""" Contains values used to approximate the critical value and p-value from statistics that follow the Dickey-Fuller distribution. Most values are from MacKinnon (1994) or (2010). A small number of these did not appear in the original paper and have been computed using an identical simulation. """ from __future__ import annotations from numpy import array, asarray, inf from arch.typing import Float64Array small_scaling = asarray([1, 1, 1e-2]) tau_small_p = {} tau_large_p = {} tau_small_p["n"] = [ [0.6344, 1.2378, 3.2496], [1.9129, 1.3857, 3.5322], [2.7648, 1.4502, 3.4186], [3.4336, 1.4835, 3.1900], [4.0999, 1.5533, 3.5900], [4.5388, 1.5344, 2.9807], ] tau_small_p["n"] = asarray(tau_small_p["n"]) * small_scaling tau_small_p["c"] = [ [2.1659, 1.4412, 3.8269], [2.9200, 1.5012, 3.9796], [3.4699, 1.4856, 3.1640], [3.9673, 1.4777, 2.6315], [4.5509, 1.5338, 2.9545], [5.1399, 1.6036, 3.4445], ] tau_small_p["c"] = asarray(tau_small_p["c"]) * small_scaling tau_small_p["ct"] = [ [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], [5.5300, 1.5914, 3.0392], ] tau_small_p["ct"] = asarray(tau_small_p["ct"]) * small_scaling tau_small_p["ctt"] = [ [4.0003, 1.6580, 4.8288], [4.3534, 1.6016, 3.7947], [4.7343, 1.5768, 3.2396], [5.2140, 1.6077, 3.3449], [5.6481, 1.6274, 3.3455], [5.9296, 1.5929, 2.8223], ] tau_small_p["ctt"] = asarray(tau_small_p["ctt"]) * small_scaling large_scaling = asarray([1, 1e-1, 1e-1, 1e-2]) tau_large_p["n"] = [ [0.4797, 9.3557, -0.6999, 3.3066], [1.5578, 8.5580, -2.0830, -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, 7.1670, -2.3648, -2.8288], ] tau_large_p["n"] = asarray(tau_large_p["n"]) * large_scaling tau_large_p["c"] = [ [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_large_p["c"] = asarray(tau_large_p["c"]) * large_scaling tau_large_p["ct"] = [ [2.5261, 6.1654, -3.7956, -6.0285], [2.8500, 5.2720, -3.6622, -5.1695], [3.2210, 5.2550, -3.2685, -4.1501], [3.6520, 5.9758, -2.7483, -3.2081], [4.0712, 6.6428, -2.3464, -2.5460], [4.4735, 7.1757, -2.0681, -2.1196], ] tau_large_p["ct"] = asarray(tau_large_p["ct"]) * large_scaling tau_large_p["ctt"] = [ [3.0778, 4.9529, -4.1477, -5.9359], [3.4713, 5.9670, -3.2507, -4.2286], [3.8637, 6.7852, -2.6286, -3.1381], [4.2736, 7.6199, -2.1534, -2.4026], [4.6679, 8.2618, -1.8220, -1.9147], [5.0009, 8.3735, -1.6994, -1.6928], ] tau_large_p["ctt"] = asarray(tau_large_p["ctt"]) * large_scaling # 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 # noinspection PyDictCreation tau_2010: dict[str, Float64Array] = {} tau_2010["n"] = array( [ [ [-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_2010["c"] = array( [ [ [-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_2010["ct"] = array( [ [ [-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_2010["ctt"] = array( [ [ [-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], ], ] ) # These are the cut-off values for the left-tail vs. the rest of the # tau distribution, for getting the p-values tau_star = { "n": [-1.04, -1.53, -2.68, -3.09, -3.07, -3.77], "c": [-1.61, -2.62, -3.13, -3.47, -3.78, -3.93], "ct": [-2.89, -3.19, -3.50, -3.65, -3.80, -4.36], "ctt": [-3.21, -3.51, -3.81, -3.83, -4.12, -4.63], } tau_min = { "n": [-19.04, -19.62, -21.21, -23.25, -21.63, -25.74], "c": [-18.83, -18.86, -23.48, -28.07, -25.96, -23.27], "ct": [-16.18, -21.15, -25.37, -26.63, -26.53, -26.18], "ctt": [-17.17, -21.1, -24.33, -24.03, -24.33, -28.22], } tau_max = { "n": [inf, 1.51, 0.86, 0.88, 1.05, 1.24], "c": [2.74, 0.92, 0.55, 0.61, 0.79, 1], "ct": [0.7, 0.63, 0.71, 0.93, 1.19, 1.42], "ctt": [0.54, 0.79, 1.08, 1.43, 3.49, 1.92], } # Z values from new simulations, 500 exercises, 250,000 per ex. adf_z_min = {"n": -inf, "c": -inf, "ct": -inf, "ctt": -inf} adf_z_star = {"n": -1.79146, "c": -5.04709, "ct": -9.22766, "ctt": -12.88512} adf_z_max = {"n": inf, "c": inf, "ct": inf, "ctt": inf} # The small p parameters are for np.log(np.abs(stat)) adf_z_small_p = { "n": [0.05872, -0.69633, 0.02471, -0.04283], "c": [1.94205, -1.47677, 0.21163, -0.06288], "ct": [4.05596, -2.34128, 0.41403, -0.08312], "ctt": [5.68974, -2.98948, 0.55752, -0.09629], } adf_z_large_p = { "n": [0.56681, 0.67544, 0.06881, 0.00235], "c": [1.70059, 0.49465, 0.02636, 0.00055], "ct": [2.60323, 0.39217, 0.01321, 0.00019], "ctt": [3.2269, 0.34323, 0.00887, 0.0001], } adf_z_cv_approx = { "n": [ [-13.30499, 331.55385, -8807.11008, 88544.76648], [-7.82957, 222.75548, -5863.14998, 58024.48295], [-5.57486, 170.79065, -4422.48027, 43264.68244], ], "c": [ [-20.6258, 119.28619, -442.99517, 1082.9222], [-14.09457, 58.46106, -164.08684, 479.02908], [-11.25118, 38.48786, -87.62853, 246.93531], ], "ct": [ [-29.3568, 232.33249, -1171.21447, 3166.83631], [-21.71085, 130.15894, -504.95264, 1170.38109], [-18.24475, 93.25896, -305.14509, 581.02963], ], "ctt": [ [-36.5955, 354.30552, -2214.58403, 7401.70512], [-28.11176, 212.46258, -1067.94737, 3169.14023], [-24.18572, 158.63387, -695.72916, 1833.08527], ], }