def test_series_both(self):
expected = pd.DataFrame(
index=self.series.index,
columns=["cpi", "cpi.L.1", "cpi.L.2", "cpi.L.3"],
)
expected["cpi"] = self.series
for lag in range(1, 4):
expected["cpi.L." + str(int(lag))] = self.series.shift(lag)
expected = expected.iloc[3:]
both = stattools.lagmat(self.series,
3,
trim="both",
original="in",
use_pandas=True)
assert_frame_equal(both, expected)
lags = stattools.lagmat(self.series,
3,
trim="both",
original="ex",
use_pandas=True)
assert_frame_equal(lags, expected.iloc[:, 1:])
lags, lead = stattools.lagmat(self.series,
3,
trim="both",
original="sep",
use_pandas=True)
assert_frame_equal(lead, expected.iloc[:, :1])
assert_frame_equal(lags, expected.iloc[:, 1:])
def test_dataframe_forward(self):
data = self.macro_df
columns = list(data.columns)
n = data.shape[0]
values = np.zeros((n + 3, 16))
values[:n, :4] = data.values
for lag in range(1, 4):
new_cols = [col + ".L." + str(lag) for col in data]
columns.extend(new_cols)
values[lag:n + lag, 4 * lag:4 * (lag + 1)] = data.values
index = data.index
values = values[:n]
expected = pd.DataFrame(values, columns=columns, index=index)
both = stattools.lagmat(self.macro_df,
3,
trim="forward",
original="in",
use_pandas=True)
assert_frame_equal(both, expected)
lags = stattools.lagmat(self.macro_df,
3,
trim="forward",
original="ex",
use_pandas=True)
assert_frame_equal(lags, expected.iloc[:, 4:])
lags, lead = stattools.lagmat(self.macro_df,
3,
trim="forward",
original="sep",
use_pandas=True)
assert_frame_equal(lags, expected.iloc[:, 4:])
assert_frame_equal(lead, expected.iloc[:, :4])
def __init__(self, y, exog=None, pmax=12, regression='c', ic='AIC'):
"""
Parameters
----------
y : array or dataframe
endogenous/response variable.
pmax : int
Maximum lag which is included in test.
regression : {"c","ct","ctt","nc"}
Constant and trend order to include in regression.
ic : {"AIC", "BIC", "t-stat", None}
Information criteria to use when automatically determining the lag.
"""
self.pmax = pmax
self.regression = regression
self.ic = ic
self.name = y.name
self.symbols = ['α₀', 'ρ₁']
# Setup for endog and exog
L1_y = lagmat(y, maxlag=1, use_pandas=True)[1:] # creating lags
exog = exog[1:] if exog is not None else exog
# Identifying optimal lags
resultsADF = adfuller(y, self.pmax, self.regression, self.ic)
lags = resultsADF[2]
Ldy = lagmat(y.diff()[1:], maxlag=lags,
use_pandas=True).add_prefix('Δ')
X = pd.concat([L1_y, Ldy, exog], axis=1)
# endog and exog
self.y = y[lags + 1:]
self.X = add_constant(X)[lags:]
def test_add_lag1d(self):
data = self.random_data
lagmat = stattools.lagmat(data, 3, trim="Both")
results = np.column_stack((data[3:], lagmat))
lag_data = tools.add_lag(data, lags=3, insert=True)
assert_equal(results, lag_data)
# add index
data = data[:, None]
lagmat = stattools.lagmat(data, 3, trim="Both") # test for lagmat too
results = np.column_stack((data[3:], lagmat))
lag_data = tools.add_lag(data, lags=3, insert=True)
assert_equal(results, lag_data)
def test_tstat(self):
exog, endog = lagmat(self.inflation, 12, original='sep', trim='both')
icbest, sel_lag = _autolag(OLS, endog, exog, 1, 11, 't-stat')
icbest2, sel_lag2 = _autolag_ols(endog, exog, 0, 12, 't-stat')
assert np.isscalar(icbest2)
assert np.isscalar(sel_lag2)
assert sel_lag == sel_lag2
exog, endog = lagmat(self.y, 12, original='sep', trim='both')
icbest, sel_lag = _autolag(OLS, endog, exog, 1, 11, 't-stat')
icbest2, sel_lag2 = _autolag_ols(endog, exog, 0, 12, 't-stat')
assert np.isscalar(icbest2)
assert np.isscalar(sel_lag2)
assert sel_lag == sel_lag2
def test_tstat(self):
exog, endog = lagmat(self.inflation, 12, original="sep", trim="both")
_, sel_lag = _autolag(OLS, endog, exog, 1, 11, "t-stat")
icbest2, sel_lag2 = _autolag_ols(endog, exog, 0, 12, "t-stat")
assert np.isscalar(icbest2)
assert np.isscalar(sel_lag2)
assert sel_lag == sel_lag2
exog, endog = lagmat(self.y, 12, original="sep", trim="both")
_, sel_lag = _autolag(OLS, endog, exog, 1, 11, "t-stat")
icbest2, sel_lag2 = _autolag_ols(endog, exog, 0, 12, "t-stat")
assert np.isscalar(icbest2)
assert np.isscalar(sel_lag2)
assert sel_lag == sel_lag2
def test_tstat(self):
exog, endog = lagmat(self.inflation, 12, original='sep', trim='both')
icbest, sel_lag = _autolag(OLS, endog, exog, 1, 11, 't-stat')
icbest2, sel_lag2 = _autolag_ols(endog, exog, 0, 12, 't-stat')
assert np.isscalar(icbest2)
assert np.isscalar(sel_lag2)
assert sel_lag == sel_lag2
exog, endog = lagmat(self.y, 12, original='sep', trim='both')
icbest, sel_lag = _autolag(OLS, endog, exog, 1, 11, 't-stat')
icbest2, sel_lag2 = _autolag_ols(endog, exog, 0, 12, 't-stat')
assert np.isscalar(icbest2)
assert np.isscalar(sel_lag2)
assert sel_lag == sel_lag2
def setup(self, endog, model=None, pmax=None, ic=None, exog=None):
# Erase previous results
self.results = None
# Custom instance changes
if model != None:
self.model = model
if pmax != None:
self.pmax = pmax
if ic != None:
self.ic = ic
if type(endog) != pd.Series:
self.endog = pd.Series(endog, name='y')
self.endog_original = pd.Series(endog, name='y')
else:
self.endog = endog
self.endog_original = endog
# Creating endog and exog
y1 = pd.DataFrame(self.endog.shift(1)[1:]).add_suffix(
'.L1') # creating lags
dy = self.endog.diff(1)[1:] # first difference
X = y1
resultsADF = adfuller(self.endog,
maxlag=self.pmax,
regression=model,
autolag=self.ic)
ADFt, p, cvADF = resultsADF[0], resultsADF[2], resultsADF[4]
# Defining series in case of possible legs
if p > 0:
dyl = pd.DataFrame(
lagmat(dy, maxlag=p),
index=dy.index,
columns=['Diff.L' + str(i) for i in range(1, 1 + p)])[p:]
X = pd.concat([y1[p:], dyl], axis=1)
# If the ic decides not to include lags
else:
X = X[p:]
# Removing tails
self.lags = p
self.extraExog = exog[p + 1:] if type(exog) != type(None) else None
self.L1 = y1[p:]
self.diff = dy[p:]
self.diffLags = dyl if self.lags > 0 else None
self.endog = self.endog[p + 1:]
if self.model == 'c':
self.exog = add_constant(X)
elif self.model == 'ct':
self.exog = add_trend(add_constant(X), 'ct')
else:
raise ValueError('Model type is not recognized: ' +
str(self.model))
# Adding additional exog if present
self.exog = pd.concat([self.exog, self.extraExog], axis=1)
return self
def test_add_lag_drop_insert(self):
data = self.macro_df.values
nddata = data.astype(float)
lagmat = stattools.lagmat(nddata[:, 2], 3, trim="Both")
results = np.column_stack((nddata[3:, :2], lagmat, nddata[3:, -1]))
lag_data = tools.add_lag(data, self.realgdp_loc, 3, drop=True)
assert_equal(lag_data, results)
def test_add_lag_noinsert_ndarray(self):
data = self.macro_df.values
nddata = data.astype(float)
lagmat = stattools.lagmat(nddata[:, 2], 3, trim="Both")
results = np.column_stack((nddata[3:, :], lagmat))
lag_data = tools.add_lag(nddata, 2, 3, insert=False)
assert_equal(lag_data, results)
def _za_thread(x, regression, start, end, nobs, basecols, baselags, res,
residx):
# first-diff y
dy = np.diff(x, axis=0)[:, 0]
zastat = bpidx = np.inf
for bp in range(start, end):
# reserve exog space
exog = np.zeros((dy[baselags:].shape[0], basecols + baselags))
# constant
exog[:, 0] = 1
# intercept dummy / trend / trend dummy
if regression != 't':
exog[(bp - (baselags + 1)):, 1] = 1
exog[:, 2] = np.arange(baselags + 2, nobs + 1)
if regression == 'ct':
exog[(bp - (baselags + 1)):, 3] = np.arange(1, nobs - bp + 1)
else:
exog[:, 1] = np.arange(baselags + 2, nobs + 1)
exog[(bp - (baselags + 1)):, 2] = np.arange(1, nobs - bp + 1)
# lagged y
exog[:, basecols - 1] = x[baselags:(nobs - 1), 0]
# lagged dy
exog[:, basecols:] = tsa.lagmat(
dy, baselags, trim='none')[baselags:exog.shape[0] + baselags]
stat = lm.OLS(dy[baselags:], exog).fit().tvalues[basecols - 1]
if stat < zastat:
zastat = stat
bpidx = bp - 1
crit = zacrit.za_crit(zastat, regression)
pval = crit[0]
cvdict = crit[1]
res[residx] = [zastat, pval, cvdict, bpidx]
def test_add_lag_1d_drop_struct(self):
data = np.zeros(100, dtype=[("variable", float)])
nddata = self.random_data
data["variable"] = nddata
lagmat = stattools.lagmat(nddata, 3, trim="Both")
lag_data = tools.add_lag(data, lags=3, drop=True)
assert_equal(lagmat, lag_data)
def test_add_lag1d_drop(self):
data = self.random_data
lagmat = stattools.lagmat(data, 3, trim="Both")
lag_data = tools.add_lag(data, lags=3, drop=True, insert=True)
assert_equal(lagmat, lag_data)
# no insert, should be the same
lag_data = tools.add_lag(data, lags=3, drop=True, insert=False)
assert_equal(lagmat, lag_data)
def test_add_lag_noinsertatend_ndarray(self):
data = self.macro_df.values
nddata = data.astype(float)
lagmat = stattools.lagmat(nddata[:, -1], 3, trim="Both")
results = np.column_stack((nddata[3:, :], lagmat))
lag_data = tools.add_lag(nddata, 3, 3, insert=False)
assert_equal(lag_data, results)
# should be the same as insert also check negative col number
lag_data2 = tools.add_lag(nddata, -1, 3, insert=True)
assert_equal(lag_data2, results)
def test_add_lag_noinsert_atend(self):
data = self.macro_df.values
nddata = data.astype(float)
lagmat = stattools.lagmat(nddata[:, -1], 3, trim="Both")
results = np.column_stack((nddata[3:, :], lagmat))
lag_data = tools.add_lag(data, self.cpi_loc, 3, insert=False)
assert_equal(lag_data, results)
# should be the same as insert
lag_data2 = tools.add_lag(data, self.cpi_loc, 3, insert=True)
assert_equal(lag_data2, results)
def test_tstat_exogenous(self):
exog, endog = lagmat(self.z, 12, original='sep', trim='both')
exog = np.concatenate([self.x[12:], exog], axis=1)
icbest, sel_lag = _autolag_ols(endog, exog, 2, 12, 't-stat')
direct = np.zeros(exog.shape[1])
for i in range(3, exog.shape[1]):
res = OLS(endog, exog[:, :i]).fit()
direct[i] = res.tvalues[-1]
crit = stats.norm.ppf(0.95)
assert np.max(np.argwhere(np.abs(direct[2:]) > crit)) == sel_lag
def test_tstat_exogenous(self):
exog, endog = lagmat(self.z, 12, original='sep', trim='both')
exog = np.concatenate([self.x[12:], exog], axis=1)
icbest, sel_lag = _autolag_ols(endog, exog, 2, 12, 't-stat')
direct = np.zeros(exog.shape[1])
for i in range(3, exog.shape[1]):
res = OLS(endog, exog[:, :i]).fit()
direct[i] = res.tvalues[-1]
crit = stats.norm.ppf(0.95)
assert np.max(np.argwhere(np.abs(direct[2:]) > crit)) == sel_lag
def test_bic_exogenous(self):
exog, endog = lagmat(self.z, 12, original='sep', trim='both')
exog = np.concatenate([self.x[12:], exog], axis=1)
icbest, sel_lag = _autolag_ols(endog, exog, 2, 12, 'bic')
direct = np.zeros(exog.shape[1])
direct.fill(np.inf)
for i in range(3, exog.shape[1]):
res = OLS(endog, exog[:, :i]).fit()
direct[i] = res.bic
assert np.argmin(direct[2:]) == sel_lag
def test_bic_exogenous(self):
exog, endog = lagmat(self.z, 12, original='sep', trim='both')
exog = np.concatenate([self.x[12:], exog], axis=1)
icbest, sel_lag = _autolag_ols(endog, exog, 2, 12, 'bic')
direct = np.zeros(exog.shape[1])
direct.fill(np.inf)
for i in range(3, exog.shape[1]):
res = OLS(endog, exog[:, :i]).fit()
direct[i] = res.bic
assert np.argmin(direct[2:]) == sel_lag
def test_sep_return(self):
data = self.random_data
n = data.shape[0]
lagmat, leads = stattools.lagmat(data, 3, trim="none", original="sep")
expected = np.zeros((n + 3, 4))
for i in range(4):
expected[i:i + n, i] = data
expected_leads = expected[:, :1]
expected_lags = expected[:, 1:]
assert_equal(expected_lags, lagmat)
assert_equal(expected_leads, leads)
def test_add_lag1d_struct(self):
data = np.zeros(100, dtype=[("variable", float)])
nddata = self.random_data
data["variable"] = nddata
lagmat = stattools.lagmat(nddata, 3, trim="Both", original="in")
lag_data = tools.add_lag(data, 0, lags=3, insert=True)
assert_equal(lagmat, lag_data)
lag_data = tools.add_lag(data, 0, lags=3, insert=False)
assert_equal(lagmat, lag_data)
lag_data = tools.add_lag(data, lags=3, insert=True)
assert_equal(lagmat, lag_data)
def _lag(self, X, numlags, holdout=None):
if len(X.shape) == 1:
ncols = 1
else:
ncols = X.shape[1]
ind = X.iloc[numlags:].index
lags, X_trim = lagmat(X, numlags, trim="both", original="sep")
if holdout is not None:
return pd.DataFrame(index=ind, data=lags[:, (holdout * ncols) :]), X_trim
else:
return pd.DataFrame(index=ind, data=lags), X_trim.flatten()
def test_dataframe_without_pandas(self):
data = self.macro_df
both = stattools.lagmat(data, 3, trim="both", original="in")
both_np = stattools.lagmat(data.values, 3, trim="both", original="in")
assert_equal(both, both_np)
lags = stattools.lagmat(data, 3, trim="none", original="ex")
lags_np = stattools.lagmat(data.values, 3, trim="none", original="ex")
assert_equal(lags, lags_np)
lags, lead = stattools.lagmat(data, 3, trim="forward", original="sep")
lags_np, lead_np = stattools.lagmat(data.values,
3,
trim="forward",
original="sep")
assert_equal(lags, lags_np)
assert_equal(lead, lead_np)
# maak 1 legenda midden bovenin het figuur met de 3 entries naast elkaar
fig.legend(handles = h, labels = l, loc=9, ncol=3)
# maak mooi en sla op
fig.tight_layout()
fig.savefig('pca-decomposition.png')
#%%
nlags=4
# verzamel alle mogelijke regressies met robuste errors in een dictionary. deze kun je dan als volgt uitlezen: regressie = estims['stability measure naam']['type regressie']
estims = {}
for col in dfz.columns:
estims[col] = { 'direct':sm.OLS(dfz[col], sm.add_constant(sep), missing='drop').fit().get_robustcov_results(),
'IV': sm.OLS(dfz[col], sm.add_constant(IV), missing='drop').fit().get_robustcov_results(),
'rem': sm.OLS(dfz[col], sm.add_constant(rem), missing='drop').fit().get_robustcov_results(),
'VARX-IV': sm.OLS(dfz[col], sm.add_constant(IV.join(pd.DataFrame(lagmat(dfz[col], maxlag=nlags),columns=['lag_1','lag_2','lag_3','lag_4'], index=dfz.index))), missing='drop').fit().get_robustcov_results(),
'VARX-rem': sm.OLS(dfz[col], sm.add_constant(rem.join(pd.DataFrame(lagmat(dfz[col], maxlag=nlags),columns=['lag_1','lag_2','lag_3','lag_4'], index=dfz.index))), missing='drop').fit().get_robustcov_results(),
'VARX-direct':sm.OLS(dfz[col], sm.add_constant(sep.join(pd.DataFrame(lagmat(dfz[col], maxlag=nlags),columns=['lag_1','lag_2','lag_3','lag_4'], index=dfz.index))), missing='drop').fit().get_robustcov_results() }
#logit regressie doen
logitregressie={}
logitregressie['NBER recessie'] = {'logit no lag': sm.Logit(dfz2['NBER_RECESSIONS'], sm.add_constant(sep), missing='drop').fit()}
sm.Logit(dfz2['NBER_RECESSIONS'], sm.add_constant(sep), missing='drop').fit().summary()
nlaglogit=1
logitregressie['NBER recessie'] = {'logit lag': sm.Logit(dfz2['NBER_RECESSIONS'], sm.add_constant(sep.join(pd.DataFrame(lagmat(dfz2['NBER_RECESSIONS'], maxlag=nlaglogit),columns=['lag_1'], index=dfz.index))), missing='drop').fit()}
sm.Logit(dfz2['NBER_RECESSIONS'], sm.add_constant(sep.join(pd.DataFrame(lagmat(dfz2['NBER_RECESSIONS'], maxlag=nlaglogit),columns=['lag_1'], index=dfz.index))), missing='drop').fit().summary()
#%% doe joint significantie test op lags en iv/resid met/zonder lags
# initialiseer de dictionary waar we de tests in gaan opslaan
tests = dict(zip(dfz.columns, [{} for _ in dfz.columns]))
def run(self, x, trim=0.15, maxlag=None, regression='c', autolag='AIC'):
"""
Zivot-Andrews structural-break unit-root test
The Zivot-Andrews test can be used to test for a unit root in a
univariate process in the presence of serial correlation and a
single structural break.
Parameters
----------
x : array_like
data series
trim : float
percentage of series at begin/end to exclude from break-period
calculation in range [0, 0.333] (default=0.15)
maxlag : int
maximum lag which is included in test, default=12*(nobs/100)^{1/4}
(Schwert, 1989)
regression : {'c','t','ct'}
Constant and trend order to include in regression
* 'c' : constant only (default)
* 't' : trend only
* 'ct' : constant and trend
autolag : {'AIC', 'BIC', 't-stat', None}
* if None, then maxlag lags are used
* if 'AIC' (default) or 'BIC', then the number of lags is chosen
to minimize the corresponding information criterion
* 't-stat' based choice of maxlag. Starts with maxlag and drops a
lag until the t-statistic on the last lag length is significant
using a 5%-sized test
Returns
-------
zastat : float
test statistic
pvalue : float
based on MC-derived critical values
cvdict : dict
critical values for the test statistic at the 1%, 5%, and 10%
levels
bpidx : int
index of x corresponding to endogenously calculated break period
with values in the range [0..nobs-1]
baselag : int
number of lags used for period regressions
Notes
-----
H0 = unit root with a single structural break
Algorithm follows Baum (2004/2015) approximation to original
Zivot-Andrews method. Rather than performing an autolag regression at
each candidate break period (as per the original paper), a single
autolag regression is run up-front on the base model (constant + trend
with no dummies) to determine the best lag length. This lag length is
then used for all subsequent break-period regressions. This results in
significant run time reduction but also slightly more pessimistic test
statistics than the original Zivot-Andrews method, although no attempt
has been made to characterize the size/power tradeoff.
References
----------
Baum, C.F. (2004). ZANDREWS: Stata module to calculate Zivot-Andrews
unit root test in presence of structural break," Statistical Software
Components S437301, Boston College Department of Economics, revised
2015.
Schwert, G.W. (1989). Tests for unit roots: A Monte Carlo
investigation. Journal of Business & Economic Statistics, 7: 147-159.
Zivot, E., and Andrews, D.W.K. (1992). Further evidence on the great
crash, the oil-price shock, and the unit-root hypothesis. Journal of
Business & Economic Studies, 10: 251-270.
"""
if regression not in ['c', 't', 'ct']:
raise ValueError('ZA: regression option \'%s\' not understood' %
regression)
if not isinstance(trim, float) or trim < 0 or trim > (1. / 3.):
raise ValueError(
'ZA: trim value must be a float in range [0, 0.333]')
x = np.asarray(x)
if x.ndim > 2 or (x.ndim == 2 and x.shape[1] != 1):
raise ValueError(
'ZA: x must be a 1d array or a 2d array with a single column')
x = np.reshape(x, (-1, 1))
nobs = x.shape[0]
if autolag:
baselags = tsa.adfuller(x[:, 0],
maxlag=maxlag,
regression='ct',
autolag=autolag)[2]
elif maxlag:
baselags = maxlag
else:
baselags = int(12. * np.power(nobs / 100., 1 / 4.))
trimcnt = int(nobs * trim)
start_period = trimcnt
end_period = nobs - trimcnt
if regression == 'ct':
basecols = 5
else:
basecols = 4
# first-diff y and standardize for numerical stability
dy = np.diff(x, axis=0)[:, 0]
dy /= np.sqrt(dy.T.dot(dy))
x = x / np.sqrt(x.T.dot(x))
# reserve exog space
exog = np.zeros((dy[baselags:].shape[0], basecols + baselags))
# normalize constant for stability in long time series
c_const = 1 / np.sqrt(nobs) # Normalize
exog[:, 0] = c_const
# lagged y and dy
exog[:, basecols - 1] = x[baselags:(nobs - 1), 0]
exog[:, basecols:] = tsa.lagmat(
dy, baselags, trim='none')[baselags:exog.shape[0] + baselags]
# better time trend: t_const @ t_const = 1 for large nobs
t_const = np.arange(1.0, nobs + 2)
t_const *= np.sqrt(3) / nobs**(3 / 2)
# iterate through the time periods
stats = np.full(end_period + 1, np.inf)
for bp in range(start_period + 1, end_period + 1):
# update intercept dummy / trend / trend dummy
cutoff = (bp - (baselags + 1))
if regression != 't':
exog[:cutoff, 1] = 0
exog[cutoff:, 1] = c_const
exog[:, 2] = t_const[(baselags + 2):(nobs + 1)]
if regression == 'ct':
exog[:cutoff, 3] = 0
exog[cutoff:, 3] = t_const[1:(nobs - bp + 1)]
else:
exog[:, 1] = t_const[(baselags + 2):(nobs + 1)]
exog[:(cutoff - 1), 2] = 0
exog[(cutoff - 1):, 2] = t_const[0:(nobs - bp + 1)]
# check exog rank on first iteration
if bp == start_period + 1:
o = lm.OLS(dy[baselags:], exog, hasconst=1).fit()
if o.df_model < exog.shape[1] - 1:
raise ValueError(
'ZA: auxiliary exog matrix is not full rank.\n \
cols (exc intercept) = {} rank = {}'.format(
exog.shape[1] - 1, o.df_model))
stats[bp] = o.tvalues[basecols - 1]
else:
stats[bp] = self.__quick_ols(dy[baselags:], exog)[basecols - 1]
# return best seen
zastat = np.min(stats)
bpidx = np.argmin(stats) - 1
crit = self.__za_crit(zastat, regression)
pval = crit[0]
cvdict = crit[1]
return zastat, pval, cvdict, baselags, bpidx
def za(x, trim=0.15, maxlag=None, regression='c', autolag='AIC'):
"""
Zivot-Andrews structural-break unit-root test
The Zivot-Andrews test can be used to test for a unit root in a
univariate process in the presence of serial correlation and a
single structural break.
Parameters
----------
x : array_like
data series
trim : float
percentage of series at begin/end to exclude from break-period
calculation in range [0, 0.333] (default=0.15)
maxlag : int
maximum lag which is included in test, default=12*(nobs/100)^{1/4}
(Schwert, 1989)
regression : {'c','t','ct'}
Constant and trend order to include in regression
* 'c' : constant only (default)
* 't' : trend only
* 'ct' : constant and trend
autolag : {'AIC', 'BIC', 't-stat', None}
* if None, then maxlag lags are used
* if 'AIC' (default) or 'BIC', then the number of lags is chosen
to minimize the corresponding information criterion
* 't-stat' based choice of maxlag. Starts with maxlag and drops a
lag until the t-statistic on the last lag length is significant
using a 5%-sized test
Returns
-------
zastat : float
test statistic
pvalue : float
based on MC-derived critical values
cvdict : dict
critical values for the test statistic at the 1%, 5%, and 10% levels
bpidx : int
index of x corresponding to endogenously calculated break period
baselag : int
number of lags used for period regressions
Notes
-----
H0 = unit root with a single structural break
Algorithm follows Baum (2004/2015) approximation to original Zivot-Andrews
method. Rather than performing an autolag regression at each candidate
break period (as per the original paper), a single autolag regression is
run up-front on the base model (constant + trend with no dummies) to
determine the best lag length. This lag length is then used for all
subsequent break-period regressions. This results in significant run time
reduction but also slightly more pessimistic test statistics than the
original Zivot-Andrews method, although no attempt has been made to
characterize the size/power tradeoff.
References
----------
Baum, C.F. (2004). ZANDREWS: Stata module to calculate Zivot-Andrews unit
root test in presence of structural break," Statistical Software Components
S437301, Boston College Department of Economics, revised 2015.
Schwert, G.W. (1989). Tests for unit roots: A Monte Carlo investigation.
Journal of Business & Economic Statistics, 7: 147-159.
Zivot, E., and Andrews, D.W.K. (1992). Further evidence on the great crash,
the oil-price shock, and the unit-root hypothesis. Journal of Business &
Economic Studies, 10: 251-270.
"""
if regression not in ['c', 't', 'ct']:
raise ValueError('ZA: regression option \'%s\' not understood' %
regression)
if not isinstance(trim, float) or trim < 0 or trim > (1. / 3.):
raise ValueError('ZA: trim value must be a float in range [0, 0.333]')
x = np.asarray(x)
nobs = x.shape[0]
if autolag:
baselags = tsa.adfuller(x[:, 0],
maxlag=maxlag,
regression='ct',
autolag=autolag)[2]
elif maxlag:
baselags = maxlag
else:
baselags = int(12. * np.power(nobs / 100., 1 / 4.))
trimcnt = int(nobs * trim)
start_period = trimcnt
end_period = nobs - trimcnt
if regression == 'ct':
basecols = 5
else:
basecols = 4
# first-diff y
dy = np.diff(x, axis=0)[:, 0]
zastat = np.inf
for bp in range(start_period, end_period + 1):
# reserve exog space
exog = np.zeros((dy[baselags:].shape[0], basecols + baselags))
# constant
exog[:, 0] = 1
# intercept dummy / trend / trend dummy
if regression != 't':
exog[(bp - (baselags + 1)):, 1] = 1
exog[:, 2] = np.arange(baselags + 2, nobs + 1)
if regression == 'ct':
exog[(bp - (baselags + 1)):, 3] = np.arange(1, nobs - bp + 1)
else:
exog[:, 1] = np.arange(baselags + 2, nobs + 1)
exog[(bp - (baselags + 1)):, 2] = np.arange(1, nobs - bp + 1)
# lagged y
exog[:, basecols - 1] = x[baselags:(nobs - 1), 0]
# lagged dy
exog[:, basecols:] = tsa.lagmat(
dy, baselags, trim='none')[baselags:exog.shape[0] + baselags]
stat = lm.OLS(dy[baselags:], exog).fit().tvalues[basecols - 1]
if stat < zastat:
zastat = stat
bpidx = bp - 1
crit = zacrit.za_crit(zastat, regression)
pval = crit[0]
cvdict = crit[1]
return zastat, pval, cvdict, baselags, bpidx