vals
max_stats = np.max(simulated_vals, 0)
max_loss_diff = np.max(spa._loss_diff.mean(0), 0)
pvalues = np.mean(max_loss_diff <= max_stats, 0)
pvalues = pd.Series(pvalues, index=['lower', 'consistent', 'upper'])
assert_series_equal(pvalues, spa.pvalues)
crit_vals = np.percentile(max_stats, 90.0, axis=0)
crit_vals = pd.Series(crit_vals, index=['lower', 'consistent', 'upper'])
assert_series_equal(spa.critical_values(0.10), crit_vals)
def test_pvalues_and_critvals(self):
spa = SPA(self.benchmark, self.models, reps=100)
spa.compute()
spa.seed(23456)
simulated_vals = spa._simulated_vals
max_stats = np.max(simulated_vals, 0)
max_loss_diff = np.max(spa._loss_diff.mean(0), 0)
pvalues = np.mean(max_loss_diff <= max_stats, 0)
pvalues = pd.Series(pvalues, index=['lower', 'consistent', 'upper'])
assert_series_equal(pvalues, spa.pvalues)
crit_vals = np.percentile(max_stats, 90.0, axis=0)
crit_vals = pd.Series(crit_vals,
index=['lower', 'consistent', 'upper'])
assert_series_equal(spa.critical_values(0.10), crit_vals)
def test_variances_and_selection(self):
adj_models = self.models + linspace(-2, 0.5, self.k)
spa = SPA(self.benchmark, adj_models, block_size=10, reps=10)
spa.seed(23456)
spa.compute()
variances = spa._loss_diff_var
loss_diffs = spa._loss_diff
demeaned = spa._loss_diff - loss_diffs.mean(0)
t = loss_diffs.shape[0]
kernel_weights = np.zeros(t)
p = 1 / 10.0
for i in range(1, t):
kernel_weights[i] = ((1.0 - (i / t)) *
((1 - p)**i)) + ((i / t) * ((1 - p)**(t - i)))
direct_vars = (demeaned**2).sum(0) / t
for i in range(1, t):
direct_vars += 2 * kernel_weights[i] * (demeaned[:t - i, :] *
demeaned[i:, :]).sum(0) / t
assert_allclose(direct_vars, variances)
selection_criteria = -1.0 * np.sqrt(
(direct_vars / t) * 2 * np.log(np.log(t)))
valid = loss_diffs.mean(0) >= selection_criteria
assert_equal(valid, spa._valid_columns)
# Bootstrap variances
spa = SPA(self.benchmark,
self.models,
block_size=10,
reps=100,
nested=True)
spa.seed(23456)
spa.compute()
spa.reset()
bs = spa.bootstrap.clone(demeaned)
variances = spa._loss_diff_var
bootstrap_variances = t * bs.var(
lambda x: x.mean(0), reps=100, recenter=True)
assert_allclose(bootstrap_variances, variances)
def exp_symbols_statistics(fout_path=os.path.join(
DATA_DIR, 'exp_symbols_statistics.xlsx')):
"""
statistics of experiment symbols
output the results to xlsx
"""
t0 = time()
fin_path = os.path.join(SYMBOLS_PKL_DIR,
'TAIEX_2005_largest50cap_panel.pkl')
# shape: (n_exp_period, n_stock, ('simple_roi', 'close_price'))
panel = pd.read_pickle(fin_path)
assert panel.major_axis.tolist() == EXP_SYMBOLS
panel = panel.loc[date(2005, 1, 3):date(2014, 12, 31)]
# the roi in the first experiment date is zero
panel.loc[date(2005, 1, 3), :, 'simple_roi'] = 0.
stat_indices = (
# basic information
'start_date', 'end_date',
'n_exp_period', 'n_period_up', 'n_period_down',
# roi
'cum_roi', 'daily_roi', 'daily_mean_roi',
'daily_std_roi', 'daily_skew_roi', 'daily_kurt_roi',
# roi/risk indices
'sharpe', 'sortino_full', 'sortino_full_semi_std',
'sortino_partial', 'sortino_partial_semi_std',
'max_abs_drawdown',
# normal tests
'JB', 'JB_pvalue',
# uni-root tests
'ADF_c',
'ADF_c_pvalue',
'ADF_ct',
'ADF_ct_pvalue',
'ADF_ctt',
'ADF_ctt_pvalue',
'ADF_nc',
'ADF_nc_pvalue',
'DFGLS_c',
'DFGLS_c_pvalue',
'DFGLS_ct',
'DFGLS_ct_pvalue',
'PP_c',
'PP_c_pvalue',
'PP_ct',
'PP_ct_pvalue',
'PP_nc',
'PP_nc_pvalue',
'KPSS_c',
'KPSS_c_pvalue',
'KPSS_ct',
'KPSS_ct_pvalue',
# performance
'SPA_l_pvalue', 'SPA_c_pvalue', 'SPA_u_pvalue'
)
stat_df = pd.DataFrame(np.zeros((len(stat_indices), len(EXP_SYMBOLS))),
index=stat_indices,
columns=EXP_SYMBOLS)
for rdx, symbol in enumerate(EXP_SYMBOLS):
t1 = time()
rois = panel[:, symbol, 'simple_roi']
# basic
stat_df.loc['start_date', symbol] = rois.index[0].strftime("%Y/%b/%d")
stat_df.loc['end_date', symbol] = rois.index[-1].strftime("%Y/%b/%d")
stat_df.loc['n_exp_period', symbol] = len(rois)
stat_df.loc['n_period_up', symbol] = (rois > 0).sum()
stat_df.loc['n_period_down', symbol] = (rois < 0).sum()
# roi
stat_df.loc['cum_roi', symbol] = (rois + 1.).prod() - 1
stat_df.loc['daily_roi', symbol] = np.power((rois + 1.).prod(),
1. / len(rois)) - 1
stat_df.loc['daily_mean_roi', symbol] = rois.mean()
stat_df.loc['daily_std_roi', symbol] = rois.std()
stat_df.loc['daily_skew_roi', symbol] = rois.skew()
stat_df.loc['daily_kurt_roi', symbol] = rois.kurt() # excess
# roi/risk indices
stat_df.loc['sharpe', symbol] = sharpe(rois)
(stat_df.loc['sortino_full', symbol],
stat_df.loc['sortino_full_semi_std', symbol]) = sortino_full(rois)
(stat_df.loc['sortino_partial', symbol],
stat_df.loc['sortino_partial_semi_std', symbol]) = sortino_partial(
rois)
stat_df.loc['max_abs_drawdown', symbol] = maximum_drawdown(rois)
# normal tests
jb = jarque_bera(rois)
stat_df.loc['JB', symbol] = jb[0]
stat_df.loc['JB_pvalue', symbol] = jb[1]
# uniroot tests
adf_c = adfuller(rois, regression='c')
stat_df.loc['ADF_c', symbol] = adf_c[0]
stat_df.loc['ADF_c_pvalue', symbol] = adf_c[1]
adf_ct = adfuller(rois, regression='ct')
stat_df.loc['ADF_ct', symbol] = adf_ct[0]
stat_df.loc['ADF_ct_pvalue', symbol] = adf_ct[1]
adf_ctt = adfuller(rois, regression='ctt')
stat_df.loc['ADF_ctt', symbol] = adf_ctt[0]
stat_df.loc['ADF_ctt_pvalue', symbol] = adf_ctt[1]
adf_nc = adfuller(rois, regression='nc')
stat_df.loc['ADF_nc', symbol] = adf_nc[0]
stat_df.loc['ADF_nc_pvalue', symbol] = adf_nc[1]
dfgls_c_instance = DFGLS(rois, trend='c')
dfgls_c, dfgls_c_pvalue = (dfgls_c_instance.stat,
dfgls_c_instance.pvalue)
stat_df.loc['DFGLS_c', symbol] = dfgls_c
stat_df.loc['DFGLS_c_pvalue', symbol] = dfgls_c_pvalue
dfgls_ct_instance = DFGLS(rois, trend='ct')
dfgls_ct, dfgls_ct_pvalue = (dfgls_ct_instance.stat,
dfgls_ct_instance.pvalue)
stat_df.loc['DFGLS_ct', symbol] = dfgls_ct
stat_df.loc['DFGLS_ct_pvalue', symbol] = dfgls_ct_pvalue
pp_c_instance = PhillipsPerron(rois, trend='c')
pp_c, pp_c_pvalue = (pp_c_instance.stat, pp_c_instance.pvalue)
stat_df.loc['PP_c', symbol] = pp_c
stat_df.loc['PP_c_pvalue', symbol] = pp_c_pvalue
pp_ct_instance = PhillipsPerron(rois, trend='ct')
pp_ct, pp_ct_pvalue = (pp_ct_instance.stat, pp_ct_instance.pvalue)
stat_df.loc['PP_ct', symbol] = pp_ct
stat_df.loc['PP_ct_pvalue', symbol] = pp_ct_pvalue
pp_nc_instance = PhillipsPerron(rois, trend='nc')
pp_nc, pp_nc_pvalue = (pp_nc_instance.stat, pp_nc_instance.pvalue)
stat_df.loc['PP_nc', symbol] = pp_nc
stat_df.loc['PP_nc_pvalue', symbol] = pp_nc_pvalue
kpss_c_instance = KPSS(rois, trend='c')
kpss_c, kpss_c_pvalue = (kpss_c_instance.stat, kpss_c_instance.pvalue)
stat_df.loc['KPSS_c', symbol] = kpss_c
stat_df.loc['KPSS_c_pvalue', symbol] = kpss_c_pvalue
kpss_ct_instance = KPSS(rois, trend='ct')
kpss_ct, kpss_ct_pvalue = (kpss_ct_instance.stat,
kpss_ct_instance.pvalue)
stat_df.loc['KPSS_ct', symbol] = kpss_ct
stat_df.loc['KPSS_ct_pvalue', symbol] = kpss_ct_pvalue
# performance
spa = SPA(rois, np.zeros(len(rois)), reps=5000)
spa.seed(np.random.randint(0, 2 ** 31 - 1))
spa.compute()
stat_df.loc['SPA_l_pvalue', symbol] = spa.pvalues[0]
stat_df.loc['SPA_c_pvalue', symbol] = spa.pvalues[1]
stat_df.loc['SPA_u_pvalue', symbol] = spa.pvalues[2]
print ("[{}/{}] {} roi statistics OK, {:.3f} secs".format(
rdx + 1, len(EXP_SYMBOLS), symbol, time() - t1
))
# write to excel
writer = pd.ExcelWriter(fout_path, engine='xlsxwriter')
stat_df = stat_df.T
stat_df.to_excel(writer, sheet_name='stats')
# Get the xlsxwriter workbook and worksheet objects.
workbook = writer.book
worksheet = writer.sheets['stats']
# basic formats.
# set header
header_fmt = workbook.add_format()
header_fmt.set_text_wrap()
worksheet.set_row(0, 15, header_fmt)
# set date
date_fmt = workbook.add_format({'num_format': 'yy/mmm/dd'})
date_fmt.set_align('right')
worksheet.set_column('B:C', 12, date_fmt)
# set percentage
percent_fmt = workbook.add_format({'num_format': '0.00%'})
worksheet.set_column('G:J', 8, percent_fmt)
worksheet.set_column('M:Q', 8, percent_fmt)
worksheet.set_column('T:T', 8, percent_fmt)
worksheet.set_column('V:V', 8, percent_fmt)
worksheet.set_column('X:X', 8, percent_fmt)
worksheet.set_column('Z:Z', 8, percent_fmt)
worksheet.set_column('AB:AB', 8, percent_fmt)
worksheet.set_column('AD:AD', 8, percent_fmt)
worksheet.set_column('AF:AF', 8, percent_fmt)
worksheet.set_column('AH:AH', 8, percent_fmt)
worksheet.set_column('AJ:AJ', 8, percent_fmt)
worksheet.set_column('AL:AL', 8, percent_fmt)
worksheet.set_column('AN:AN', 8, percent_fmt)
worksheet.set_column('AP:AP', 8, percent_fmt)
worksheet.set_column('AQ:AS', 8, percent_fmt)
writer.save()
print ("all roi statistics OK, {:.3f} secs".format(time() - t0))
def exp_symbols_statistics(fout_path=os.path.join(
DATA_DIR, 'exp_symbols_statistics.xlsx')):
"""
statistics of experiment symbols
output the results to xlsx
"""
t0 = time()
fin_path = os.path.join(SYMBOLS_PKL_DIR,
'TAIEX_2005_largest50cap_panel.pkl')
# shape: (n_exp_period, n_stock, ('simple_roi', 'close_price'))
panel = pd.read_pickle(fin_path)
assert panel.major_axis.tolist() == EXP_SYMBOLS
panel = panel.loc[date(2005, 1, 3):date(2014, 12, 31)]
# the roi in the first experiment date is zero
panel.loc[date(2005, 1, 3), :, 'simple_roi'] = 0.
stat_indices = (
# basic information
'start_date',
'end_date',
'n_exp_period',
'n_period_up',
'n_period_down',
# roi
'cum_roi',
'daily_roi',
'daily_mean_roi',
'daily_std_roi',
'daily_skew_roi',
'daily_kurt_roi',
# roi/risk indices
'sharpe',
'sortino_full',
'sortino_full_semi_std',
'sortino_partial',
'sortino_partial_semi_std',
'max_abs_drawdown',
# normal tests
'JB',
'JB_pvalue',
# uni-root tests
'ADF_c',
'ADF_c_pvalue',
'ADF_ct',
'ADF_ct_pvalue',
'ADF_ctt',
'ADF_ctt_pvalue',
'ADF_nc',
'ADF_nc_pvalue',
'DFGLS_c',
'DFGLS_c_pvalue',
'DFGLS_ct',
'DFGLS_ct_pvalue',
'PP_c',
'PP_c_pvalue',
'PP_ct',
'PP_ct_pvalue',
'PP_nc',
'PP_nc_pvalue',
'KPSS_c',
'KPSS_c_pvalue',
'KPSS_ct',
'KPSS_ct_pvalue',
# performance
'SPA_l_pvalue',
'SPA_c_pvalue',
'SPA_u_pvalue')
stat_df = pd.DataFrame(np.zeros((len(stat_indices), len(EXP_SYMBOLS))),
index=stat_indices,
columns=EXP_SYMBOLS)
for rdx, symbol in enumerate(EXP_SYMBOLS):
t1 = time()
rois = panel[:, symbol, 'simple_roi']
# basic
stat_df.loc['start_date', symbol] = rois.index[0].strftime("%Y/%b/%d")
stat_df.loc['end_date', symbol] = rois.index[-1].strftime("%Y/%b/%d")
stat_df.loc['n_exp_period', symbol] = len(rois)
stat_df.loc['n_period_up', symbol] = (rois > 0).sum()
stat_df.loc['n_period_down', symbol] = (rois < 0).sum()
# roi
stat_df.loc['cum_roi', symbol] = (rois + 1.).prod() - 1
stat_df.loc['daily_roi', symbol] = np.power(
(rois + 1.).prod(), 1. / len(rois)) - 1
stat_df.loc['daily_mean_roi', symbol] = rois.mean()
stat_df.loc['daily_std_roi', symbol] = rois.std()
stat_df.loc['daily_skew_roi', symbol] = rois.skew()
stat_df.loc['daily_kurt_roi', symbol] = rois.kurt() # excess
# roi/risk indices
stat_df.loc['sharpe', symbol] = sharpe(rois)
(stat_df.loc['sortino_full',
symbol], stat_df.loc['sortino_full_semi_std',
symbol]) = sortino_full(rois)
(stat_df.loc['sortino_partial',
symbol], stat_df.loc['sortino_partial_semi_std',
symbol]) = sortino_partial(rois)
stat_df.loc['max_abs_drawdown', symbol] = maximum_drawdown(rois)
# normal tests
jb = jarque_bera(rois)
stat_df.loc['JB', symbol] = jb[0]
stat_df.loc['JB_pvalue', symbol] = jb[1]
# uniroot tests
adf_c = adfuller(rois, regression='c')
stat_df.loc['ADF_c', symbol] = adf_c[0]
stat_df.loc['ADF_c_pvalue', symbol] = adf_c[1]
adf_ct = adfuller(rois, regression='ct')
stat_df.loc['ADF_ct', symbol] = adf_ct[0]
stat_df.loc['ADF_ct_pvalue', symbol] = adf_ct[1]
adf_ctt = adfuller(rois, regression='ctt')
stat_df.loc['ADF_ctt', symbol] = adf_ctt[0]
stat_df.loc['ADF_ctt_pvalue', symbol] = adf_ctt[1]
adf_nc = adfuller(rois, regression='nc')
stat_df.loc['ADF_nc', symbol] = adf_nc[0]
stat_df.loc['ADF_nc_pvalue', symbol] = adf_nc[1]
dfgls_c_instance = DFGLS(rois, trend='c')
dfgls_c, dfgls_c_pvalue = (dfgls_c_instance.stat,
dfgls_c_instance.pvalue)
stat_df.loc['DFGLS_c', symbol] = dfgls_c
stat_df.loc['DFGLS_c_pvalue', symbol] = dfgls_c_pvalue
dfgls_ct_instance = DFGLS(rois, trend='ct')
dfgls_ct, dfgls_ct_pvalue = (dfgls_ct_instance.stat,
dfgls_ct_instance.pvalue)
stat_df.loc['DFGLS_ct', symbol] = dfgls_ct
stat_df.loc['DFGLS_ct_pvalue', symbol] = dfgls_ct_pvalue
pp_c_instance = PhillipsPerron(rois, trend='c')
pp_c, pp_c_pvalue = (pp_c_instance.stat, pp_c_instance.pvalue)
stat_df.loc['PP_c', symbol] = pp_c
stat_df.loc['PP_c_pvalue', symbol] = pp_c_pvalue
pp_ct_instance = PhillipsPerron(rois, trend='ct')
pp_ct, pp_ct_pvalue = (pp_ct_instance.stat, pp_ct_instance.pvalue)
stat_df.loc['PP_ct', symbol] = pp_ct
stat_df.loc['PP_ct_pvalue', symbol] = pp_ct_pvalue
pp_nc_instance = PhillipsPerron(rois, trend='nc')
pp_nc, pp_nc_pvalue = (pp_nc_instance.stat, pp_nc_instance.pvalue)
stat_df.loc['PP_nc', symbol] = pp_nc
stat_df.loc['PP_nc_pvalue', symbol] = pp_nc_pvalue
kpss_c_instance = KPSS(rois, trend='c')
kpss_c, kpss_c_pvalue = (kpss_c_instance.stat, kpss_c_instance.pvalue)
stat_df.loc['KPSS_c', symbol] = kpss_c
stat_df.loc['KPSS_c_pvalue', symbol] = kpss_c_pvalue
kpss_ct_instance = KPSS(rois, trend='ct')
kpss_ct, kpss_ct_pvalue = (kpss_ct_instance.stat,
kpss_ct_instance.pvalue)
stat_df.loc['KPSS_ct', symbol] = kpss_ct
stat_df.loc['KPSS_ct_pvalue', symbol] = kpss_ct_pvalue
# performance
spa = SPA(rois, np.zeros(len(rois)), reps=5000)
spa.seed(np.random.randint(0, 2**31 - 1))
spa.compute()
stat_df.loc['SPA_l_pvalue', symbol] = spa.pvalues[0]
stat_df.loc['SPA_c_pvalue', symbol] = spa.pvalues[1]
stat_df.loc['SPA_u_pvalue', symbol] = spa.pvalues[2]
print("[{}/{}] {} roi statistics OK, {:.3f} secs".format(
rdx + 1, len(EXP_SYMBOLS), symbol,
time() - t1))
# write to excel
writer = pd.ExcelWriter(fout_path, engine='xlsxwriter')
stat_df = stat_df.T
stat_df.to_excel(writer, sheet_name='stats')
# Get the xlsxwriter workbook and worksheet objects.
workbook = writer.book
worksheet = writer.sheets['stats']
# basic formats.
# set header
header_fmt = workbook.add_format()
header_fmt.set_text_wrap()
worksheet.set_row(0, 15, header_fmt)
# set date
date_fmt = workbook.add_format({'num_format': 'yy/mmm/dd'})
date_fmt.set_align('right')
worksheet.set_column('B:C', 12, date_fmt)
# set percentage
percent_fmt = workbook.add_format({'num_format': '0.00%'})
worksheet.set_column('G:J', 8, percent_fmt)
worksheet.set_column('M:Q', 8, percent_fmt)
worksheet.set_column('T:T', 8, percent_fmt)
worksheet.set_column('V:V', 8, percent_fmt)
worksheet.set_column('X:X', 8, percent_fmt)
worksheet.set_column('Z:Z', 8, percent_fmt)
worksheet.set_column('AB:AB', 8, percent_fmt)
worksheet.set_column('AD:AD', 8, percent_fmt)
worksheet.set_column('AF:AF', 8, percent_fmt)
worksheet.set_column('AH:AH', 8, percent_fmt)
worksheet.set_column('AJ:AJ', 8, percent_fmt)
worksheet.set_column('AL:AL', 8, percent_fmt)
worksheet.set_column('AN:AN', 8, percent_fmt)
worksheet.set_column('AP:AP', 8, percent_fmt)
worksheet.set_column('AQ:AS', 8, percent_fmt)
writer.save()
print("all roi statistics OK, {:.3f} secs".format(time() - t0))