451 lines
16 KiB
Python
451 lines
16 KiB
Python
|
from scipy.stats import norm
|
||
|
|
from numpy import array, polyval, inf, asarray
|
||
|
|
|
||
|
|
__all__ = ['mackinnonp', 'mackinnoncrit']
|
||
|
|
|
||
|
|
# These are the cut-off values for the left-tail vs. the rest of the
|
||
|
|
# tau distribution, for getting the p-values
|
||
|
|
|
||
|
|
tau_star_nc = [-1.04, -1.53, -2.68, -3.09, -3.07, -3.77]
|
||
|
|
tau_min_nc = [-19.04, -19.62, -21.21, -23.25, -21.63, -25.74]
|
||
|
|
tau_max_nc = [inf, 1.51, 0.86, 0.88, 1.05, 1.24]
|
||
|
|
tau_star_c = [-1.61, -2.62, -3.13, -3.47, -3.78, -3.93]
|
||
|
|
tau_min_c = [-18.83, -18.86, -23.48, -28.07, -25.96, -23.27]
|
||
|
|
tau_max_c = [2.74, 0.92, 0.55, 0.61, 0.79, 1]
|
||
|
|
tau_star_ct = [-2.89, -3.19, -3.50, -3.65, -3.80, -4.36]
|
||
|
|
tau_min_ct = [-16.18, -21.15, -25.37, -26.63, -26.53, -26.18]
|
||
|
|
tau_max_ct = [0.7, 0.63, 0.71, 0.93, 1.19, 1.42]
|
||
|
|
tau_star_ctt = [-3.21, -3.51, -3.81, -3.83, -4.12, -4.63]
|
||
|
|
tau_min_ctt = [-17.17, -21.1, -24.33, -24.03, -24.33, -28.22]
|
||
|
|
tau_max_ctt = [0.54, 0.79, 1.08, 1.43, 3.49, 1.92]
|
||
|
|
|
||
|
|
_tau_maxs = {
|
||
|
|
"n": tau_max_nc,
|
||
|
|
"c": tau_max_c,
|
||
|
|
"ct": tau_max_ct,
|
||
|
|
"ctt": tau_max_ctt,
|
||
|
|
}
|
||
|
|
_tau_mins = {
|
||
|
|
"n": tau_min_nc,
|
||
|
|
"c": tau_min_c,
|
||
|
|
"ct": tau_min_ct,
|
||
|
|
"ctt": tau_min_ctt,
|
||
|
|
}
|
||
|
|
_tau_stars = {
|
||
|
|
"n": tau_star_nc,
|
||
|
|
"c": tau_star_c,
|
||
|
|
"ct": tau_star_ct,
|
||
|
|
"ctt": tau_star_ctt,
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
small_scaling = array([1, 1, 1e-2])
|
||
|
|
tau_nc_smallp = [
|
||
|
|
[0.6344, 1.2378, 3.2496],
|
||
|
|
[1.9129, 1.3857, 3.5322],
|
||
|
|
[2.7648, 1.4502, 3.4186],
|
||
|
|
[3.4336, 1.4835, 3.19],
|
||
|
|
[4.0999, 1.5533, 3.59],
|
||
|
|
[4.5388, 1.5344, 2.9807]]
|
||
|
|
tau_nc_smallp = asarray(tau_nc_smallp)*small_scaling
|
||
|
|
|
||
|
|
tau_c_smallp = [
|
||
|
|
[2.1659, 1.4412, 3.8269],
|
||
|
|
[2.92, 1.5012, 3.9796],
|
||
|
|
[3.4699, 1.4856, 3.164],
|
||
|
|
[3.9673, 1.4777, 2.6315],
|
||
|
|
[4.5509, 1.5338, 2.9545],
|
||
|
|
[5.1399, 1.6036, 3.4445]]
|
||
|
|
tau_c_smallp = asarray(tau_c_smallp)*small_scaling
|
||
|
|
|
||
|
|
tau_ct_smallp = [
|
||
|
|
[3.2512, 1.6047, 4.9588],
|
||
|
|
[3.6646, 1.5419, 3.6448],
|
||
|
|
[4.0983, 1.5173, 2.9898],
|
||
|
|
[4.5844, 1.5338, 2.8796],
|
||
|
|
[5.0722, 1.5634, 2.9472],
|
||
|
|
[5.53, 1.5914, 3.0392]]
|
||
|
|
tau_ct_smallp = asarray(tau_ct_smallp)*small_scaling
|
||
|
|
|
||
|
|
tau_ctt_smallp = [
|
||
|
|
[4.0003, 1.658, 4.8288],
|
||
|
|
[4.3534, 1.6016, 3.7947],
|
||
|
|
[4.7343, 1.5768, 3.2396],
|
||
|
|
[5.214, 1.6077, 3.3449],
|
||
|
|
[5.6481, 1.6274, 3.3455],
|
||
|
|
[5.9296, 1.5929, 2.8223]]
|
||
|
|
tau_ctt_smallp = asarray(tau_ctt_smallp)*small_scaling
|
||
|
|
|
||
|
|
_tau_smallps = {
|
||
|
|
"n": tau_nc_smallp,
|
||
|
|
"c": tau_c_smallp,
|
||
|
|
"ct": tau_ct_smallp,
|
||
|
|
"ctt": tau_ctt_smallp,
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
large_scaling = array([1, 1e-1, 1e-1, 1e-2])
|
||
|
|
tau_nc_largep = [
|
||
|
|
[0.4797, 9.3557, -0.6999, 3.3066],
|
||
|
|
[1.5578, 8.558, -2.083, -3.3549],
|
||
|
|
[2.2268, 6.8093, -3.2362, -5.4448],
|
||
|
|
[2.7654, 6.4502, -3.0811, -4.4946],
|
||
|
|
[3.2684, 6.8051, -2.6778, -3.4972],
|
||
|
|
[3.7268, 7.167, -2.3648, -2.8288]]
|
||
|
|
tau_nc_largep = asarray(tau_nc_largep)*large_scaling
|
||
|
|
|
||
|
|
tau_c_largep = [
|
||
|
|
[1.7339, 9.3202, -1.2745, -1.0368],
|
||
|
|
[2.1945, 6.4695, -2.9198, -4.2377],
|
||
|
|
[2.5893, 4.5168, -3.6529, -5.0074],
|
||
|
|
[3.0387, 4.5452, -3.3666, -4.1921],
|
||
|
|
[3.5049, 5.2098, -2.9158, -3.3468],
|
||
|
|
[3.9489, 5.8933, -2.5359, -2.721]]
|
||
|
|
tau_c_largep = asarray(tau_c_largep)*large_scaling
|
||
|
|
|
||
|
|
tau_ct_largep = [
|
||
|
|
[2.5261, 6.1654, -3.7956, -6.0285],
|
||
|
|
[2.85, 5.272, -3.6622, -5.1695],
|
||
|
|
[3.221, 5.255, -3.2685, -4.1501],
|
||
|
|
[3.652, 5.9758, -2.7483, -3.2081],
|
||
|
|
[4.0712, 6.6428, -2.3464, -2.546],
|
||
|
|
[4.4735, 7.1757, -2.0681, -2.1196]]
|
||
|
|
tau_ct_largep = asarray(tau_ct_largep)*large_scaling
|
||
|
|
|
||
|
|
tau_ctt_largep = [
|
||
|
|
[3.0778, 4.9529, -4.1477, -5.9359],
|
||
|
|
[3.4713, 5.967, -3.2507, -4.2286],
|
||
|
|
[3.8637, 6.7852, -2.6286, -3.1381],
|
||
|
|
[4.2736, 7.6199, -2.1534, -2.4026],
|
||
|
|
[4.6679, 8.2618, -1.822, -1.9147],
|
||
|
|
[5.0009, 8.3735, -1.6994, -1.6928]]
|
||
|
|
tau_ctt_largep = asarray(tau_ctt_largep)*large_scaling
|
||
|
|
|
||
|
|
_tau_largeps = {
|
||
|
|
"n": tau_nc_largep,
|
||
|
|
"c": tau_c_largep,
|
||
|
|
"ct": tau_ct_largep,
|
||
|
|
"ctt": tau_ctt_largep,
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
# NOTE: The Z-statistic is used when lags are included to account for
|
||
|
|
# serial correlation in the error term
|
||
|
|
|
||
|
|
z_star_nc = [-2.9, -8.7, -14.8, -20.9, -25.7, -30.5]
|
||
|
|
z_star_c = [-8.9, -14.3, -19.5, -25.1, -29.6, -34.4]
|
||
|
|
z_star_ct = [-15.0, -19.6, -25.3, -29.6, -31.8, -38.4]
|
||
|
|
z_star_ctt = [-20.7, -25.3, -29.9, -34.4, -38.5, -44.2]
|
||
|
|
|
||
|
|
|
||
|
|
# These are Table 5 from MacKinnon (1994)
|
||
|
|
# small p is defined as p in .005 to .150 ie p = .005 up to z_star
|
||
|
|
# Z* is the largest value for which it is appropriate to use these
|
||
|
|
# approximations
|
||
|
|
# the left tail approximation is
|
||
|
|
# p = norm.cdf(d_0 + d_1*log(abs(z)) + d_2*log(abs(z))**2 + d_3*log(abs(z))**3)
|
||
|
|
# there is no Z-min, ie., it is well-behaved in the left tail
|
||
|
|
|
||
|
|
z_nc_smallp = array([
|
||
|
|
[.0342, -.6376, 0, -.03872],
|
||
|
|
[1.3426, -.7680, 0, -.04104],
|
||
|
|
[3.8607, -2.4159, .51293, -.09835],
|
||
|
|
[6.1072, -3.7250, .85887, -.13102],
|
||
|
|
[7.7800, -4.4579, 1.00056, -.14014],
|
||
|
|
[4.0253, -.8815, 0, -.04887]])
|
||
|
|
|
||
|
|
z_c_smallp = array([
|
||
|
|
[2.2142, -1.7863, .32828, -.07727],
|
||
|
|
[1.1662, .1814, -.36707, 0],
|
||
|
|
[6.6584, -4.3486, 1.04705, -.15011],
|
||
|
|
[3.3249, -.8456, 0, -.04818],
|
||
|
|
[4.0356, -.9306, 0, -.04776],
|
||
|
|
[13.9959, -8.4314, 1.97411, -.22234]])
|
||
|
|
|
||
|
|
z_ct_smallp = array([
|
||
|
|
[4.6476, -2.8932, 0.5832, -0.0999],
|
||
|
|
[7.2453, -4.7021, 1.127, -.15665],
|
||
|
|
[3.4893, -0.8914, 0, -.04755],
|
||
|
|
[1.6604, 1.0375, -0.53377, 0],
|
||
|
|
[2.006, 1.1197, -0.55315, 0],
|
||
|
|
[11.1626, -5.6858, 1.21479, -.15428]])
|
||
|
|
|
||
|
|
z_ctt_smallp = array([
|
||
|
|
[3.6739, -1.1549, 0, -0.03947],
|
||
|
|
[3.9783, -1.0619, 0, -0.04394],
|
||
|
|
[2.0062, 0.8907, -0.51708, 0],
|
||
|
|
[4.9218, -1.0663, 0, -0.04691],
|
||
|
|
[5.1433, -0.9877, 0, -0.04993],
|
||
|
|
[23.6812, -14.6485, 3.42909, -.33794]])
|
||
|
|
# These are Table 6 from MacKinnon (1994).
|
||
|
|
# These are well-behaved in the right tail.
|
||
|
|
# the approximation function is
|
||
|
|
# p = norm.cdf(d_0 + d_1 * z + d_2*z**2 + d_3*z**3 + d_4*z**4)
|
||
|
|
z_large_scaling = array([1, 1e-1, 1e-2, 1e-3, 1e-5])
|
||
|
|
z_nc_largep = array([
|
||
|
|
[0.4927, 6.906, 13.2331, 12.099, 0],
|
||
|
|
[1.5167, 4.6859, 4.2401, 2.7939, 7.9601],
|
||
|
|
[2.2347, 3.9465, 2.2406, 0.8746, 1.4239],
|
||
|
|
[2.8239, 3.6265, 1.6738, 0.5408, 0.7449],
|
||
|
|
[3.3174, 3.3492, 1.2792, 0.3416, 0.3894],
|
||
|
|
[3.729, 3.0611, 0.9579, 0.2087, 0.1943]])
|
||
|
|
z_nc_largep *= z_large_scaling
|
||
|
|
|
||
|
|
z_c_largep = array([
|
||
|
|
[1.717, 5.5243, 4.3463, 1.6671, 0],
|
||
|
|
[2.2394, 4.2377, 2.432, 0.9241, 0.4364],
|
||
|
|
[2.743, 3.626, 1.5703, 0.4612, 0.567],
|
||
|
|
[3.228, 3.3399, 1.2319, 0.3162, 0.3482],
|
||
|
|
[3.6583, 3.0934, 0.9681, 0.2111, 0.1979],
|
||
|
|
[4.0379, 2.8735, 0.7694, 0.1433, 0.1146]])
|
||
|
|
z_c_largep *= z_large_scaling
|
||
|
|
|
||
|
|
z_ct_largep = array([
|
||
|
|
[2.7117, 4.5731, 2.2868, 0.6362, 0.5],
|
||
|
|
[3.0972, 4.0873, 1.8982, 0.5796, 0.7384],
|
||
|
|
[3.4594, 3.6326, 1.4284, 0.3813, 0.4325],
|
||
|
|
[3.806, 3.2634, 1.0689, 0.2402, 0.2304],
|
||
|
|
[4.1402, 2.9867, 0.8323, 0.16, 0.1315],
|
||
|
|
[4.4497, 2.7534, 0.6582, 0.1089, 0.0773]])
|
||
|
|
z_ct_largep *= z_large_scaling
|
||
|
|
|
||
|
|
z_ctt_largep = array([
|
||
|
|
[3.4671, 4.3476, 1.9231, 0.5381, 0.6216],
|
||
|
|
[3.7827, 3.9421, 1.5699, 0.4093, 0.4485],
|
||
|
|
[4.052, 3.4947, 1.1772, 0.2642, 0.2502],
|
||
|
|
[4.3311, 3.1625, 0.9126, 0.1775, 0.1462],
|
||
|
|
[4.594, 2.8739, 0.707, 0.1181, 0.0838],
|
||
|
|
[4.8479, 2.6447, 0.5647, 0.0827, 0.0518]])
|
||
|
|
z_ctt_largep *= z_large_scaling
|
||
|
|
|
||
|
|
|
||
|
|
# TODO: finish this and then integrate them into adf function
|
||
|
|
def mackinnonp(teststat, regression="c", N=1, lags=None):
|
||
|
|
"""
|
||
|
|
Returns MacKinnon's approximate p-value for teststat.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
teststat : float
|
||
|
|
"T-value" from an Augmented Dickey-Fuller regression.
|
||
|
|
regression : str {"c", "n", "ct", "ctt"}
|
||
|
|
This is the method of regression that was used. Following MacKinnon's
|
||
|
|
notation, this can be "c" for constant, "n" for no constant, "ct" for
|
||
|
|
constant and trend, and "ctt" for constant, trend, and trend-squared.
|
||
|
|
N : int
|
||
|
|
The number of series believed to be I(1). For (Augmented) Dickey-
|
||
|
|
Fuller N = 1.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
p-value : float
|
||
|
|
The p-value for the ADF statistic estimated using MacKinnon 1994.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [*] MacKinnon, J.G. 1994 "Approximate Asymptotic Distribution Functions
|
||
|
|
for Unit-Root and Cointegration Tests." Journal of Business & Economics
|
||
|
|
Statistics, 12.2, 167-76.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
For (A)DF
|
||
|
|
H_0: AR coefficient = 1
|
||
|
|
H_a: AR coefficient < 1
|
||
|
|
"""
|
||
|
|
maxstat = _tau_maxs[regression]
|
||
|
|
minstat = _tau_mins[regression]
|
||
|
|
starstat = _tau_stars[regression]
|
||
|
|
if teststat > maxstat[N-1]:
|
||
|
|
return 1.0
|
||
|
|
elif teststat < minstat[N-1]:
|
||
|
|
return 0.0
|
||
|
|
if teststat <= starstat[N-1]:
|
||
|
|
tau_coef = _tau_smallps[regression][N-1]
|
||
|
|
else:
|
||
|
|
# Note: above is only for z stats
|
||
|
|
tau_coef = _tau_largeps[regression][N-1]
|
||
|
|
return norm.cdf(polyval(tau_coef[::-1], teststat))
|
||
|
|
|
||
|
|
|
||
|
|
# These are the new estimates from MacKinnon 2010
|
||
|
|
# the first axis is N -1
|
||
|
|
# the second axis is 1 %, 5 %, 10 %
|
||
|
|
# the last axis is the coefficients
|
||
|
|
|
||
|
|
tau_nc_2010 = [[
|
||
|
|
[-2.56574, -2.2358, -3.627, 0], # N = 1
|
||
|
|
[-1.94100, -0.2686, -3.365, 31.223],
|
||
|
|
[-1.61682, 0.2656, -2.714, 25.364]]]
|
||
|
|
tau_nc_2010 = asarray(tau_nc_2010)
|
||
|
|
|
||
|
|
tau_c_2010 = [
|
||
|
|
[[-3.43035, -6.5393, -16.786, -79.433], # N = 1, 1%
|
||
|
|
[-2.86154, -2.8903, -4.234, -40.040], # 5 %
|
||
|
|
[-2.56677, -1.5384, -2.809, 0]], # 10 %
|
||
|
|
[[-3.89644, -10.9519, -33.527, 0], # N = 2
|
||
|
|
[-3.33613, -6.1101, -6.823, 0],
|
||
|
|
[-3.04445, -4.2412, -2.720, 0]],
|
||
|
|
[[-4.29374, -14.4354, -33.195, 47.433], # N = 3
|
||
|
|
[-3.74066, -8.5632, -10.852, 27.982],
|
||
|
|
[-3.45218, -6.2143, -3.718, 0]],
|
||
|
|
[[-4.64332, -18.1031, -37.972, 0], # N = 4
|
||
|
|
[-4.09600, -11.2349, -11.175, 0],
|
||
|
|
[-3.81020, -8.3931, -4.137, 0]],
|
||
|
|
[[-4.95756, -21.8883, -45.142, 0], # N = 5
|
||
|
|
[-4.41519, -14.0405, -12.575, 0],
|
||
|
|
[-4.13157, -10.7417, -3.784, 0]],
|
||
|
|
[[-5.24568, -25.6688, -57.737, 88.639], # N = 6
|
||
|
|
[-4.70693, -16.9178, -17.492, 60.007],
|
||
|
|
[-4.42501, -13.1875, -5.104, 27.877]],
|
||
|
|
[[-5.51233, -29.5760, -69.398, 164.295], # N = 7
|
||
|
|
[-4.97684, -19.9021, -22.045, 110.761],
|
||
|
|
[-4.69648, -15.7315, -5.104, 27.877]],
|
||
|
|
[[-5.76202, -33.5258, -82.189, 256.289], # N = 8
|
||
|
|
[-5.22924, -23.0023, -24.646, 144.479],
|
||
|
|
[-4.95007, -18.3959, -7.344, 94.872]],
|
||
|
|
[[-5.99742, -37.6572, -87.365, 248.316], # N = 9
|
||
|
|
[-5.46697, -26.2057, -26.627, 176.382],
|
||
|
|
[-5.18897, -21.1377, -9.484, 172.704]],
|
||
|
|
[[-6.22103, -41.7154, -102.680, 389.33], # N = 10
|
||
|
|
[-5.69244, -29.4521, -30.994, 251.016],
|
||
|
|
[-5.41533, -24.0006, -7.514, 163.049]],
|
||
|
|
[[-6.43377, -46.0084, -106.809, 352.752], # N = 11
|
||
|
|
[-5.90714, -32.8336, -30.275, 249.994],
|
||
|
|
[-5.63086, -26.9693, -4.083, 151.427]],
|
||
|
|
[[-6.63790, -50.2095, -124.156, 579.622], # N = 12
|
||
|
|
[-6.11279, -36.2681, -32.505, 314.802],
|
||
|
|
[-5.83724, -29.9864, -2.686, 184.116]]]
|
||
|
|
tau_c_2010 = asarray(tau_c_2010)
|
||
|
|
|
||
|
|
tau_ct_2010 = [
|
||
|
|
[[-3.95877, -9.0531, -28.428, -134.155], # N = 1
|
||
|
|
[-3.41049, -4.3904, -9.036, -45.374],
|
||
|
|
[-3.12705, -2.5856, -3.925, -22.380]],
|
||
|
|
[[-4.32762, -15.4387, -35.679, 0], # N = 2
|
||
|
|
[-3.78057, -9.5106, -12.074, 0],
|
||
|
|
[-3.49631, -7.0815, -7.538, 21.892]],
|
||
|
|
[[-4.66305, -18.7688, -49.793, 104.244], # N = 3
|
||
|
|
[-4.11890, -11.8922, -19.031, 77.332],
|
||
|
|
[-3.83511, -9.0723, -8.504, 35.403]],
|
||
|
|
[[-4.96940, -22.4694, -52.599, 51.314], # N = 4
|
||
|
|
[-4.42871, -14.5876, -18.228, 39.647],
|
||
|
|
[-4.14633, -11.2500, -9.873, 54.109]],
|
||
|
|
[[-5.25276, -26.2183, -59.631, 50.646], # N = 5
|
||
|
|
[-4.71537, -17.3569, -22.660, 91.359],
|
||
|
|
[-4.43422, -13.6078, -10.238, 76.781]],
|
||
|
|
[[-5.51727, -29.9760, -75.222, 202.253], # N = 6
|
||
|
|
[-4.98228, -20.3050, -25.224, 132.03],
|
||
|
|
[-4.70233, -16.1253, -9.836, 94.272]],
|
||
|
|
[[-5.76537, -33.9165, -84.312, 245.394], # N = 7
|
||
|
|
[-5.23299, -23.3328, -28.955, 182.342],
|
||
|
|
[-4.95405, -18.7352, -10.168, 120.575]],
|
||
|
|
[[-6.00003, -37.8892, -96.428, 335.92], # N = 8
|
||
|
|
[-5.46971, -26.4771, -31.034, 220.165],
|
||
|
|
[-5.19183, -21.4328, -10.726, 157.955]],
|
||
|
|
[[-6.22288, -41.9496, -109.881, 466.068], # N = 9
|
||
|
|
[-5.69447, -29.7152, -33.784, 273.002],
|
||
|
|
[-5.41738, -24.2882, -8.584, 169.891]],
|
||
|
|
[[-6.43551, -46.1151, -120.814, 566.823], # N = 10
|
||
|
|
[-5.90887, -33.0251, -37.208, 346.189],
|
||
|
|
[-5.63255, -27.2042, -6.792, 177.666]],
|
||
|
|
[[-6.63894, -50.4287, -128.997, 642.781], # N = 11
|
||
|
|
[-6.11404, -36.4610, -36.246, 348.554],
|
||
|
|
[-5.83850, -30.1995, -5.163, 210.338]],
|
||
|
|
[[-6.83488, -54.7119, -139.800, 736.376], # N = 12
|
||
|
|
[-6.31127, -39.9676, -37.021, 406.051],
|
||
|
|
[-6.03650, -33.2381, -6.606, 317.776]]]
|
||
|
|
tau_ct_2010 = asarray(tau_ct_2010)
|
||
|
|
|
||
|
|
tau_ctt_2010 = [
|
||
|
|
[[-4.37113, -11.5882, -35.819, -334.047], # N = 1
|
||
|
|
[-3.83239, -5.9057, -12.490, -118.284],
|
||
|
|
[-3.55326, -3.6596, -5.293, -63.559]],
|
||
|
|
[[-4.69276, -20.2284, -64.919, 88.884], # N =2
|
||
|
|
[-4.15387, -13.3114, -28.402, 72.741],
|
||
|
|
[-3.87346, -10.4637, -17.408, 66.313]],
|
||
|
|
[[-4.99071, -23.5873, -76.924, 184.782], # N = 3
|
||
|
|
[-4.45311, -15.7732, -32.316, 122.705],
|
||
|
|
[-4.17280, -12.4909, -17.912, 83.285]],
|
||
|
|
[[-5.26780, -27.2836, -78.971, 137.871], # N = 4
|
||
|
|
[-4.73244, -18.4833, -31.875, 111.817],
|
||
|
|
[-4.45268, -14.7199, -17.969, 101.92]],
|
||
|
|
[[-5.52826, -30.9051, -92.490, 248.096], # N = 5
|
||
|
|
[-4.99491, -21.2360, -37.685, 194.208],
|
||
|
|
[-4.71587, -17.0820, -18.631, 136.672]],
|
||
|
|
[[-5.77379, -34.7010, -105.937, 393.991], # N = 6
|
||
|
|
[-5.24217, -24.2177, -39.153, 232.528],
|
||
|
|
[-4.96397, -19.6064, -18.858, 174.919]],
|
||
|
|
[[-6.00609, -38.7383, -108.605, 365.208], # N = 7
|
||
|
|
[-5.47664, -27.3005, -39.498, 246.918],
|
||
|
|
[-5.19921, -22.2617, -17.910, 208.494]],
|
||
|
|
[[-6.22758, -42.7154, -119.622, 421.395], # N = 8
|
||
|
|
[-5.69983, -30.4365, -44.300, 345.48],
|
||
|
|
[-5.42320, -24.9686, -19.688, 274.462]],
|
||
|
|
[[-6.43933, -46.7581, -136.691, 651.38], # N = 9
|
||
|
|
[-5.91298, -33.7584, -42.686, 346.629],
|
||
|
|
[-5.63704, -27.8965, -13.880, 236.975]],
|
||
|
|
[[-6.64235, -50.9783, -145.462, 752.228], # N = 10
|
||
|
|
[-6.11753, -37.056, -48.719, 473.905],
|
||
|
|
[-5.84215, -30.8119, -14.938, 316.006]],
|
||
|
|
[[-6.83743, -55.2861, -152.651, 792.577], # N = 11
|
||
|
|
[-6.31396, -40.5507, -46.771, 487.185],
|
||
|
|
[-6.03921, -33.8950, -9.122, 285.164]],
|
||
|
|
[[-7.02582, -59.6037, -166.368, 989.879], # N = 12
|
||
|
|
[-6.50353, -44.0797, -47.242, 543.889],
|
||
|
|
[-6.22941, -36.9673, -10.868, 418.414]]]
|
||
|
|
tau_ctt_2010 = asarray(tau_ctt_2010)
|
||
|
|
|
||
|
|
tau_2010s = {
|
||
|
|
"n": tau_nc_2010,
|
||
|
|
"c": tau_c_2010,
|
||
|
|
"ct": tau_ct_2010,
|
||
|
|
"ctt": tau_ctt_2010,
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
def mackinnoncrit(N=1, regression="c", nobs=inf):
|
||
|
|
"""
|
||
|
|
Returns the critical values for cointegrating and the ADF test.
|
||
|
|
|
||
|
|
In 2010 MacKinnon updated the values of his 1994 paper with critical values
|
||
|
|
for the augmented Dickey-Fuller tests. These new values are to be
|
||
|
|
preferred and are used here.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
N : int
|
||
|
|
The number of series of I(1) series for which the null of
|
||
|
|
non-cointegration is being tested. For N > 12, the critical values
|
||
|
|
are linearly interpolated (not yet implemented). For the ADF test,
|
||
|
|
N = 1.
|
||
|
|
reg : str {'c', 'tc', 'ctt', 'n'}
|
||
|
|
Following MacKinnon (1996), these stand for the type of regression run.
|
||
|
|
'c' for constant and no trend, 'tc' for constant with a linear trend,
|
||
|
|
'ctt' for constant with a linear and quadratic trend, and 'n' for
|
||
|
|
no constant. The values for the no constant case are taken from the
|
||
|
|
1996 paper, as they were not updated for 2010 due to the unrealistic
|
||
|
|
assumptions that would underlie such a case.
|
||
|
|
nobs : int or np.inf
|
||
|
|
This is the sample size. If the sample size is numpy.inf, then the
|
||
|
|
asymptotic critical values are returned.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [*] MacKinnon, J.G. 1994 "Approximate Asymptotic Distribution Functions
|
||
|
|
for Unit-Root and Cointegration Tests." Journal of Business & Economics
|
||
|
|
Statistics, 12.2, 167-76.
|
||
|
|
.. [*] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests."
|
||
|
|
Queen's University, Dept of Economics Working Papers 1227.
|
||
|
|
http://ideas.repec.org/p/qed/wpaper/1227.html
|
||
|
|
"""
|
||
|
|
reg = regression
|
||
|
|
if reg not in ['c', 'ct', 'n', 'ctt']:
|
||
|
|
raise ValueError("regression keyword %s not understood" % reg)
|
||
|
|
tau = tau_2010s[reg]
|
||
|
|
if nobs is inf:
|
||
|
|
return tau[N-1, :, 0]
|
||
|
|
else:
|
||
|
|
val = tau[N-1, :, ::-1]
|
||
|
|
return polyval(val.T, 1./nobs)
|