def test_hac_simple():
from gwstatsmodels.datasets import macrodata
d2 = macrodata.load().data
g_gdp = 400 * np.diff(np.log(d2["realgdp"]))
g_inv = 400 * np.diff(np.log(d2["realinv"]))
exogg = add_constant(np.c_[g_gdp, d2["realint"][:-1]], prepend=True)
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, se1 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=True)
cov2, se2 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=False)
assert_almost_equal(cov1, cov1_r, decimal=14)
assert_almost_equal(cov2, cov2_r, decimal=14)
def test_hac_simple():
from gwstatsmodels.datasets import macrodata
d2 = macrodata.load().data
g_gdp = 400 * np.diff(np.log(d2['realgdp']))
g_inv = 400 * np.diff(np.log(d2['realinv']))
exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1]], prepend=True)
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, se1 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=True)
cov2, se2 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=False)
assert_almost_equal(cov1, cov1_r, decimal=14)
assert_almost_equal(cov2, cov2_r, decimal=14)
def notyet_atst():
d = macrodata.load().data
realinv = d['realinv']
realgdp = d['realgdp']
realint = d['realint']
endog = realinv
exog = add_constant(np.c_[realgdp, realint],prepend=True)
res_ols1 = OLS(endog, exog).fit()
#growth rates
gs_l_realinv = 400 * np.diff(np.log(d['realinv']))
gs_l_realgdp = 400 * np.diff(np.log(d['realgdp']))
lint = d['realint'][:-1]
tbilrate = d['tbilrate'][:-1]
endogg = gs_l_realinv
exogg = add_constant(np.c_[gs_l_realgdp, lint], prepend=True)
exogg2 = add_constant(np.c_[gs_l_realgdp, tbilrate], prepend=True)
res_ols = OLS(endogg, exogg).fit()
res_ols2 = OLS(endogg, exogg2).fit()
#the following were done accidentally with res_ols1 in R,
#with original Greene data
params = np.array([-272.3986041341653, 0.1779455206941112,
0.2149432424658157])
cov_hac_4 = np.array([1321.569466333051, -0.2318836566017612,
37.01280466875694, -0.2318836566017614, 4.602339488102263e-05,
-0.0104687835998635, 37.012804668757, -0.0104687835998635,
21.16037144168061]).reshape(3,3, order='F')
cov_hac_10 = np.array([2027.356101193361, -0.3507514463299015,
54.81079621448568, -0.350751446329901, 6.953380432635583e-05,
-0.01268990195095196, 54.81079621448564, -0.01268990195095195,
22.92512402151113]).reshape(3,3, order='F')
#goldfeld-quandt
het_gq_greater = dict(statistic=13.20512768685082, df1=99, df2=98,
pvalue=1.246141976112324e-30, distr='f')
het_gq_less = dict(statistic=13.20512768685082, df1=99, df2=98, pvalue=1.)
het_gq_2sided = dict(statistic=13.20512768685082, df1=99, df2=98,
pvalue=1.246141976112324e-30, distr='f')
#goldfeld-quandt, fraction = 0.5
het_gq_greater_2 = dict(statistic=87.1328934692124, df1=48, df2=47,
pvalue=2.154956842194898e-33, distr='f')
gq = smsdia.het_goldfeldquandt(endog, exog, split=0.5)
compare_t_est(gq, het_gq_greater, decimal=(13, 14))
assert_equal(gq[-1], 'increasing')
harvey_collier = dict(stat=2.28042114041313, df=199,
pvalue=0.02364236161988260, distr='t')
#hc = harvtest(fm, order.by=ggdp , data = list())
harvey_collier_2 = dict(stat=0.7516918462158783, df=199,
pvalue=0.4531244858006127, distr='t')
class CheckCorrGram(object):
"""
Set up for ACF, PACF tests.
"""
data = macrodata.load()
x = data.data['realgdp']
filename = os.path.dirname(os.path.abspath(__file__))+\
"/results/results_corrgram.csv"
results = genfromtxt(open(filename, "rb"),
delimiter=",",
names=True,
dtype=float)
def test_grangercausality():
# some example data
mdata = macrodata.load().data
mdata = mdata[['realgdp','realcons']]
data = mdata.view((float,2))
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)
class CheckCoint(object):
"""
Test Cointegration Test Results for 2-variable system
Test values taken from Stata
"""
levels = ['1%', '5%', '10%']
data = macrodata.load()
y1 = data.data['realcons']
y2 = data.data['realgdp']
def test_tstat(self):
assert_almost_equal(self.coint_t, self.teststat, DECIMAL_4)
def test_grangercausality():
# some example data
mdata = macrodata.load().data
mdata = mdata[['realgdp', 'realcons']]
data = mdata.view((float, 2))
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_bking1d():
"""
Test Baxter King band-pass filter. Results are taken from Stata
"""
bking_results = 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().data['realinv']
Y = bkfilter(X, 6, 32, 12)
assert_almost_equal(Y,bking_results,4)
class CheckADF(object):
"""
Test Augmented Dickey-Fuller
Test values taken from Stata.
"""
levels = ['1%', '5%', '10%']
data = macrodata.load()
x = data.data['realgdp']
y = data.data['infl']
def test_teststat(self):
assert_almost_equal(self.res1[0], self.teststat, DECIMAL_5)
def test_pvalue(self):
assert_almost_equal(self.res1[1], self.pvalue, DECIMAL_5)
def test_critvalues(self):
critvalues = [self.res1[4][lev] for lev in self.levels]
assert_almost_equal(critvalues, self.critvalues, DECIMAL_2)
def __init__(self):
d = macrodata.load().data
#growth rates
gs_l_realinv = 400 * np.diff(np.log(d['realinv']))
gs_l_realgdp = 400 * np.diff(np.log(d['realgdp']))
lint = d['realint'][:-1]
tbilrate = d['tbilrate'][:-1]
endogg = gs_l_realinv
exogg = add_constant(np.c_[gs_l_realgdp, lint], prepend=True)
exogg2 = add_constant(np.c_[gs_l_realgdp, tbilrate], prepend=True)
exogg3 = add_constant(np.c_[gs_l_realgdp], prepend=True)
res_ols = OLS(endogg, exogg).fit()
res_ols2 = OLS(endogg, exogg2).fit()
res_ols3 = OLS(endogg, exogg3).fit()
self.res = res_ols
self.res2 = res_ols2
self.res3 = res_ols3
self.endog = self.res.model.endog
self.exog = self.res.model.exog
def test_all(self):
d = macrodata.load().data
#import datasetswsm.greene as g
#d = g.load('5-1')
#growth rates
gs_l_realinv = 400 * np.diff(np.log(d['realinv']))
gs_l_realgdp = 400 * np.diff(np.log(d['realgdp']))
#simple diff, not growthrate, I want heteroscedasticity later for testing
endogd = np.diff(d['realinv'])
exogd = add_constant(np.c_[np.diff(d['realgdp']), d['realint'][:-1]],
prepend=True)
endogg = gs_l_realinv
exogg = add_constant(np.c_[gs_l_realgdp, d['realint'][:-1]],
prepend=True)
res_ols = OLS(endogg, exogg).fit()
#print res_ols.params
mod_g1 = GLSAR(endogg, exogg, rho=-0.108136)
res_g1 = mod_g1.fit()
#print res_g1.params
mod_g2 = GLSAR(endogg, exogg, rho=-0.108136) #-0.1335859) from R
res_g2 = mod_g2.iterative_fit(maxiter=5)
#print res_g2.params
rho = -0.108136
# coefficient std. error t-ratio p-value 95% CONFIDENCE INTERVAL
partable = np.array([
[-9.50990, 0.990456, -9.602, 3.65e-018, -11.4631, -7.55670], # ***
[4.37040, 0.208146, 21.00, 2.93e-052, 3.95993, 4.78086], # ***
[-0.579253, 0.268009, -2.161, 0.0319, -1.10777, -0.0507346]
]) # **
#Statistics based on the rho-differenced data:
result_gretl_g1 = dict(endog_mean=("Mean dependent var", 3.113973),
endog_std=("S.D. dependent var", 18.67447),
ssr=("Sum squared resid", 22530.90),
mse_resid_sqrt=("S.E. of regression", 10.66735),
rsquared=("R-squared", 0.676973),
rsquared_adj=("Adjusted R-squared", 0.673710),
fvalue=("F(2, 198)", 221.0475),
f_pvalue=("P-value(F)", 3.56e-51),
resid_acf1=("rho", -0.003481),
dw=("Durbin-Watson", 1.993858))
#fstatistic, p-value, df1, df2
reset_2_3 = [5.219019, 0.00619, 2, 197, "f"]
reset_2 = [7.268492, 0.00762, 1, 198, "f"]
reset_3 = [5.248951, 0.023, 1, 198, "f"]
#LM-statistic, p-value, df
arch_4 = [7.30776, 0.120491, 4, "chi2"]
#multicollinearity
vif = [1.002, 1.002]
cond_1norm = 6862.0664
determinant = 1.0296049e+009
reciprocal_condition_number = 0.013819244
#Chi-square(2): test-statistic, pvalue, df
normality = [20.2792, 3.94837e-005, 2]
#tests
res = res_g1 #with rho from Gretl
#basic
assert_almost_equal(res.params, partable[:, 0], 4)
assert_almost_equal(res.bse, partable[:, 1], 6)
assert_almost_equal(res.tvalues, partable[:, 2], 2)
assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
#assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
#assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL
#assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL
assert_almost_equal(np.sqrt(res.mse_resid),
result_gretl_g1['mse_resid_sqrt'][1],
decimal=5)
assert_almost_equal(res.fvalue,
result_gretl_g1['fvalue'][1],
decimal=4)
assert_approx_equal(res.f_pvalue,
result_gretl_g1['f_pvalue'][1],
significant=2)
#assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO
#arch
#sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None)
sm_arch = smsdia.het_arch(res.wresid, maxlag=4)
assert_almost_equal(sm_arch[0], arch_4[0], decimal=4)
assert_almost_equal(sm_arch[1], arch_4[1], decimal=6)
#tests
res = res_g2 #with estimated rho
#estimated lag coefficient
assert_almost_equal(res.model.rho, rho, decimal=3)
#basic
assert_almost_equal(res.params, partable[:, 0], 4)
assert_almost_equal(res.bse, partable[:, 1], 3)
assert_almost_equal(res.tvalues, partable[:, 2], 2)
assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
#assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
#assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL
#assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL
assert_almost_equal(np.sqrt(res.mse_resid),
result_gretl_g1['mse_resid_sqrt'][1],
decimal=5)
assert_almost_equal(res.fvalue,
result_gretl_g1['fvalue'][1],
decimal=0)
assert_almost_equal(res.f_pvalue,
result_gretl_g1['f_pvalue'][1],
decimal=6)
#assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO
c = oi.reset_ramsey(res, degree=2)
compare_ftest(c, reset_2, decimal=(2, 4))
c = oi.reset_ramsey(res, degree=3)
compare_ftest(c, reset_2_3, decimal=(2, 4))
#arch
#sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None)
sm_arch = smsdia.het_arch(res.wresid, maxlag=4)
assert_almost_equal(sm_arch[0], arch_4[0], decimal=1)
assert_almost_equal(sm_arch[1], arch_4[1], decimal=2)
'''
Performing iterative calculation of rho...
ITER RHO ESS
1 -0.10734 22530.9
2 -0.10814 22530.9
Model 4: Cochrane-Orcutt, using observations 1959:3-2009:3 (T = 201)
Dependent variable: ds_l_realinv
rho = -0.108136
coefficient std. error t-ratio p-value
-------------------------------------------------------------
const -9.50990 0.990456 -9.602 3.65e-018 ***
ds_l_realgdp 4.37040 0.208146 21.00 2.93e-052 ***
realint_1 -0.579253 0.268009 -2.161 0.0319 **
Statistics based on the rho-differenced data:
Mean dependent var 3.113973 S.D. dependent var 18.67447
Sum squared resid 22530.90 S.E. of regression 10.66735
R-squared 0.676973 Adjusted R-squared 0.673710
F(2, 198) 221.0475 P-value(F) 3.56e-51
rho -0.003481 Durbin-Watson 1.993858
'''
'''
RESET test for specification (squares and cubes)
Test statistic: F = 5.219019,
with p-value = P(F(2,197) > 5.21902) = 0.00619
RESET test for specification (squares only)
Test statistic: F = 7.268492,
with p-value = P(F(1,198) > 7.26849) = 0.00762
RESET test for specification (cubes only)
Test statistic: F = 5.248951,
with p-value = P(F(1,198) > 5.24895) = 0.023:
'''
'''
Test for ARCH of order 4
coefficient std. error t-ratio p-value
--------------------------------------------------------
alpha(0) 97.0386 20.3234 4.775 3.56e-06 ***
alpha(1) 0.176114 0.0714698 2.464 0.0146 **
alpha(2) -0.0488339 0.0724981 -0.6736 0.5014
alpha(3) -0.0705413 0.0737058 -0.9571 0.3397
alpha(4) 0.0384531 0.0725763 0.5298 0.5968
Null hypothesis: no ARCH effect is present
Test statistic: LM = 7.30776
with p-value = P(Chi-square(4) > 7.30776) = 0.120491:
'''
'''
Variance Inflation Factors
Minimum possible value = 1.0
Values > 10.0 may indicate a collinearity problem
ds_l_realgdp 1.002
realint_1 1.002
VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlation coefficient
between variable j and the other independent variables
Properties of matrix X'X:
1-norm = 6862.0664
Determinant = 1.0296049e+009
Reciprocal condition number = 0.013819244
'''
'''
Test for ARCH of order 4 -
Null hypothesis: no ARCH effect is present
Test statistic: LM = 7.30776
with p-value = P(Chi-square(4) > 7.30776) = 0.120491
Test of common factor restriction -
Null hypothesis: restriction is acceptable
Test statistic: F(2, 195) = 0.426391
with p-value = P(F(2, 195) > 0.426391) = 0.653468
Test for normality of residual -
Null hypothesis: error is normally distributed
Test statistic: Chi-square(2) = 20.2792
with p-value = 3.94837e-005:
'''
#no idea what this is
'''
Augmented regression for common factor test
OLS, using observations 1959:3-2009:3 (T = 201)
Dependent variable: ds_l_realinv
coefficient std. error t-ratio p-value
---------------------------------------------------------------
const -10.9481 1.35807 -8.062 7.44e-014 ***
ds_l_realgdp 4.28893 0.229459 18.69 2.40e-045 ***
realint_1 -0.662644 0.334872 -1.979 0.0492 **
ds_l_realinv_1 -0.108892 0.0715042 -1.523 0.1294
ds_l_realgdp_1 0.660443 0.390372 1.692 0.0923 *
realint_2 0.0769695 0.341527 0.2254 0.8219
Sum of squared residuals = 22432.8
Test of common factor restriction
Test statistic: F(2, 195) = 0.426391, with p-value = 0.653468
'''
################ with OLS, HAC errors
#Model 5: OLS, using observations 1959:2-2009:3 (T = 202)
#Dependent variable: ds_l_realinv
#HAC standard errors, bandwidth 4 (Bartlett kernel)
#coefficient std. error t-ratio p-value 95% CONFIDENCE INTERVAL
#for confidence interval t(199, 0.025) = 1.972
partable = np.array([
[-9.48167, 1.17709, -8.055, 7.17e-014, -11.8029, -7.16049], # ***
[4.37422, 0.328787, 13.30, 2.62e-029, 3.72587, 5.02258], #***
[-0.613997, 0.293619, -2.091, 0.0378, -1.19300, -0.0349939]
]) # **
result_gretl_g1 = dict(endog_mean=("Mean dependent var", 3.257395),
endog_std=("S.D. dependent var", 18.73915),
ssr=("Sum squared resid", 22799.68),
mse_resid_sqrt=("S.E. of regression", 10.70380),
rsquared=("R-squared", 0.676978),
rsquared_adj=("Adjusted R-squared", 0.673731),
fvalue=("F(2, 199)", 90.79971),
f_pvalue=("P-value(F)", 9.53e-29),
llf=("Log-likelihood", -763.9752),
aic=("Akaike criterion", 1533.950),
bic=("Schwarz criterion", 1543.875),
hqic=("Hannan-Quinn", 1537.966),
resid_acf1=("rho", -0.107341),
dw=("Durbin-Watson", 2.213805))
linear_logs = [1.68351, 0.430953, 2, "chi2"]
#for logs: dropping 70 nan or incomplete observations, T=133
#(res_ols.model.exog <=0).any(1).sum() = 69 ?not 70
linear_squares = [7.52477, 0.0232283, 2, "chi2"]
#Autocorrelation, Breusch-Godfrey test for autocorrelation up to order 4
lm_acorr4 = [1.17928, 0.321197, 4, 195, "F"]
lm2_acorr4 = [4.771043, 0.312, 4, "chi2"]
acorr_ljungbox4 = [5.23587, 0.264, 4, "chi2"]
#break
cusum_Harvey_Collier = [0.494432, 0.621549, 198,
"t"] #stats.t.sf(0.494432, 198)*2
#see cusum results in files
break_qlr = [3.01985, 0.1, 3, 196,
"maxF"] #TODO check this, max at 2001:4
break_chow = [13.1897, 0.00424384, 3, "chi2"] # break at 1984:1
arch_4 = [3.43473, 0.487871, 4, "chi2"]
normality = [23.962, 0.00001, 2, "chi2"]
het_white = [33.503723, 0.000003, 5, "chi2"]
het_breush_pagan = [1.302014, 0.521520, 2,
"chi2"] #TODO: not available
het_breush_pagan_konker = [0.709924, 0.701200, 2, "chi2"]
reset_2_3 = [5.219019, 0.00619, 2, 197, "f"]
reset_2 = [7.268492, 0.00762, 1, 198, "f"]
reset_3 = [5.248951, 0.023, 1, 198, "f"] #not available
cond_1norm = 5984.0525
determinant = 7.1087467e+008
reciprocal_condition_number = 0.013826504
vif = [1.001, 1.001]
names = 'date residual leverage influence DFFITS'.split(
)
cur_dir = os.path.abspath(os.path.dirname(__file__))
fpath = os.path.join(cur_dir,
'results/leverage_influence_ols_nostars.txt')
lev = np.genfromtxt(fpath,
skip_header=3,
skip_footer=1,
converters={0: lambda s: s})
#either numpy 1.6 or python 3.2 changed behavior
if np.isnan(lev[-1]['f1']):
lev = np.genfromtxt(fpath,
skip_header=3,
skip_footer=2,
converters={0: lambda s: s})
lev.dtype.names = names
res = res_ols #for easier copying
cov_hac, bse_hac = sw.cov_hac_simple(res,
nlags=4,
use_correction=False)
assert_almost_equal(res.params, partable[:, 0], 5)
assert_almost_equal(bse_hac, partable[:, 1], 5)
#TODO
assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
#assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
assert_almost_equal(res.rsquared,
result_gretl_g1['rsquared'][1],
decimal=6) #FAIL
assert_almost_equal(res.rsquared_adj,
result_gretl_g1['rsquared_adj'][1],
decimal=6) #FAIL
assert_almost_equal(np.sqrt(res.mse_resid),
result_gretl_g1['mse_resid_sqrt'][1],
decimal=5)
#f-value is based on cov_hac I guess
#assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=0) #FAIL
#assert_approx_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], significant=1) #FAIL
#assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO
c = oi.reset_ramsey(res, degree=2)
compare_ftest(c, reset_2, decimal=(6, 5))
c = oi.reset_ramsey(res, degree=3)
compare_ftest(c, reset_2_3, decimal=(6, 5))
linear_sq = smsdia.linear_lm(res.resid, res.model.exog)
assert_almost_equal(linear_sq[0], linear_squares[0], decimal=6)
assert_almost_equal(linear_sq[1], linear_squares[1], decimal=7)
hbpk = smsdia.het_breushpagan(res.resid, res.model.exog)
assert_almost_equal(hbpk[0], het_breush_pagan_konker[0], decimal=6)
assert_almost_equal(hbpk[1], het_breush_pagan_konker[1], decimal=6)
hw = smsdia.het_white(res.resid, res.model.exog)
assert_almost_equal(hw[:2], het_white[:2], 6)
#arch
#sm_arch = smsdia.acorr_lm(res.resid**2, maxlag=4, autolag=None)
sm_arch = smsdia.het_arch(res.resid, maxlag=4)
assert_almost_equal(sm_arch[0], arch_4[0], decimal=5)
assert_almost_equal(sm_arch[1], arch_4[1], decimal=6)
vif2 = [
oi.variance_inflation_factor(res.model.exog, k) for k in [1, 2]
]
infl = oi.OLSInfluence(res_ols)
#print np.max(np.abs(lev['DFFITS'] - infl.dffits[0]))
#print np.max(np.abs(lev['leverage'] - infl.hat_matrix_diag))
#print np.max(np.abs(lev['influence'] - infl.influence)) #just added this based on Gretl
#just rough test, low decimal in Gretl output,
assert_almost_equal(lev['residual'], res.resid, decimal=3)
assert_almost_equal(lev['DFFITS'], infl.dffits[0], decimal=3)
assert_almost_equal(lev['leverage'], infl.hat_matrix_diag, decimal=3)
assert_almost_equal(lev['influence'], infl.influence, decimal=4)
def test_all(self):
d = macrodata.load().data
#import datasetswsm.greene as g
#d = g.load('5-1')
#growth rates
gs_l_realinv = 400 * np.diff(np.log(d['realinv']))
gs_l_realgdp = 400 * np.diff(np.log(d['realgdp']))
#simple diff, not growthrate, I want heteroscedasticity later for testing
endogd = np.diff(d['realinv'])
exogd = add_constant(np.c_[np.diff(d['realgdp']), d['realint'][:-1]],
prepend=True)
endogg = gs_l_realinv
exogg = add_constant(np.c_[gs_l_realgdp, d['realint'][:-1]],prepend=True)
res_ols = OLS(endogg, exogg).fit()
#print res_ols.params
mod_g1 = GLSAR(endogg, exogg, rho=-0.108136)
res_g1 = mod_g1.fit()
#print res_g1.params
mod_g2 = GLSAR(endogg, exogg, rho=-0.108136) #-0.1335859) from R
res_g2 = mod_g2.iterative_fit(maxiter=5)
#print res_g2.params
rho = -0.108136
# coefficient std. error t-ratio p-value 95% CONFIDENCE INTERVAL
partable = np.array([
[-9.50990, 0.990456, -9.602, 3.65e-018, -11.4631, -7.55670], # ***
[ 4.37040, 0.208146, 21.00, 2.93e-052, 3.95993, 4.78086], # ***
[-0.579253, 0.268009, -2.161, 0.0319, -1.10777, -0.0507346]]) # **
#Statistics based on the rho-differenced data:
result_gretl_g1 = dict(
endog_mean = ("Mean dependent var", 3.113973),
endog_std = ("S.D. dependent var", 18.67447),
ssr = ("Sum squared resid", 22530.90),
mse_resid_sqrt = ("S.E. of regression", 10.66735),
rsquared = ("R-squared", 0.676973),
rsquared_adj = ("Adjusted R-squared", 0.673710),
fvalue = ("F(2, 198)", 221.0475),
f_pvalue = ("P-value(F)", 3.56e-51),
resid_acf1 = ("rho", -0.003481),
dw = ("Durbin-Watson", 1.993858))
#fstatistic, p-value, df1, df2
reset_2_3 = [5.219019, 0.00619, 2, 197, "f"]
reset_2 = [7.268492, 0.00762, 1, 198, "f"]
reset_3 = [5.248951, 0.023, 1, 198, "f"]
#LM-statistic, p-value, df
arch_4 = [7.30776, 0.120491, 4, "chi2"]
#multicollinearity
vif = [1.002, 1.002]
cond_1norm = 6862.0664
determinant = 1.0296049e+009
reciprocal_condition_number = 0.013819244
#Chi-square(2): test-statistic, pvalue, df
normality = [20.2792, 3.94837e-005, 2]
#tests
res = res_g1 #with rho from Gretl
#basic
assert_almost_equal(res.params, partable[:,0], 4)
assert_almost_equal(res.bse, partable[:,1], 6)
assert_almost_equal(res.tvalues, partable[:,2], 2)
assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
#assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
#assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL
#assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL
assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5)
assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=4)
assert_approx_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], significant=2)
#assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO
#arch
#sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None)
sm_arch = smsdia.het_arch(res.wresid, maxlag=4)
assert_almost_equal(sm_arch[0], arch_4[0], decimal=4)
assert_almost_equal(sm_arch[1], arch_4[1], decimal=6)
#tests
res = res_g2 #with estimated rho
#estimated lag coefficient
assert_almost_equal(res.model.rho, rho, decimal=3)
#basic
assert_almost_equal(res.params, partable[:,0], 4)
assert_almost_equal(res.bse, partable[:,1], 3)
assert_almost_equal(res.tvalues, partable[:,2], 2)
assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
#assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
#assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL
#assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL
assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5)
assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=0)
assert_almost_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], decimal=6)
#assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO
c = oi.reset_ramsey(res, degree=2)
compare_ftest(c, reset_2, decimal=(2,4))
c = oi.reset_ramsey(res, degree=3)
compare_ftest(c, reset_2_3, decimal=(2,4))
#arch
#sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None)
sm_arch = smsdia.het_arch(res.wresid, maxlag=4)
assert_almost_equal(sm_arch[0], arch_4[0], decimal=1)
assert_almost_equal(sm_arch[1], arch_4[1], decimal=2)
'''
Performing iterative calculation of rho...
ITER RHO ESS
1 -0.10734 22530.9
2 -0.10814 22530.9
Model 4: Cochrane-Orcutt, using observations 1959:3-2009:3 (T = 201)
Dependent variable: ds_l_realinv
rho = -0.108136
coefficient std. error t-ratio p-value
-------------------------------------------------------------
const -9.50990 0.990456 -9.602 3.65e-018 ***
ds_l_realgdp 4.37040 0.208146 21.00 2.93e-052 ***
realint_1 -0.579253 0.268009 -2.161 0.0319 **
Statistics based on the rho-differenced data:
Mean dependent var 3.113973 S.D. dependent var 18.67447
Sum squared resid 22530.90 S.E. of regression 10.66735
R-squared 0.676973 Adjusted R-squared 0.673710
F(2, 198) 221.0475 P-value(F) 3.56e-51
rho -0.003481 Durbin-Watson 1.993858
'''
'''
RESET test for specification (squares and cubes)
Test statistic: F = 5.219019,
with p-value = P(F(2,197) > 5.21902) = 0.00619
RESET test for specification (squares only)
Test statistic: F = 7.268492,
with p-value = P(F(1,198) > 7.26849) = 0.00762
RESET test for specification (cubes only)
Test statistic: F = 5.248951,
with p-value = P(F(1,198) > 5.24895) = 0.023:
'''
'''
Test for ARCH of order 4
coefficient std. error t-ratio p-value
--------------------------------------------------------
alpha(0) 97.0386 20.3234 4.775 3.56e-06 ***
alpha(1) 0.176114 0.0714698 2.464 0.0146 **
alpha(2) -0.0488339 0.0724981 -0.6736 0.5014
alpha(3) -0.0705413 0.0737058 -0.9571 0.3397
alpha(4) 0.0384531 0.0725763 0.5298 0.5968
Null hypothesis: no ARCH effect is present
Test statistic: LM = 7.30776
with p-value = P(Chi-square(4) > 7.30776) = 0.120491:
'''
'''
Variance Inflation Factors
Minimum possible value = 1.0
Values > 10.0 may indicate a collinearity problem
ds_l_realgdp 1.002
realint_1 1.002
VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlation coefficient
between variable j and the other independent variables
Properties of matrix X'X:
1-norm = 6862.0664
Determinant = 1.0296049e+009
Reciprocal condition number = 0.013819244
'''
'''
Test for ARCH of order 4 -
Null hypothesis: no ARCH effect is present
Test statistic: LM = 7.30776
with p-value = P(Chi-square(4) > 7.30776) = 0.120491
Test of common factor restriction -
Null hypothesis: restriction is acceptable
Test statistic: F(2, 195) = 0.426391
with p-value = P(F(2, 195) > 0.426391) = 0.653468
Test for normality of residual -
Null hypothesis: error is normally distributed
Test statistic: Chi-square(2) = 20.2792
with p-value = 3.94837e-005:
'''
#no idea what this is
'''
Augmented regression for common factor test
OLS, using observations 1959:3-2009:3 (T = 201)
Dependent variable: ds_l_realinv
coefficient std. error t-ratio p-value
---------------------------------------------------------------
const -10.9481 1.35807 -8.062 7.44e-014 ***
ds_l_realgdp 4.28893 0.229459 18.69 2.40e-045 ***
realint_1 -0.662644 0.334872 -1.979 0.0492 **
ds_l_realinv_1 -0.108892 0.0715042 -1.523 0.1294
ds_l_realgdp_1 0.660443 0.390372 1.692 0.0923 *
realint_2 0.0769695 0.341527 0.2254 0.8219
Sum of squared residuals = 22432.8
Test of common factor restriction
Test statistic: F(2, 195) = 0.426391, with p-value = 0.653468
'''
################ with OLS, HAC errors
#Model 5: OLS, using observations 1959:2-2009:3 (T = 202)
#Dependent variable: ds_l_realinv
#HAC standard errors, bandwidth 4 (Bartlett kernel)
#coefficient std. error t-ratio p-value 95% CONFIDENCE INTERVAL
#for confidence interval t(199, 0.025) = 1.972
partable = np.array([
[-9.48167, 1.17709, -8.055, 7.17e-014, -11.8029, -7.16049], # ***
[4.37422, 0.328787, 13.30, 2.62e-029, 3.72587, 5.02258], #***
[-0.613997, 0.293619, -2.091, 0.0378, -1.19300, -0.0349939]]) # **
result_gretl_g1 = dict(
endog_mean = ("Mean dependent var", 3.257395),
endog_std = ("S.D. dependent var", 18.73915),
ssr = ("Sum squared resid", 22799.68),
mse_resid_sqrt = ("S.E. of regression", 10.70380),
rsquared = ("R-squared", 0.676978),
rsquared_adj = ("Adjusted R-squared", 0.673731),
fvalue = ("F(2, 199)", 90.79971),
f_pvalue = ("P-value(F)", 9.53e-29),
llf = ("Log-likelihood", -763.9752),
aic = ("Akaike criterion", 1533.950),
bic = ("Schwarz criterion", 1543.875),
hqic = ("Hannan-Quinn", 1537.966),
resid_acf1 = ("rho", -0.107341),
dw = ("Durbin-Watson", 2.213805))
linear_logs = [1.68351, 0.430953, 2, "chi2"]
#for logs: dropping 70 nan or incomplete observations, T=133
#(res_ols.model.exog <=0).any(1).sum() = 69 ?not 70
linear_squares = [7.52477, 0.0232283, 2, "chi2"]
#Autocorrelation, Breusch-Godfrey test for autocorrelation up to order 4
lm_acorr4 = [1.17928, 0.321197, 4, 195, "F"]
lm2_acorr4 = [4.771043, 0.312, 4, "chi2"]
acorr_ljungbox4 = [5.23587, 0.264, 4, "chi2"]
#break
cusum_Harvey_Collier = [0.494432, 0.621549, 198, "t"] #stats.t.sf(0.494432, 198)*2
#see cusum results in files
break_qlr = [3.01985, 0.1, 3, 196, "maxF"] #TODO check this, max at 2001:4
break_chow = [13.1897, 0.00424384, 3, "chi2"] # break at 1984:1
arch_4 = [3.43473, 0.487871, 4, "chi2"]
normality = [23.962, 0.00001, 2, "chi2"]
het_white = [33.503723, 0.000003, 5, "chi2"]
het_breush_pagan = [1.302014, 0.521520, 2, "chi2"] #TODO: not available
het_breush_pagan_konker = [0.709924, 0.701200, 2, "chi2"]
reset_2_3 = [5.219019, 0.00619, 2, 197, "f"]
reset_2 = [7.268492, 0.00762, 1, 198, "f"]
reset_3 = [5.248951, 0.023, 1, 198, "f"] #not available
cond_1norm = 5984.0525
determinant = 7.1087467e+008
reciprocal_condition_number = 0.013826504
vif = [1.001, 1.001]
names = 'date residual leverage influence DFFITS'.split()
cur_dir = os.path.abspath(os.path.dirname(__file__))
fpath = os.path.join(cur_dir, 'results/leverage_influence_ols_nostars.txt')
lev = np.genfromtxt(fpath, skip_header=3, skip_footer=1,
converters={0:lambda s: s})
#either numpy 1.6 or python 3.2 changed behavior
if np.isnan(lev[-1]['f1']):
lev = np.genfromtxt(fpath, skip_header=3, skip_footer=2,
converters={0:lambda s: s})
lev.dtype.names = names
res = res_ols #for easier copying
cov_hac, bse_hac = sw.cov_hac_simple(res, nlags=4, use_correction=False)
assert_almost_equal(res.params, partable[:,0], 5)
assert_almost_equal(bse_hac, partable[:,1], 5)
#TODO
assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
#assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=6) #FAIL
assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=6) #FAIL
assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5)
#f-value is based on cov_hac I guess
#assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=0) #FAIL
#assert_approx_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], significant=1) #FAIL
#assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO
c = oi.reset_ramsey(res, degree=2)
compare_ftest(c, reset_2, decimal=(6,5))
c = oi.reset_ramsey(res, degree=3)
compare_ftest(c, reset_2_3, decimal=(6,5))
linear_sq = smsdia.linear_lm(res.resid, res.model.exog)
assert_almost_equal(linear_sq[0], linear_squares[0], decimal=6)
assert_almost_equal(linear_sq[1], linear_squares[1], decimal=7)
hbpk = smsdia.het_breushpagan(res.resid, res.model.exog)
assert_almost_equal(hbpk[0], het_breush_pagan_konker[0], decimal=6)
assert_almost_equal(hbpk[1], het_breush_pagan_konker[1], decimal=6)
hw = smsdia.het_white(res.resid, res.model.exog)
assert_almost_equal(hw[:2], het_white[:2], 6)
#arch
#sm_arch = smsdia.acorr_lm(res.resid**2, maxlag=4, autolag=None)
sm_arch = smsdia.het_arch(res.resid, maxlag=4)
assert_almost_equal(sm_arch[0], arch_4[0], decimal=5)
assert_almost_equal(sm_arch[1], arch_4[1], decimal=6)
vif2 = [oi.variance_inflation_factor(res.model.exog, k) for k in [1,2]]
infl = oi.OLSInfluence(res_ols)
#print np.max(np.abs(lev['DFFITS'] - infl.dffits[0]))
#print np.max(np.abs(lev['leverage'] - infl.hat_matrix_diag))
#print np.max(np.abs(lev['influence'] - infl.influence)) #just added this based on Gretl
#just rough test, low decimal in Gretl output,
assert_almost_equal(lev['residual'], res.resid, decimal=3)
assert_almost_equal(lev['DFFITS'], infl.dffits[0], decimal=3)
assert_almost_equal(lev['leverage'], infl.hat_matrix_diag, decimal=3)
assert_almost_equal(lev['influence'], infl.influence, decimal=4)
def test_bking2d():
"""
Test Baxter-King band-pass filter with 2d input
"""
bking_results = 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().data[['realinv','cpi']].view((float,2))
Y = bkfilter(X, 6, 32, 12)
assert_almost_equal(Y,bking_results,4)
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 = 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().data[['tbilrate','infl']].view((float,2))[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 = 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],
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[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],
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[2.380067926824722235e+01,7.095149320731752596e+03],
[-7.119129802169481991e+00,7.160478129802169860e+03],
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[2.489047706403016491e+01,7.471709522935970199e+03],
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[1.129819097095369216e+02,7.693621090290463144e+03],
[1.204662123176703972e+02,7.744549787682329224e+03],
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[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],
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[-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],
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[-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().data['realgdp']
res = column_stack((hpfilter(dta,1600)))
assert_almost_equal(res,hpfilt_res,6)