""" Results for SARIMAX tests Results from Stata using script `test_sarimax_stata.do`. See also Stata time series documentation. Data from: https://www.stata-press.com/data/r12/wpi1 https://www.stata-press.com/data/r12/air2 https://www.stata-press.com/data/r12/friedman2 Author: Chad Fulton License: Simplified-BSD """ wpi1_data = [ 30.70000076, 30.79999924, 30.70000076, 30.70000076, 30.79999924, 30.5, 30.5, 30.60000038, 30.70000076, 30.60000038, 30.70000076, 30.70000076, 30.60000038, 30.5, 30.60000038, 30.70000076, 30.70000076, 30.60000038, 30.70000076, 30.70000076, 30.89999962, 31.20000076, 31.39999962, 31.60000038, 32.09999847, 32.20000076, 32.59999847, 32.40000153, 32.29999924, 32.29999924, 32.40000153, 32.5, 32.90000153, 33.09999847, 33.29999924, 33.40000153, 33.90000153, 34.40000153, 34.70000076, 35., 35.5, 35.70000076, 35.90000153, 35.90000153, 36.5, 36.90000153, 37.20000076, 37.20000076, 37.90000153, 38.29999924, 38.79999924, 39.20000076, 41.09999847, 43.09999847, 44.90000153, 45.29999924, 48.29999924, 50., 53.59999847, 55.40000153, 55.40000153, 56., 57.20000076, 57.79999924, 58.09999847, 59., 59.70000076, 60.20000076, 61.59999847, 63., 63.09999847, 63.90000153, 65.40000153, 67.40000153, 68.40000153, 70., 72.5, 75.09999847, 77.40000153, 80.19999695, 83.90000153, 85.59999847, 88.40000153, 90.40000153, 93.09999847, 95.19999695, 95.90000153, 95.80000305, 96.59999847, 96.69999695, 97.09999847, 97.19999695, 97.30000305, 97.59999847, 98.59999847, 99.09999847, 100.19999695, 100.80000305, 100.59999847, 100.30000305, 100.09999847, 100.19999695, 99.5, 100.09999847, 98.59999847, 96.80000305, 96.30000305, 96.69999695, 97.80000305, 99.40000153, 100.5, 101., 101.59999847, 103.19999695, 104.69999695, 105.19999695, 107.5, 109.40000153, 109., 109.40000153, 111., 110.80000305, 112.80000305, 116.19999695 ] wpi1_ar3 = { 'data': wpi1_data, 'params_ar': [.52707154, .09526127, .25803547], 'se_ar': [.09031296, .10143699, .09271067], 'params_ma': [], 'se_ma': [], 'params_mean': [], 'se_mean': [], 'params_variance': [.53074593], 'se_variance': [.067705], 'loglike': -136.21782, 'aic': 280.43565, 'bic': 291.68438, } wpi1_stationary = { 'data': wpi1_data, 'params_ar': [.8742288], 'se_ar_opg': [.0545435], 'se_ar_oim': [.0637705], 'se_ar_robust': [.0811246], 'params_ma': [-.4120458], 'se_ma_opg': [.1000284], 'se_ma_oim': [.1220756], 'se_ma_robust': [.1503862], 'params_mean': [.7498197], 'se_mean': [.3340968], 'se_mean_oim': [.2920992], 'params_variance': [.7250436**2], 'se_stddev_opg': [.0368065], 'se_stddev_oim': [.0462345], 'loglike': -135.35131, 'aic': 278.7026, 'bic': 289.9514, } wpi1_diffuse = { 'data': wpi1_data, 'initial_variance': 1e9, 'params_ar': [.864419], 'se_ar_opg': [.0563637], 'se_ar_oim': [.0716638], 'params_ma': [-.3960891], 'se_ma_opg': [.1018369], 'se_ma_oim': [.1384683], 'params_mean': [.8412064], 'se_mean_opg': [.3159328], 'se_mean_oim': [.3052621], 'params_variance': [.7282775**2], 'se_stddev_opg': [.0373227], 'se_stddev_oim': [.0468532], 'loglike': -154.29177, 'aic': 316.5835, 'bic': 327.8323, } wpi1_seasonal = { 'data': wpi1_data, 'params_ar': [.7806991], 'se_ar_opg': [.0944946], 'se_ar_oim': [.0811792], 'params_ma': [-.3990039, .3090813], 'se_ma_opg': [.1258753, .1200945], 'se_ma_oim': [.1058495, .1054576], 'params_mean': [.0110493], 'se_mean_opg': [.0048349], 'se_mean_oim': [.0037734], 'params_variance': [.0104394**2], 'se_stddev_opg': [.0004702], 'se_stddev_oim': [.0006658], 'loglike': 386.03357, 'aic': -762.0671, 'bic': -748.0062, } air2_data = [ 112, 118, 132, 129, 121, 135, 148, 148, 136, 119, 104, 118, 115, 126, 141, 135, 125, 149, 170, 170, 158, 133, 114, 140, 145, 150, 178, 163, 172, 178, 199, 199, 184, 162, 146, 166, 171, 180, 193, 181, 183, 218, 230, 242, 209, 191, 172, 194, 196, 196, 236, 235, 229, 243, 264, 272, 237, 211, 180, 201, 204, 188, 235, 227, 234, 264, 302, 293, 259, 229, 203, 229, 242, 233, 267, 269, 270, 315, 364, 347, 312, 274, 237, 278, 284, 277, 317, 313, 318, 374, 413, 405, 355, 306, 271, 306, 315, 301, 356, 348, 355, 422, 465, 467, 404, 347, 305, 336, 340, 318, 362, 348, 363, 435, 491, 505, 404, 359, 310, 337, 360, 342, 406, 396, 420, 472, 548, 559, 463, 407, 362, 405, 417, 391, 419, 461, 472, 535, 622, 606, 508, 461, 390, 432 ] air2_stationary = { 'data': air2_data, 'params_ma': [-.4018324], 'se_ma_opg': [.0730307], 'se_ma_oim': [.0896442], 'params_seasonal_ma': [-.5569342], 'se_seasonal_ma_opg': [.0963129], 'se_seasonal_ma_oim': [.0731055], 'params_variance': [.0367167**2], 'se_stddev_opg': [.0020132], 'se_stddev_oim': [.002277], 'loglike': 244.69651, 'aic': -483.393, 'bic': -474.7674, } friedman2_data = {'consump': [ 310.3999939, 316.3999939, 321.70001221, 323.79998779, 327.29998779, 333.20001221, 333.1000061, 335., 335.70001221, 340.6000061, 343.5, 350.70001221, 355.29998779, 361.29998779, 365.3999939, 371.70001221, 375.1000061, 379.3999939, 386.3999939, 391.1000061, 400.5, 408.29998779, 417.1000061, 419.79998779, 430.6000061, 437.79998779, 447.20001221, 461.5, 472., 477.1000061, 486.3999939, 492., 496.79998779, 506.20001221, 513.70001221, 521.20001221, 539.5, 553.20001221, 569.09997559, 577.5, 588.79998779, 599.40002441, 609.20001221, 621.09997559, 632.40002441, 642.70001221, 655.20001221, 662.09997559, 681.59997559, 695.79998779, 708.20001221, 724.5, 741.90002441, 759.90002441, 778.09997559, 802.90002441, 827.20001221, 842.09997559, 860.79998779, 876.09997559, 894.40002441, 922.40002441, 950.09997559, 957.79998779, 982.70001221, 1012.40002441, 1046.30004883, 1075.09997559, 1110.19995117, 1130.19995117, 1159.80004883, 1195., 1230.69995117, 1259.09997559, 1290.30004883, 1328.09997559, 1358.30004883, 1417.40002441, 1450.59997559, 1488.69995117, 1529.30004883, 1563.90002441, 1617.40002441, 1663.5, 1713.09997559, 1716.90002441, 1774.90002441, 1836.80004883, 1890.30004883, 1923.5, 1967.40002441, 1983.90002441 ], 'm2': [ 289.1499939, 294.04998779, 296.73001099, 297.79998779, 299.3500061, 302.32998657, 308.45001221, 312.36999512, 318.29000854, 324.29000854, 329.54000854, 335.5, 343.1000061, 349.25, 354.86999512, 362.72000122, 370.66000366, 378.42001343, 386.01998901, 393.23999023, 399.76000977, 407.07998657, 416.88000488, 424.73999023, 433.22000122, 440.1000061, 449.48999023, 459.17001343, 467.22000122, 471.1499939, 475.42999268, 480.16000366, 489.67001343, 502., 514.65997314, 524.77001953, 533.16998291, 542.60998535, 553.55999756, 566.84997559, 574.35998535, 578.4699707, 582.05999756, 587.90002441, 587.26000977, 595.15997314, 611.20001221, 626.54998779, 649.90002441, 672.96002197, 692.4699707, 710.26000977, 733.5, 749.66998291, 778.35998535, 802.2800293, 815.30999756, 833.22998047, 839.27001953, 855.52001953, 870.11999512, 877.82000732, 888.15997314, 902.41998291, 925.55999756, 963.30999756, 991.7199707, 1016.98999023, 1050.0300293, 1077.70996094, 1111.31005859, 1152.7800293, 1188.80004883, 1217.67004395, 1246.90002441, 1271.4699707, 1292.86999512, 1318.09997559, 1346.81005859, 1368.01000977, 1388.9699707, 1423.2199707, 1456.85998535, 1475.75, 1501.81994629, 1529.52001953, 1576.0300293, 1601.09997559, 1638., 1670.55004883, 1708.38000488, 1756.18994141 ]} friedman2_mle = { 'data': friedman2_data, 'params_exog': [-36.09872, 1.122029], 'se_exog_opg': [56.56703, .0363563], 'se_exog_oim': [33.95924, .0324069], 'params_ar': [.9348486], 'se_ar_opg': [.0411323], 'se_ar_oim': [.039903], 'params_ma': [.3090592], 'se_ma_opg': [.0885883], 'se_ma_oim': [.1125186], 'params_variance': [9.655308**2], 'se_stddev_opg': [.5635157], 'se_stddev_oim': [.7122745], 'loglike': -340.50774, 'aic': 691.0155, 'bic': 703.6244, } # 1959q1 - 1981q4 friedman2_prediction = [ 300.7722, 314.699, 318.3328, 322.1395, 324.1479, 329.3138, 338.3326, 334.2127, 340.1221, 340.1285, 345.7686, 348.9585, 358.8476, 360.8798, 367.4761, 373.4112, 380.132, 383.0179, 388.0034, 395.276, 398.8789, 410.393, 419.7131, 426.5234, 429.3965, 440.4875, 449.2072, 459.1391, 472.4367, 477.6227, 482.9371, 493.2135, 502.3943, 509.5284, 520.3149, 524.9484, 531.8344, 553.2029, 565.8674, 584.5371, 584.7531, 595.1661, 604.5025, 616.0223, 620.5868, 641.1515, 656.7986, 668.2184, 683.2755, 704.2855, 714.1062, 726.3972, 749.7296, 758.9711, 792.2435, 802.7343, 820.1996, 850.1489, 849.0018, 882.2756, 891.0745, 904.4603, 936.7991, 965.2041, 977.2533, 1020.77, 1038.109, 1072.798, 1107.716, 1137.204, 1161.788, 1201.592, 1230.821, 1261.099, 1289.544, 1316.565, 1352.555, 1384.148, 1450.45, 1466.267, 1508.321, 1560.003, 1589.353, 1631.959, 1683.234, 1731.301, 1745.414, 1792.131, 1866.122, 1907.568, 1944.034, 1999.784 ] # 1959q1 - 1981q4 # Dynamic after 1978q1 friedman2_dynamic_prediction = [ 300.7722, 314.699, 318.3328, 322.1395, 324.1479, 329.3138, 338.3326, 334.2127, 340.1221, 340.1285, 345.7686, 348.9585, 358.8476, 360.8798, 367.4761, 373.4112, 380.132, 383.0179, 388.0034, 395.276, 398.8789, 410.393, 419.7131, 426.5234, 429.3965, 440.4875, 449.2072, 459.1391, 472.4367, 477.6227, 482.9371, 493.2135, 502.3943, 509.5284, 520.3149, 524.9484, 531.8344, 553.2029, 565.8674, 584.5371, 584.7531, 595.1661, 604.5025, 616.0223, 620.5868, 641.1515, 656.7986, 668.2184, 683.2755, 704.2855, 714.1062, 726.3972, 749.7296, 758.9711, 792.2435, 802.7343, 820.1996, 850.1489, 849.0018, 882.2756, 891.0745, 904.4603, 936.7991, 965.2041, 977.2533, 1020.77, 1038.109, 1072.798, 1107.716, 1137.204, 1161.788, 1201.592, 1230.821, 1261.099, 1289.544, 1316.565, 1352.555, 1377.515, 1406.237, 1427.295, 1448.221, 1483.042, 1517.318, 1536.364, 1562.931, 1591.249, 1639.144, 1664.832, 1702.839, 1736.367, 1775.407, 1824.832 ] # 1959q1 - 1981q4 # Forecasts after 1978q1 friedman2_forecast = [ 300.7722, 314.699, 318.3328, 322.1395, 324.1479, 329.3138, 338.3326, 334.2127, 340.1221, 340.1285, 345.7686, 348.9585, 358.8476, 360.8798, 367.4761, 373.4112, 380.132, 383.0179, 388.0034, 395.276, 398.8789, 410.393, 419.7131, 426.5234, 429.3965, 440.4875, 449.2072, 459.1391, 472.4367, 477.6227, 482.9371, 493.2135, 502.3943, 509.5284, 520.3149, 524.9484, 531.8344, 553.2029, 565.8674, 584.5371, 584.7531, 595.1661, 604.5025, 616.0223, 620.5868, 641.1515, 656.7986, 668.2184, 683.2755, 704.2855, 714.1062, 726.3972, 749.7296, 758.9711, 792.2435, 802.7343, 820.1996, 850.1489, 849.0018, 882.2756, 891.0745, 904.4603, 936.7991, 965.2041, 977.2533, 1020.77, 1038.109, 1072.798, 1107.716, 1137.204, 1161.788, 1201.592, 1230.821, 1261.099, 1289.544, 1316.565, 1352.555, 1384.148, 1412.057, 1432.403, 1452.703, 1486.975, 1520.77, 1539.393, 1565.588, 1593.582, 1641.19, 1666.628, 1704.415, 1737.75, 1776.62, 1825.897 ] # 1959q1 - 1981q4 # Forecasts after 1978q1 (and dynamic) # This (the dynamic part) is not necessarily a sensible thing to do, but this # is just a unit test friedman2_dynamic_forecast = [ 300.7722, 314.699, 318.3328, 322.1395, 324.1479, 329.3138, 338.3326, 334.2127, 340.1221, 340.1285, 345.7686, 348.9585, 358.8476, 360.8798, 367.4761, 373.4112, 380.132, 383.0179, 388.0034, 395.276, 398.8789, 410.393, 419.7131, 426.5234, 429.3965, 440.4875, 449.2072, 459.1391, 472.4367, 477.6227, 482.9371, 493.2135, 502.3943, 509.5284, 520.3149, 524.9484, 531.8344, 553.2029, 565.8674, 584.5371, 584.7531, 595.1661, 604.5025, 616.0223, 620.5868, 641.1515, 656.7986, 668.2184, 683.2755, 704.2855, 714.1062, 726.3972, 749.7296, 758.9711, 792.2435, 802.7343, 820.1996, 850.1489, 849.0018, 882.2756, 891.0745, 904.4603, 936.7991, 965.2041, 977.2533, 1020.77, 1038.109, 1072.798, 1107.716, 1137.204, 1161.788, 1201.592, 1230.821, 1261.099, 1289.544, 1316.565, 1352.555, 1377.515, 1406.237, 1427.295, 1448.221, 1483.042, 1517.318, 1536.364, 1562.931, 1591.249, 1639.144, 1664.832, 1702.839, 1736.367, 1775.407, 1824.832 ] friedman2_predict = { 'data': friedman2_data, 'predict': friedman2_prediction, 'dynamic_predict': friedman2_dynamic_prediction, 'forecast': friedman2_forecast, 'dynamic_forecast': friedman2_dynamic_forecast, 'params_exog': [.66189, 1.037905], 'params_ar': [.8775207], 'params_ma': [.2770867], 'params_variance': [5.630046**2], 'loglike': -243.31642, 'aic': 496.6328, 'bic': 508.3519, }