class CheckADF(object):
"""
Test Augmented Dickey-Fuller
Test values taken from Stata.
"""
levels = ['1%', '5%', '10%']
data = macrodata.load_pandas()
x = data.data['realgdp'].values
y = data.data['infl'].values
def test_teststat(self):
assert_almost_equal(self.res1[0],
self.teststat,
5)
def test_pvalue(self):
assert_almost_equal(self.res1[1],
self.pvalue,
5)
def test_critvalues(self):
critvalues = [self.res1[4][lev] for lev in self.levels]
assert_almost_equal(critvalues,
self.critvalues,
2)
def setup_class(cls):
d = macrodata.load_pandas().data
# growth rates
d['gs_l_realinv'] = 400 * np.log(d['realinv']).diff()
d['gs_l_realgdp'] = 400 * np.log(d['realgdp']).diff()
d['lint'] = d['realint'].shift(1)
d['tbilrate'] = d['tbilrate'].shift(1)
d = d.dropna()
cls.d = d
endogg = d['gs_l_realinv']
exogg = add_constant(d[['gs_l_realgdp', 'lint']])
exogg2 = add_constant(d[['gs_l_realgdp', 'tbilrate']])
exogg3 = add_constant(d[['gs_l_realgdp']])
res_ols = OLS(endogg, exogg).fit()
res_ols2 = OLS(endogg, exogg2).fit()
res_ols3 = OLS(endogg, exogg3).fit()
cls.res = res_ols
cls.res2 = res_ols2
cls.res3 = res_ols3
cls.endog = cls.res.model.endog
cls.exog = cls.res.model.exog
class CheckCorrGram(object):
"""
Set up for ACF, PACF tests.
"""
data = macrodata.load_pandas()
x = data.data['realgdp']
results = results_corrgram
def test_bking1d():
# Test Baxter King band-pass filter. Results are taken from Stata
bking_results = np.array([
7.320813, 2.886914, -6.818976, -13.49436, -13.27936, -9.405913,
-5.691091, -5.133076, -7.273468, -9.243364, -8.482916, -4.447764,
2.406559, 10.68433, 19.46414, 28.09749, 34.11066, 33.48468, 24.64598,
9.952399, -4.265528, -12.59471, -13.46714, -9.049501, -3.011248,
.5655082, 2.897976, 7.406077, 14.67959, 18.651, 13.05891, -2.945415,
-24.08659, -41.86147, -48.68383, -43.32689, -31.66654, -20.38356,
-13.76411, -9.978693, -3.7704, 10.27108, 31.02847, 51.87613, 66.93117,
73.51951, 73.4053, 69.17468, 59.8543, 38.23899, -.2604809, -49.0107,
-91.1128, -112.1574, -108.3227, -86.51453, -59.91258, -40.01185,
-29.70265, -22.76396, -13.08037, 1.913622, 20.44045, 37.32873,
46.79802, 51.95937, 59.67393, 70.50803, 81.27311, 83.53191, 67.72536,
33.78039, -6.509092, -37.31579, -46.05207, -29.81496, 1.416417,
28.31503, 32.90134, 8.949259, -35.41895, -84.65775, -124.4288,
-144.6036, -140.2204, -109.2624, -53.6901, 15.07415, 74.44268,
104.0403, 101.0725, 76.58291, 49.27925, 36.15751, 36.48799, 37.60897,
27.75998, 4.216643, -23.20579, -39.33292, -36.6134, -20.90161,
-4.143123, 5.48432, 9.270075, 13.69573, 22.16675, 33.01987, 41.93186,
47.12222, 48.62164, 47.30701, 40.20537, 22.37898, -7.133002, -43.3339,
-78.51229, -101.3684, -105.2179, -90.97147, -68.30824, -48.10113,
-35.60709, -31.15775, -31.82346, -32.49278, -28.22499, -14.42852,
10.1827, 36.64189, 49.43468, 38.75517, 6.447761, -33.15883, -62.60446,
-72.87829, -66.54629, -52.61205, -38.06676, -26.19963, -16.51492,
-7.007577, .6125674, 7.866972, 14.8123, 22.52388, 30.65265, 39.47801,
49.05027, 59.02925, 72.88999, 95.08865, 125.8983, 154.4283, 160.7638,
130.6092, 67.84406, -7.070272, -68.08128, -99.39944, -104.911,
-100.2372, -98.11596, -104.2051, -114.0125, -113.3475, -92.98669,
-51.91707, -.7313812, 43.22938, 64.62762, 64.07226, 59.35707, 67.06026,
91.87247, 124.4591, 151.2402, 163.0648, 154.6432
])
X = macrodata.load_pandas().data['realinv'].values
Y = bkfilter(X, 6, 32, 12)
assert_almost_equal(Y, bking_results, 4)
def test_influence_wrapped():
d = macrodata.load_pandas().data
# growth rates
gs_l_realinv = 400 * np.log(d['realinv']).diff().dropna()
gs_l_realgdp = 400 * np.log(d['realgdp']).diff().dropna()
lint = d['realint'][:-1]
# re-index these because they won't conform to lint
gs_l_realgdp.index = lint.index
gs_l_realinv.index = lint.index
data = dict(const=np.ones_like(lint), lint=lint, lrealgdp=gs_l_realgdp)
# order is important
exog = pd.DataFrame(data, columns=['const', 'lrealgdp', 'lint'])
res = OLS(gs_l_realinv, exog).fit()
# basic
# already tested
# cov.scaled and cov.unscaled have already been tested
# TODO: check that above is correct;
# comment is (roughly) copied from upstream
infl = oi.OLSInfluence(res)
# smoke test just to make sure it works, results separately tested
df = infl.summary_frame()
assert isinstance(df, pd.DataFrame)
# this test is slow
path = os.path.join(cur_dir, "results", "influence_lsdiag_R.json")
with open(path, 'r') as fp:
lsdiag = json.load(fp)
c0, c1 = infl.cooks_distance # TODO: what's c1, it's pvalues? -ss
# NOTE: we get a hard-cored 5 decimals with pandas testing
assert_almost_equal(c0, lsdiag['cooks'], 14)
assert_almost_equal(infl.hat_matrix_diag, (lsdiag['hat']), 14)
assert_almost_equal(infl.resid_studentized_internal,
lsdiag['std.res'], 14)
# slow
dffits, dffth = infl.dffits
assert_almost_equal(dffits, lsdiag['dfits'], 14)
assert_almost_equal(infl.resid_studentized_external,
lsdiag['stud.res'], 14)
fn = os.path.join(cur_dir, "results", "influence_measures_R.csv")
infl_r = pd.read_csv(fn, index_col=0)
# not used yet:
# fn = os.path.join(cur_dir, "results", "influence_measures_bool_R.csv")
# conv = lambda s: 1 if s == 'TRUE' else 0
#infl_bool_r = pd.read_csv(fn, index_col=0,
# converters=dict(zip(lrange(7), [conv]*7)))
infl_r2 = np.asarray(infl_r)
# TODO: finish wrapping this stuff
assert_almost_equal(infl.dfbetas, infl_r2[:, :3], decimal=13)
assert_almost_equal(infl.cov_ratio, infl_r2[:, 4], decimal=14)
def setup_class(cls):
d2 = macrodata.load_pandas().data
g_gdp = 400 * np.diff(np.log(d2['realgdp'].values))
g_inv = 400 * np.diff(np.log(d2['realinv'].values))
exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1].values],
prepend=False)
cls.res1 = OLS(g_inv, exogg).fit()
def setup_class(cls):
d2 = macrodata.load_pandas().data
g_gdp = 400 * np.diff(np.log(d2['realgdp'].values))
g_inv = 400 * np.diff(np.log(d2['realinv'].values))
exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1].values],
prepend=False)
mod1 = GLSAR(g_inv, exogg, 1)
cls.res = mod1.iterative_fit(5)
def test_hpfilter_pandas():
dta = macrodata.load_pandas().data
index = pd.DatetimeIndex(start='1959-01-01', end='2009-10-01', freq='Q')
dta.index = index
cycle, trend = hpfilter(dta["realgdp"])
ndcycle, ndtrend = hpfilter(dta['realgdp'].values)
assert_equal(cycle.values, ndcycle)
assert cycle.index[0] == datetime(1959, 3, 31)
assert cycle.index[-1] == datetime(2009, 9, 30)
assert cycle.name == "realgdp"
def test_webuse_pandas():
# test copied and adjusted from iolib/tests/test_foreign
dta = macrodata.load_pandas().data
base_gh = ("https://github.com/statsmodels/statsmodels/raw/master/"
"statsmodels/datasets/macrodata/")
internet_available = check_internet(base_gh)
if not internet_available:
raise pytest.skip('Unable to retrieve file - skipping test')
res1 = webuse('macrodata', baseurl=base_gh)
res1 = res1.astype(float)
assert_frame_equal(res1, dta.astype(float))
def test_grangercausality():
# some example data
mdata = macrodata.load_pandas().data
mdata = mdata[['realgdp', 'realcons']].values
data = mdata.astype(float)
data = np.diff(np.log(data), axis=0)
# R: lmtest:grangertest
r_result = [0.243097, 0.7844328, 195, 2] # f_test
gr = grangercausalitytests(data[:, 1::-1], 2, verbose=False)
assert_almost_equal(r_result, gr[2][0]['ssr_ftest'], decimal=7)
assert_almost_equal(gr[2][0]['params_ftest'],
gr[2][0]['ssr_ftest'],
decimal=7)
def test_webuse():
# test copied and adjusted from iolib/tests/test_foreign
base_gh = ("https://github.com/statsmodels/statsmodels/raw/master/"
"statsmodels/datasets/macrodata/")
internet_available = check_internet(base_gh)
if not internet_available:
raise pytest.skip('Unable to retrieve file - skipping test')
df = macrodata.load_pandas().data.astype('f4')
df['year'] = df['year'].astype('i2')
df['quarter'] = df['quarter'].astype('i1')
expected = df.to_records(index=False)
expected = np.array([list(row) for row in expected])
res1 = webuse('macrodata', baseurl=base_gh, as_df=False)
assert_array_equal(res1, expected)
def test_alignment():
# GH#206
d = macrodata.load_pandas().data
# growth rates
gs_l_realinv = 400 * np.log(d['realinv']).diff().dropna()
gs_l_realgdp = 400 * np.log(d['realgdp']).diff().dropna()
lint = d['realint'][:-1] # incorrect indexing for test purposes
endog = gs_l_realinv
# re-index because they won't conform to lint
realgdp = gs_l_realgdp.reindex(lint.index, method='bfill')
data = dict(const=np.ones_like(lint), lrealgdp=realgdp, lint=lint)
exog = pd.DataFrame(data)
# which index do we get??
with pytest.raises(ValueError):
OLS(endog, exog)
def test_GLSARlag():
# test that results for lag>1 is close to lag=1, and smaller ssr
d2 = macrodata.load_pandas().data
g_gdp = 400 * np.diff(np.log(d2['realgdp'].values))
g_inv = 400 * np.diff(np.log(d2['realinv'].values))
exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1].values],
prepend=False)
mod1 = GLSAR(g_inv, exogg, 1)
res1 = mod1.iterative_fit(5)
mod4 = GLSAR(g_inv, exogg, 4)
res4 = mod4.iterative_fit(10)
assert (np.abs(res1.params / res4.params - 1) < 0.03).all()
assert res4.ssr < res1.ssr
assert (np.abs(res4.bse / res1.bse) - 1 < 0.015).all()
assert np.abs((res4.fittedvalues / res1.fittedvalues - 1).mean()) < 0.015
assert len(mod4.rho) == 4
def test_bking_pandas():
# 1d
dta = macrodata.load_pandas().data
index = pd.DatetimeIndex(start='1959-01-01', end='2009-10-01', freq='Q')
dta.index = index
filtered = bkfilter(dta["infl"])
nd_filtered = bkfilter(dta['infl'].values)
assert_equal(filtered.values, nd_filtered)
assert filtered.index[0] == datetime(1962, 3, 31)
assert filtered.index[-1] == datetime(2006, 9, 30)
assert filtered.name == "infl"
# 2d
filtered = bkfilter(dta[["infl", "unemp"]])
nd_filtered = bkfilter(dta[['infl', 'unemp']].values)
assert_equal(filtered.values, nd_filtered)
assert filtered.index[0] == datetime(1962, 3, 31)
assert filtered.index[-1] == datetime(2006, 9, 30)
assert_equal(filtered.columns.values, ["infl", "unemp"])
def test_cfitz_pandas():
# 1d
dta = macrodata.load_pandas().data
index = pd.DatetimeIndex(start='1959-01-01', end='2009-10-01', freq='Q')
dta.index = index
cycle, trend = cffilter(dta["infl"])
ndcycle, ndtrend = cffilter(dta['infl'].values)
assert_allclose(cycle.values, ndcycle, rtol=1e-14)
assert cycle.index[0] == datetime(1959, 3, 31)
assert cycle.index[-1] == datetime(2009, 9, 30)
assert cycle.name == "infl"
# 2d
cycle, trend = cffilter(dta[["infl", "unemp"]])
ndcycle, ndtrend = cffilter(dta[['infl', 'unemp']].values)
assert_allclose(cycle.values, ndcycle, rtol=1e-14)
assert cycle.index[0] == datetime(1959, 3, 31)
assert cycle.index[-1] == datetime(2009, 9, 30)
assert_equal(cycle.columns.values, ["infl", "unemp"])
def setup_class(cls):
d = macrodata.load_pandas().data
# growth rates
gs_l_realinv = 400 * np.diff(np.log(d['realinv'].values))
gs_l_realgdp = 400 * np.diff(np.log(d['realgdp'].values))
endogg = gs_l_realinv
exogg = add_constant(np.c_[gs_l_realgdp, d['realint'][:-1].values])
res_ols = OLS(endogg, exogg).fit()
mod_g1 = GLSAR(endogg, exogg, rho=-0.108136)
res_g1 = mod_g1.fit()
mod_g2 = GLSAR(endogg, exogg, rho=-0.108136) # -0.1335859) from R
res_g2 = mod_g2.iterative_fit(maxiter=5)
cls.res_ols = res_ols
cls.res_g1 = res_g1
cls.res_g2 = res_g2
def test_hac_simple():
d2 = macrodata.load_pandas().data
g_gdp = 400 * np.diff(np.log(d2['realgdp'].values))
g_inv = 400 * np.diff(np.log(d2['realinv'].values))
exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1].values])
res_olsg = OLS(g_inv, exogg).fit()
# > NeweyWest(fm, lag = 4, prewhite = FALSE, sandwich = TRUE,
# verbose=TRUE, adjust=TRUE)
# Lag truncation parameter chosen: 4
# (Intercept) ggdp lint
cov1_r = [
[1.40643899878678802, -0.3180328707083329709, -0.060621111216488610],
[-0.31803287070833292, 0.1097308348999818661, 0.000395311760301478],
[-0.06062111121648865, 0.0003953117603014895, 0.087511528912470993]
]
# > NeweyWest(fm, lag = 4, prewhite = FALSE, sandwich = TRUE,
# verbose=TRUE, adjust=FALSE)
# Lag truncation parameter chosen: 4
# (Intercept) ggdp lint
cov2_r = [
[1.3855512908840137, -0.313309610252268500, -0.059720797683570477],
[-0.3133096102522685, 0.108101169035130618, 0.000389440793564339],
[-0.0597207976835705, 0.000389440793564336, 0.086211852740503622]
]
cov1 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=True)
sw.se_cov(cov1) # smoke?
cov2 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=False)
sw.se_cov(cov2) # smoke?
assert_almost_equal(cov1, cov1_r, decimal=14)
assert_almost_equal(cov2, cov2_r, decimal=14)
# compare default for nlags
cov3 = sw.cov_hac_simple(res_olsg, use_correction=False)
cov4 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=False)
assert_almost_equal(cov3, cov4, decimal=14)
def setup_class(cls):
d = macrodata.load_pandas().data
# growth rates
gs_l_realinv = 400 * np.diff(np.log(d['realinv'].values))
gs_l_realgdp = 400 * np.diff(np.log(d['realgdp'].values))
lint = d['realint'][:-1].values
tbilrate = d['tbilrate'][:-1].values
endogg = gs_l_realinv
exogg = add_constant(np.c_[gs_l_realgdp, lint])
exogg2 = add_constant(np.c_[gs_l_realgdp, tbilrate])
exogg3 = add_constant(np.c_[gs_l_realgdp])
res_ols = OLS(endogg, exogg).fit()
res_ols2 = OLS(endogg, exogg2).fit()
res_ols3 = OLS(endogg, exogg3).fit()
cls.res = res_ols
cls.res2 = res_ols2
cls.res3 = res_ols3
cls.endog = cls.res.model.endog
cls.exog = cls.res.model.exog
class TestCoint_t(object):
"""
Get AR(1) parameter on residuals
Test Cointegration Test Results for 2-variable system
Test values taken from Stata
"""
levels = ['1%', '5%', '10%']
data = macrodata.load_pandas()
y1 = data.data['realcons'].values
y2 = data.data['realgdp'].values
@classmethod
def setup_class(cls):
cls.coint_t = unit_root.coint(cls.y1, cls.y2, trend="c",
maxlag=0, autolag=None)[0]
cls.teststat = -1.8208817
cls.teststat = -1.830170986148
# FIXME: WTF why are we overwriting this?
def test_tstat(self):
assert_almost_equal(self.coint_t, self.teststat, 4)
def test_adf_autolag():
# GH#246
d2 = macrodata.load_pandas().data
for k_trend, tr in enumerate(['nc', 'c', 'ct', 'ctt']):
x = np.log(d2['realgdp'].values)
xd = np.diff(x)
# check exog
adf3 = unit_root.adfuller(x, maxlag=None, autolag='aic',
regression=tr, store=True, regresults=True)
st2 = adf3[-1]
assert len(st2.autolag_results) == 15 + 1 # +1 for lagged level
for l, res in sorted(list(st2.autolag_results.items()))[:5]:
lag = l - k_trend
# assert correct design matrices in _autolag
assert_equal(res.model.exog[-10:, k_trend], x[-11:-1])
assert_equal(res.model.exog[-1, k_trend + 1:], xd[-lag:-1][::-1])
# min-ic lag of dfgls in Stata is also 2, or 9 for maic
# with notrend
assert st2.usedlag == 2
# same result with lag fixed at usedlag of autolag
adf2 = unit_root.adfuller(x, maxlag=2, autolag=None, regression=tr)
assert_almost_equal(adf3[:2], adf2[:2], decimal=12)
tr = 'c'
# check maxlag with autolag
adf3 = unit_root.adfuller(x, maxlag=5, autolag='aic',
regression=tr, store=True, regresults=True)
assert len(adf3[-1].autolag_results) == 5 + 1
adf3 = unit_root.adfuller(x, maxlag=0, autolag='aic',
regression=tr, store=True, regresults=True)
assert len(adf3[-1].autolag_results) == 0 + 1
def test_cfitz_filter():
# Test Christiano-Fitzgerald Filter. Results taken from R.
# NOTE: The Stata mata code and the matlab code it's based on are wrong.
cfilt_res = np.array([[0.712599537179426, 0.439563468233128],
[1.06824041304411, 0.352886666575907],
[1.19422467791128, 0.257297004260607],
[0.970845473140327, 0.114504692143872],
[0.467026976628563, -0.070734782329146],
[-0.089153511514031, -0.238609685132605],
[-0.452339254128573, -0.32376584042956],
[-0.513231214461187, -0.314288554228112],
[-0.352372578720063, -0.258815055101336],
[-0.160282602521333, -0.215076844089567],
[-0.0918782593827686, -0.194120745417214],
[-0.168083823205437, -0.158327420072693],
[-0.291595204965808, -0.0742727139742986],
[-0.348638756841307, 0.037008291163602],
[-0.304328040874631, 0.108196527328748],
[-0.215933150969686, 0.0869231107437175],
[-0.165632621390694, -0.0130556619786275],
[-0.182326839507151, -0.126570926191824],
[-0.223737786804725, -0.205535321806185],
[-0.228939291453403, -0.269110078201836],
[-0.185518327227038, -0.375976507132174],
[-0.143900152461529, -0.53760115656157],
[-0.162749541550174, -0.660065018626038],
[-0.236263634756884, -0.588542352053736],
[-0.275785854309211, -0.236867929421996],
[-0.173666515108109, 0.303436335579219],
[0.0963135720251639, 0.779772338801993],
[0.427070069032285, 0.929108075350647],
[0.629034743259998, 0.658330841002647],
[0.557941248993624, 0.118500049361018],
[0.227866624051603, -0.385048321099911],
[-0.179878859883227, -0.582223992561493],
[-0.428263000051965, -0.394053702908091],
[-0.381640684645912, 0.0445437406977307],
[-0.0942745548364887, 0.493997792757968],
[0.238132391504895, 0.764519811304315],
[0.431293754256291, 0.814755206427316],
[0.455010435813661, 0.745567043101108],
[0.452800768971269, 0.709401694610443],
[0.615754619329312, 0.798293251119636],
[1.00256335412457, 0.975856845059388],
[1.44841039351691, 1.09097252730799],
[1.64651971120370, 0.967823457118036],
[1.35534532901802, 0.522397724737059],
[0.580492790312048, -0.16941343361609],
[-0.410746188031773, -0.90760401289056],
[-1.26148406066881, -1.49592867122591],
[-1.75784179124566, -1.87404167409849],
[-1.94478553960064, -2.14586210891112],
[-2.03751202708559, -2.465855239868],
[-2.20376059354166, -2.86294187189049],
[-2.39722338315852, -3.15004697654831],
[-2.38032366161537, -3.01390466643222],
[-1.91798022532025, -2.23395210271226],
[-0.982318490353716, -0.861346053067472],
[0.199047030343412, 0.790266582335616],
[1.28582776574786, 2.33731327460104],
[2.03565905376430, 3.54085486821911],
[2.41201557412526, 4.36519456268955],
[2.52011070482927, 4.84810517685452],
[2.45618479815452, 4.92906708807477],
[2.22272146945388, 4.42591058990048],
[1.78307567169034, 3.20962906108388],
[1.18234431860844, 1.42568060336985],
[0.590069172333348, -0.461896808688991],
[0.19662302949837, -1.89020992539465],
[0.048307034171166, -2.53490571941987],
[-0.0141956981899000, -2.50020338531674],
[-0.230505187108187, -2.20625973569823],
[-0.700947410386801, -2.06643697511048],
[-1.27085123163060, -2.21536883679783],
[-1.64082547897928, -2.49016921117735],
[-1.62286182971254, -2.63948740221362],
[-1.31609762181362, -2.54685250637904],
[-1.03085567704873, -2.27157435428923],
[-1.01100120380112, -1.90404507430561],
[-1.19823958399826, -1.4123209792214],
[-1.26398933608383, -0.654000086153317],
[-0.904710628949692, 0.447960016248203],
[-0.151340093679588, 1.73970411237156],
[0.592926881165989, 2.85741581650685],
[0.851660587507523, 3.4410446351716],
[0.480324393352127, 3.36870271362297],
[-0.165153230782417, 2.82003806696544],
[-0.459235919375844, 2.12858991660866],
[0.0271158842479935, 1.55840980891556],
[1.18759188180671, 1.17980298478623],
[2.43238266962309, 0.904011534980672],
[3.08277213720132, 0.595286911949837],
[2.79953663720953, 0.148014782859571],
[1.73694442845833, -0.496297332023011],
[0.357638079951977, -1.33108149877570],
[-0.891418825216945, -2.22650083183366],
[-1.77646467793627, -2.89359299718574],
[-2.24614790863088, -2.97921619243347],
[-2.29048879096607, -2.30003092779280],
[-1.87929656465888, -1.05298381273274],
[-1.04510101454788, 0.215837488618531],
[0.00413338508394524, 0.937866257924888],
[0.906870625251025, 0.92664365343019],
[1.33869057593416, 0.518564571494679],
[1.22659678454440, 0.288096869652890],
[0.79380139656044, 0.541053084632774],
[0.38029431865832, 1.01905199983437],
[0.183929413600038, 1.10529586616777],
[0.140045425897033, 0.393618564826736],
[0.0337313182352219, -0.86431819007665],
[-0.269208622829813, -1.85638085246792],
[-0.687276639992166, -1.82275359004533],
[-1.00161592325614, -0.692695765071617],
[-1.06320089194036, 0.803577361347341],
[-0.927152307196776, 1.67366338751788],
[-0.786802101366614, 1.42564362251793],
[-0.772970884572502, 0.426446388877964],
[-0.81275662801789, -0.437721213831647],
[-0.686831250382476, -0.504255468075149],
[-0.237936463020255, 0.148656301898438],
[0.459631879129522, 0.832925905720478],
[1.12717379822508, 0.889455302576383],
[1.48640453200855, 0.268042676202216],
[1.46515245776211, -0.446505038539178],
[1.22993484959115, -0.563868578181134],
[1.0272100765927, 0.0996849952196907],
[0.979191212438404, 1.05053652824665],
[1.00733490030391, 1.51658415000556],
[0.932192535457706, 1.06262774912638],
[0.643374300839414, -0.0865180803476065],
[0.186885168954461, -1.24799408923277],
[-0.290842337365465, -1.80035611156538],
[-0.669446735516495, -1.58847333561510],
[-0.928915624595538, -0.932116966867929],
[-1.11758635926997, -0.307879396807850],
[-1.26832454569756, -0.00856199983957032],
[-1.35755577149251, -0.0303537516690989],
[-1.34244112665546, -0.196807620887435],
[-1.22227976023299, -0.342062643495923],
[-1.04601473486818, -0.390474392372016],
[-0.85158508717846, -0.322164402093596],
[-0.605033439160543, -0.126930141915954],
[-0.218304303942818, 0.179551077808122],
[0.352173017779006, 0.512327303000081],
[1.01389600097229, 0.733397490572755],
[1.55149778750607, 0.748740387440165],
[1.75499674757591, 0.601759717901009],
[1.56636057468633, 0.457705308377562],
[1.12239792537274, 0.470849913286519],
[0.655802600286141, 0.646142040378738],
[0.335285115340180, 0.824103600255079],
[0.173454596506888, 0.808068498175582],
[0.0666753011315252, 0.521488214487996],
[-0.0842367474816212, 0.0583493276173476],
[-0.285604762631464, -0.405958418332253],
[-0.465735422869919, -0.747800086512926],
[-0.563586691231348, -0.94982272350799],
[-0.598110322024572, -1.04736894794361],
[-0.65216025756061, -1.04858365218822],
[-0.789663117801624, -0.924145633093637],
[-0.984704045337959, -0.670740724179446],
[-1.12449565589348, -0.359476803003931],
[-1.07878318723543, -0.092290938944355],
[-0.775555435407062, 0.102132527529259],
[-0.231610677329856, 0.314409560305622],
[0.463192794235131, 0.663523546243286],
[1.17416973448423, 1.13156902460931],
[1.74112278814906, 1.48967153067024],
[2.00320855757084, 1.42571085941843],
[1.8529912317336, 0.802460519079555],
[1.30747261947211, -0.169219078629572],
[0.540237070403222, -1.01621539672694],
[-0.177136817092375, -1.3130784867977],
[-0.611981468823591, -0.982477824460773],
[-0.700240028737747, -0.344919609255406],
[-0.572396497740112, 0.125083535035390],
[-0.450934466600975, 0.142553112732280],
[-0.494020014254326, -0.211429053871656],
[-0.701707589094918, -0.599602868825992],
[-0.94721339346157, -0.710669870591623],
[-1.09297139748946, -0.47846194092245],
[-1.08850658866583, -0.082258450179988],
[-0.976082880696692, 0.235758921309309],
[-0.81885695346771, 0.365298185204303],
[-0.63165529525553, 0.384725179378064],
[-0.37983149226421, 0.460240196164378],
[-0.0375551354277652, 0.68580913832794],
[0.361996927427804, 0.984470835955107],
[0.739920615366072, 1.13195975020298],
[1.03583478061534, 0.88812510421667],
[1.25614938962160, 0.172561520611839],
[1.45295030231799, -0.804979390544485],
[1.64887158748426, -1.55662011197859],
[1.78022721495313, -1.52921975346218],
[1.71945683859668, -0.462240366424548],
[1.36728880239190, 1.31213774341268],
[0.740173894315912, 2.88362740582926],
[-0.0205364331835904, 3.20319080963167],
[-0.725643970956428, 1.75222466531151],
[-1.23900506689782, -0.998432917440275],
[-1.52651897508678, -3.72752870885448],
[-1.62857516631435, -5.00551707196292],
[-1.59657420180451, -4.18499132634584],
[-1.45489013276495, -1.81759097305637],
[-1.21309542313047, 0.722029457352468]])
dta = macrodata.load_pandas().data[['tbilrate', 'infl']].values[1:]
cyc, trend = cffilter(dta)
assert_almost_equal(cyc, cfilt_res, 8)
# do 1d
cyc, trend = cffilter(dta[:, 1])
assert_almost_equal(cyc, cfilt_res[:, 1], 8)
def test_hpfilter():
# Test Hodrick-Prescott Filter. Results taken from Stata.
hpfilt_res = np.array(
[[3.951191484487844718e+01, 2.670837085155121713e+03],
[8.008853245681075350e+01, 2.698712467543189177e+03],
[4.887545512195401898e+01, 2.726612544878045810e+03],
[3.059193256079834100e+01, 2.754612067439201837e+03],
[6.488266733421960453e+01, 2.782816332665780465e+03],
[2.304024204546703913e+01, 2.811349757954532834e+03],
[-1.355312369487364776e+00, 2.840377312369487299e+03],
[-6.746236512580753697e+01, 2.870078365125807522e+03],
[-8.136743836853429457e+01, 2.900631438368534418e+03],
[-6.016789026443257171e+01, 2.932172890264432681e+03],
[-4.636922433138215638e+01, 2.964788224331382025e+03],
[-2.069533915570400495e+01, 2.998525339155703932e+03],
[-2.162152558595607843e+00, 3.033403152558595593e+03],
[-4.718647774311648391e+00, 3.069427647774311481e+03],
[-1.355645669169007306e+01, 3.106603456691690099e+03],
[-4.436926204475639679e+01, 3.144932262044756499e+03],
[-4.332027378211660107e+01, 3.184407273782116590e+03],
[-4.454697106352068658e+01, 3.224993971063520803e+03],
[-2.629875787765286077e+01, 3.266630757877652741e+03],
[-4.426119635629265758e+01, 3.309228196356292756e+03],
[-1.443441190762496262e+01, 3.352680411907625057e+03],
[-2.026686669186437939e+01, 3.396853866691864368e+03],
[-1.913700136208899494e+01, 3.441606001362089046e+03],
[-5.482458977940950717e+01, 3.486781589779409387e+03],
[-1.596244517937793717e+01, 3.532213445179378141e+03],
[-1.374011542874541192e+01, 3.577700115428745448e+03],
[1.325482813403914406e+01, 3.623030171865960710e+03],
[5.603040174253828809e+01, 3.667983598257461836e+03],
[1.030743373627105939e+02, 3.712348662637289181e+03],
[7.217534795943993231e+01, 3.755948652040559864e+03],
[5.462972503693208637e+01, 3.798671274963067845e+03],
[4.407065050666142270e+01, 3.840449349493338559e+03],
[3.749016270204992907e+01, 3.881249837297949853e+03],
[-1.511244199923112319e+00, 3.921067244199923152e+03],
[-9.093507374079763395e+00, 3.959919507374079785e+03],
[-1.685361946760258434e+01, 3.997823619467602384e+03],
[2.822211031434289907e+01, 4.034790889685657021e+03],
[6.117590627896424849e+01, 4.070822093721035344e+03],
[5.433135391434370831e+01, 4.105935646085656117e+03],
[3.810480376716623141e+01, 4.140188196232833434e+03],
[7.042964928802848590e+01, 4.173670350711971878e+03],
[4.996346842507591646e+01, 4.206496531574924120e+03],
[4.455282059571254649e+01, 4.238825179404287155e+03],
[-7.584961950576143863e+00, 4.270845961950576566e+03],
[-4.620339247697120300e+01, 4.302776392476971523e+03],
[-7.054024364552969928e+01, 4.334829243645529459e+03],
[-6.492941099801464588e+01, 4.367188410998014660e+03],
[-1.433567024239555394e+02, 4.399993702423955256e+03],
[-5.932834493089012540e+01, 4.433344344930889747e+03],
[-6.842096758743628016e+01, 4.467249967587436004e+03],
[-6.774011924654860195e+01, 4.501683119246548813e+03],
[-9.030958565658056614e+01, 4.536573585656580690e+03],
[-4.603981499136807543e+01, 4.571808814991368308e+03],
[2.588118806672991923e+01, 4.607219811933269739e+03],
[3.489419371912299539e+01, 4.642608806280876706e+03],
[7.675179642495095322e+01, 4.677794203575049323e+03],
[1.635497817724171910e+02, 4.712616218227582976e+03],
[1.856079654765617306e+02, 4.746963034523438182e+03],
[1.254269446392718237e+02, 4.780825055360728584e+03],
[1.387413113837174024e+02, 4.814308688616282780e+03],
[6.201826599282230745e+01, 4.847598734007177882e+03],
[4.122129542972197669e+01, 4.880966704570278125e+03],
[-4.120287475842360436e+01, 4.914722874758424041e+03],
[-9.486328233441963675e+01, 4.949203282334419782e+03],
[-1.894232132641573116e+02, 4.984718213264157384e+03],
[-1.895766639620087517e+02, 5.021518663962008759e+03],
[-1.464092413342650616e+02, 5.059737241334265491e+03],
[-1.218770668721217589e+02, 5.099388066872122181e+03],
[-4.973075629078175552e+01, 5.140393756290781312e+03],
[-5.365375213897277717e+01, 5.182600752138972894e+03],
[-7.175241524251214287e+01, 5.225824415242512259e+03],
[-7.834757283225462743e+01, 5.269846572832254424e+03],
[-6.264220687943907251e+01, 5.314404206879438789e+03],
[-3.054332122210325906e+00, 5.359185332122210639e+03],
[4.808218808024685131e+01, 5.403838811919753425e+03],
[2.781399326736391231e+00, 5.448011600673263274e+03],
[-2.197570415173231595e+01, 5.491380704151732061e+03],
[1.509441335012807031e+02, 5.533624866498719712e+03],
[1.658909029574851957e+02, 5.574409097042514986e+03],
[2.027292548049981633e+02, 5.613492745195001589e+03],
[1.752101578176061594e+02, 5.650738842182393455e+03],
[1.452808749847536092e+02, 5.686137125015246056e+03],
[1.535481629475025329e+02, 5.719786837052497503e+03],
[1.376169777998875361e+02, 5.751878022200112355e+03],
[1.257703080340770612e+02, 5.782696691965922582e+03],
[-2.524186846895645431e+01, 5.812614868468956047e+03],
[-6.546618027042404719e+01, 5.842083180270424236e+03],
[1.192352023580315290e+01, 5.871536479764196883e+03],
[1.043482970188742911e+02, 5.901368702981125352e+03],
[2.581376184768396342e+01, 5.931981238152316109e+03],
[6.634330880534071184e+01, 5.963840691194659485e+03],
[-4.236780162594641297e+01, 5.997429801625946311e+03],
[-1.759397735321817891e+02, 6.033272773532181418e+03],
[-1.827933311233055065e+02, 6.071867331123305121e+03],
[-2.472312362505917918e+02, 6.113601236250591683e+03],
[-2.877470049336488955e+02, 6.158748004933649099e+03],
[-2.634066336693540507e+02, 6.207426633669354487e+03],
[-1.819572770763625158e+02, 6.259576277076362203e+03],
[-1.175034606274621183e+02, 6.314971460627461965e+03],
[-4.769898649718379602e+01, 6.373272986497183410e+03],
[1.419578280287896632e+01, 6.434068217197121157e+03],
[6.267929662760798237e+01, 6.496914703372392069e+03],
[6.196413196753746888e+01, 6.561378868032462378e+03],
[5.019769125317907310e+01, 6.627066308746821051e+03],
[4.665364933213822951e+01, 6.693621350667861407e+03],
[3.662430749527266016e+01, 6.760719692504727391e+03],
[7.545680850246480986e+01, 6.828066191497535328e+03],
[6.052940492147536133e+01, 6.895388595078524304e+03],
[6.029518881462354329e+01, 6.962461811185376064e+03],
[2.187042136652689805e+01, 7.029098578633473153e+03],
[2.380067926824722235e+01, 7.095149320731752596e+03],
[-7.119129802169481991e+00, 7.160478129802169860e+03],
[-3.194497359120850888e+01, 7.224963973591208742e+03],
[-1.897137038934124575e+01, 7.288481370389341464e+03],
[-1.832687287845146784e+01, 7.350884872878451461e+03],
[4.600482336597542599e+01, 7.412017176634024509e+03],
[2.489047706403016491e+01, 7.471709522935970199e+03],
[6.305909392127250612e+01, 7.529821906078727807e+03],
[4.585212309498183458e+01, 7.586229876905018500e+03],
[9.314260180878318351e+01, 7.640848398191216802e+03],
[1.129819097095369216e+02, 7.693621090290463144e+03],
[1.204662123176703972e+02, 7.744549787682329224e+03],
[1.336860614601246198e+02, 7.793706938539875409e+03],
[1.034567175813735957e+02, 7.841240282418626521e+03],
[1.403118873372050075e+02, 7.887381112662795204e+03],
[1.271726169351004501e+02, 7.932425383064899506e+03],
[8.271925765282139764e+01, 7.976756742347178260e+03],
[-3.197432211752584408e+01, 8.020838322117525422e+03],
[-1.150209535194062482e+02, 8.065184953519406008e+03],
[-1.064694837456772802e+02, 8.110291483745677397e+03],
[-1.190428718925368230e+02, 8.156580871892536379e+03],
[-1.353635336292991269e+02, 8.204409533629299403e+03],
[-9.644348283027102298e+01, 8.254059482830271008e+03],
[-6.143413116116607853e+01, 8.305728131161165948e+03],
[-3.019161311097923317e+01, 8.359552613110980019e+03],
[1.384333163552582846e+00, 8.415631666836447039e+03],
[-4.156016073666614830e+01, 8.474045160736666730e+03],
[-4.843882841860977351e+01, 8.534873828418609264e+03],
[-6.706442838867042155e+01, 8.598172428388670596e+03],
[-2.019644488579979225e+01, 8.663965444885800025e+03],
[-4.316446881084630149e+00, 8.732235446881084499e+03],
[4.435061943264736328e+01, 8.802952380567352520e+03],
[2.820550564155564643e+01, 8.876083494358445023e+03],
[5.155624419490777655e+01, 8.951623755805092514e+03],
[-4.318760899315748247e+00, 9.029585760899315574e+03],
[-6.534632828542271454e+01, 9.110014328285422380e+03],
[-7.226757738268497633e+01, 9.192951577382684263e+03],
[-9.412378615444868046e+01, 9.278398786154448317e+03],
[-1.191240653288368776e+02, 9.366312065328836979e+03],
[-4.953669826751865912e+01, 9.456588698267518339e+03],
[-6.017251579067487910e+01, 9.549051515790675694e+03],
[-5.103438828313483100e+01, 9.643492388283135369e+03],
[-7.343057830678117170e+01, 9.739665578306781754e+03],
[-2.774245193054957781e+01, 9.837293451930549054e+03],
[-3.380481112519191811e+00, 9.936052481112519672e+03],
[-2.672779877794346248e+01, 1.003560179877794326e+04],
[-3.217342505148371856e+01, 1.013559842505148299e+04],
[-4.140567518359966925e+01, 1.023568267518359971e+04],
[-6.687756033938057953e+00, 1.033547475603393832e+04],
[7.300600408459467872e+01, 1.043456899591540605e+04],
[6.862345670680042531e+01, 1.053255554329319966e+04],
[5.497882461487461114e+01, 1.062907017538512628e+04],
[9.612244093055960548e+01, 1.072379155906944106e+04],
[1.978212770103891671e+02, 1.081643272298961165e+04],
[1.362772276848754700e+02, 1.090676677231512440e+04],
[2.637635494867263333e+02, 1.099469045051327339e+04],
[1.876813256815166824e+02, 1.108018567431848351e+04],
[1.711447873158413131e+02, 1.116339921268415856e+04],
[5.257586460826678376e+01, 1.124459513539173349e+04],
[4.710652228531762375e+01, 1.132414447771468258e+04],
[-6.237613484241046535e+01, 1.140245113484241119e+04],
[-9.982044354035315337e+01, 1.147994844354035376e+04],
[-7.916275548997509759e+01, 1.155703075548997549e+04],
[-9.526003459472303803e+01, 1.163403003459472347e+04],
[-1.147987680369169539e+02, 1.171122876803691724e+04],
[-1.900259054765901965e+02, 1.178884990547659072e+04],
[-2.212256473439556430e+02, 1.186704464734395515e+04],
[-2.071394278781845060e+02, 1.194584542787818464e+04],
[-8.968541528904825100e+01, 1.202514641528904758e+04],
[-6.189531564415665343e+01, 1.210471231564415575e+04],
[-5.662878162551714922e+01, 1.218425178162551674e+04],
[-4.961678134413705266e+01, 1.226343478134413635e+04],
[-3.836288992144181975e+01, 1.234189588992144127e+04],
[-8.956671991456460091e+00, 1.241923867199145570e+04],
[3.907028461866866564e+01, 1.249504271538133071e+04],
[1.865299000184495526e+01, 1.256888200999815490e+04],
[4.279803532226833340e+01, 1.264035496467773191e+04],
[3.962735362631610769e+01, 1.270907164637368442e+04],
[1.412691291877854383e+02, 1.277466887081221466e+04],
[1.256537791844366438e+02, 1.283680822081556289e+04],
[7.067642758858892194e+01, 1.289523957241141034e+04],
[1.108876647603192396e+02, 1.294979133523968085e+04],
[9.956490829291760747e+01, 1.300033609170708223e+04],
[1.571612709880937473e+02, 1.304681572901190702e+04],
[2.318746375812715996e+02, 1.308923436241872878e+04],
[2.635546670125277160e+02, 1.312769433298747208e+04],
[2.044220965739259555e+02, 1.316244290342607383e+04],
[2.213739418903714977e+02, 1.319389205810962812e+04],
[1.020184547767112235e+02, 1.322258154522328914e+04],
[-1.072694716663390864e+02, 1.324918947166633916e+04],
[-3.490477058718843182e+02, 1.327445770587188417e+04],
[-3.975570728533530200e+02, 1.329906107285335383e+04],
[-3.331152428080622485e+02, 1.332345624280806260e+04]])
dta = macrodata.load_pandas().data['realgdp'].values
res = np.column_stack((hpfilter(dta, 1600)))
assert_almost_equal(res, hpfilt_res, 6)
class TestKPSS(object):
"""
R-code
------
library(tseries)
kpss.stat(x, "Level")
kpss.stat(x, "Trend")
In this context, x is the vector containing the
macrodata['realgdp'] series.
"""
data = macrodata.load_pandas()
x = data.data['realgdp'].values
def test_fail_nonvector_input(self):
with warnings.catch_warnings(record=True):
unit_root.kpss(self.x) # should be fine
x = np.random.rand(20, 2)
with pytest.raises(ValueError):
unit_root.kpss(x)
@pytest.mark.smoke # TODO: the last one isnt smoke
def test_fail_unclear_hypothesis(self):
# these should be fine
with warnings.catch_warnings(record=True):
unit_root.kpss(self.x, 'c')
unit_root.kpss(self.x, 'C')
unit_root.kpss(self.x, 'ct')
unit_root.kpss(self.x, 'CT')
with pytest.raises(ValueError):
unit_root.kpss(self.x, "unclear hypothesis")
def test_teststat(self):
with warnings.catch_warnings(record=True):
kpss_stat, pval, lags, crits = unit_root.kpss(self.x, 'c', 3)
assert_almost_equal(kpss_stat, 5.0169, 3)
with warnings.catch_warnings(record=True):
kpss_stat, pval, lags, crits = unit_root.kpss(self.x, 'ct', 3)
assert_almost_equal(kpss_stat, 1.1828, 3)
def test_pval(self):
with warnings.catch_warnings(record=True):
kpss_stat, pval, lags, crits = unit_root.kpss(self.x, 'c', 3)
assert pval == 0.01
with warnings.catch_warnings(record=True):
kpss_stat, pval, lags, crits = unit_root.kpss(self.x, 'ct', 3)
assert pval == 0.01
def test_store(self):
with warnings.catch_warnings(record=True):
kpss_stat, pval, crit, store = unit_root.kpss(self.x, 'c', 3, True)
# assert attributes, and make sure they're correct
assert store.nobs == len(self.x)
assert store.lags == 3
def test_lags(self):
with warnings.catch_warnings(record=True):
kpss_stat, pval, lags, crits = unit_root.kpss(self.x, 'c')
assert_equal(lags,
int(np.ceil(12. * np.power(len(self.x) / 100., 1 / 4.))))
def test_bking2d():
# Test Baxter-King band-pass filter with 2d input
bking_results = np.array([[7.320813, -.0374475], [2.886914, -.0430094],
[-6.818976, -.053456], [-13.49436, -.0620739],
[-13.27936, -.0626929], [-9.405913, -.0603022],
[-5.691091, -.0630016], [-5.133076, -.0832268],
[-7.273468, -.1186448], [-9.243364, -.1619868],
[-8.482916, -.2116604], [-4.447764, -.2670747],
[2.406559, -.3209931], [10.68433, -.3583075],
[19.46414, -.3626742], [28.09749, -.3294618],
[34.11066, -.2773388], [33.48468, -.2436127],
[24.64598, -.2605531], [9.952399, -.3305166],
[-4.265528, -.4275561], [-12.59471, -.5076068],
[-13.46714, -.537573], [-9.049501, -.5205845],
[-3.011248, -.481673], [.5655082, -.4403994],
[2.897976, -.4039957], [7.406077, -.3537394],
[14.67959, -.2687359], [18.651, -.1459743],
[13.05891, .0014926], [-2.945415, .1424277],
[-24.08659, .2451936], [-41.86147, .288541],
[-48.68383, .2727282], [-43.32689, .1959127],
[-31.66654, .0644874], [-20.38356, -.1158372],
[-13.76411, -.3518627], [-9.978693, -.6557535],
[-3.7704, -1.003754], [10.27108, -1.341632],
[31.02847, -1.614486], [51.87613, -1.779089],
[66.93117, -1.807459], [73.51951, -1.679688],
[73.4053, -1.401012], [69.17468, -.9954996],
[59.8543, -.511261], [38.23899, -.0146745],
[-.2604809, .4261311], [-49.0107, .7452514],
[-91.1128, .8879492], [-112.1574, .8282748],
[-108.3227, .5851508], [-86.51453, .2351699],
[-59.91258, -.1208998], [-40.01185, -.4297895],
[-29.70265, -.6821963], [-22.76396, -.9234254],
[-13.08037, -1.217539], [1.913622, -1.57367],
[20.44045, -1.927008], [37.32873, -2.229565],
[46.79802, -2.463154], [51.95937, -2.614697],
[59.67393, -2.681357], [70.50803, -2.609654],
[81.27311, -2.301618], [83.53191, -1.720974],
[67.72536, -.9837123], [33.78039, -.2261613],
[-6.509092, .4546985], [-37.31579, 1.005751],
[-46.05207, 1.457224], [-29.81496, 1.870815],
[1.416417, 2.263313], [28.31503, 2.599906],
[32.90134, 2.812282], [8.949259, 2.83358],
[-35.41895, 2.632667], [-84.65775, 2.201077],
[-124.4288, 1.598951], [-144.6036, .9504762],
[-140.2204, .4187932], [-109.2624, .1646726],
[-53.6901, .2034265], [15.07415, .398165],
[74.44268, .5427476], [104.0403, .5454975],
[101.0725, .4723354], [76.58291, .4626823],
[49.27925, .5840143], [36.15751, .7187981],
[36.48799, .6058422], [37.60897, .1221227],
[27.75998, -.5891272], [4.216643, -1.249841],
[-23.20579, -1.594972], [-39.33292, -1.545968],
[-36.6134, -1.275494], [-20.90161, -1.035783],
[-4.143123, -.9971732], [5.48432, -1.154264],
[9.270075, -1.29987], [13.69573, -1.240559],
[22.16675, -.9662656], [33.01987, -.6420301],
[41.93186, -.4698712], [47.12222, -.4527797],
[48.62164, -.4407153], [47.30701, -.2416076],
[40.20537, .2317583], [22.37898, .8710276],
[-7.133002, 1.426177], [-43.3339, 1.652785],
[-78.51229, 1.488021], [-101.3684, 1.072096],
[-105.2179, .6496446], [-90.97147, .4193682],
[-68.30824, .41847], [-48.10113, .5253419],
[-35.60709, .595076], [-31.15775, .5509905],
[-31.82346, .3755519], [-32.49278, .1297979],
[-28.22499, -.0916165], [-14.42852, -.2531037],
[10.1827, -.3220784], [36.64189, -.2660561],
[49.43468, -.1358522], [38.75517, -.0279508],
[6.447761, .0168735], [-33.15883, .0315687],
[-62.60446, .0819507], [-72.87829, .2274033],
[-66.54629, .4641401], [-52.61205, .7211093],
[-38.06676, .907773], [-26.19963, .9387103],
[-16.51492, .7940786], [-7.007577, .5026631],
[.6125674, .1224996], [7.866972, -.2714422],
[14.8123, -.6273921], [22.52388, -.9124271],
[30.65265, -1.108861], [39.47801, -1.199206],
[49.05027, -1.19908], [59.02925, -1.139046],
[72.88999, -.9775021], [95.08865, -.6592603],
[125.8983, -.1609712], [154.4283, .4796201],
[160.7638, 1.100565], [130.6092, 1.447148],
[67.84406, 1.359608], [-7.070272, .8931825],
[-68.08128, .2619787], [-99.39944, -.252208],
[-104.911, -.4703874], [-100.2372, -.4430657],
[-98.11596, -.390683], [-104.2051, -.5647846],
[-114.0125, -.9397582], [-113.3475, -1.341633],
[-92.98669, -1.567337], [-51.91707, -1.504943],
[-.7313812, -1.30576], [43.22938, -1.17151],
[64.62762, -1.136151], [64.07226, -1.050555],
[59.35707, -.7308369], [67.06026, -.1766731],
[91.87247, .3898467], [124.4591, .8135461],
[151.2402, .9644226], [163.0648, .6865934],
[154.6432, .0115685]])
X = macrodata.load_pandas().data[['realinv', 'cpi']].values.astype('f8')
Y = bkfilter(X, 6, 32, 12)
assert_almost_equal(Y, bking_results, 4)
