Math 关于Adfuller测试结果变化的问题

我有一个系列，我试图运行线性回归，并确定平稳性。当我将窗口移动到下一个样本时，平稳性测试从静止变为非静止。这是预期的吗？我的印象是，平稳性会随着时间慢慢改变。这是我收集到的测试用例

这里，x1，y1是第一组实验的数据。x2和y2用于第二组。x2，y2几乎与x1，y1相似（我只是降低x1和y1的第一个值，并在末尾插入新样本以获得x2，y2系列）。但adf结果却截然不同（p-val从0.001945变为0.7519）。“滞后”似乎也非常不同（0对15）。如果有人能为我澄清这一点，我将不胜感激

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输出： 使用x1，y1:（-3.9123257881734177，0.0019459855963443135，15184，{'1%：-3.466398230774071，'5%：-2.8773796387256514，'10%：-2.575213838610586}，1234.5454010045535）

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对于x2，y2:（-1.0037181258360757，0.751905785667101，0，199，{'1%：-3.4636447617687436，'5%：-2.8761761179270766，'10%：-2.574571581854}，1236.084974615374）

你的问题应该在stats.stackexchange.com上提出，而不是在这里。完成。我已经在stats.stockexchange.com上发布了。谢谢

import pandas as pd
import numpy as np
from sklearn.linear_model import LinearRegression
from statsmodels.tsa.stattools import adfuller
from regressors import stats

x1 = [966.0, 956.9, 949.85, 944.7, 970.85, 950.9, 951.35, 948.45, 954.95, 951.2, 953.6, 957.5, 967.55, 959.3, 955.15, 948.8, 947.4, 938.1, 950.8, 947.05, 935.25, 928.6, 914.15, 924, 935.55, 919.15, 925.05, 939.3, 927.75, 940.05, 945.7, 978.4, 982.45, 1001.75, 1011, 1002.15, 1009.9, 1007.5, 1019.75, 975.4, 1011.45, 1010.4, 1009, 1008.25, 1017.65, 1048.7, 1055.75, 1066.55, 1093.7, 1106.8, 1132.1, 1157.8, 1137, 1108.25, 1127.5, 1125.9, 1137.5, 1148.35, 1129.05, 1122.5, 1112.45, 1090.85, 1076.55, 1074.85, 1060.6, 1072.3, 1062.55, 1093.95, 1104, 1112.75, 1136.55, 1091.05, 1122.5, 1117.75, 1124.2, 1133.45, 1123.7, 1110.55, 1096.75, 1103.35, 1139.85, 1140.05, 1115.65, 1113.2, 1100, 1137.85, 1140.9, 1126.45, 1134.65, 1143.5, 1153.35, 1175.2, 1167.75, 1163.2, 1164.55, 1154.6, 1165.7, 1159.2, 1189.8, 1177.3, 1220.5, 1253.05, 1236.05, 1240.3, 1250.3, 1246.8, 1255.8, 1260.45, 1288.25, 1293.8, 1282.1, 1262.15, 1312.1, 1376.2, 1371.75, 1387.15, 1370.5, 1344.95, 1312.05, 1316.65, 1339.45, 1339.7, 1340.85, 1325.1, 1301, 1276.2, 1239.05, 1260.9, 1271.25, 1284.65, 1279.35, 1272.1, 1303.55, 1305.55, 1296.5, 1292.65, 1309.8, 1309.65, 1290.4, 1281.3, 1292.45, 1291.3, 1265.2, 1266.35, 1274.3, 1274.55, 1253.3, 1267, 1304.5, 1343.55, 1330.35, 1316.7, 1335.75, 1345.55, 1368.15, 1374.85, 1373.6, 1384, 1387, 1337.1, 1344.45, 1370.8, 1371.55, 1353.75, 1333.8, 1336.2, 1385.3, 1368.05, 1385.2, 1409.9, 1411.05, 1430.2, 1439.85, 1441.05, 1425.75, 1397.15, 1360.75, 1353.75, 1362.55, 1351.35, 1351.1, 1333.8, 1343.55, 1348.5, 1356, 1356.35, 1354.35, 1352.05, 1329.4, 1341.5, 1361.6, 1352.55, 1339.55, 1330.65, 1327, 1316.4, 1330.5, 1341, 1335.8, 1340.8]
x2 = [956.9, 949.85, 944.7, 970.85, 950.9, 951.35, 948.45, 954.95, 951.2, 953.6, 957.5, 967.55, 959.3, 955.15, 948.8, 947.4, 938.1, 950.8, 947.05, 935.25, 928.6, 914.15, 924, 935.55, 919.15, 925.05, 939.3, 927.75, 940.05, 945.7, 978.4, 982.45, 1001.75, 1011, 1002.15, 1009.9, 1007.5, 1019.75, 975.4, 1011.45, 1010.4, 1009, 1008.25, 1017.65, 1048.7, 1055.75, 1066.55, 1093.7, 1106.8, 1132.1, 1157.8, 1137, 1108.25, 1127.5, 1125.9, 1137.5, 1148.35, 1129.05, 1122.5, 1112.45, 1090.85, 1076.55, 1074.85, 1060.6, 1072.3, 1062.55, 1093.95, 1104, 1112.75, 1136.55, 1091.05, 1122.5, 1117.75, 1124.2, 1133.45, 1123.7, 1110.55, 1096.75, 1103.35, 1139.85, 1140.05, 1115.65, 1113.2, 1100, 1137.85, 1140.9, 1126.45, 1134.65, 1143.5, 1153.35, 1175.2, 1167.75, 1163.2, 1164.55, 1154.6, 1165.7, 1159.2, 1189.8, 1177.3, 1220.5, 1253.05, 1236.05, 1240.3, 1250.3, 1246.8, 1255.8, 1260.45, 1288.25, 1293.8, 1282.1, 1262.15, 1312.1, 1376.2, 1371.75, 1387.15, 1370.5, 1344.95, 1312.05, 1316.65, 1339.45, 1339.7, 1340.85, 1325.1, 1301, 1276.2, 1239.05, 1260.9, 1271.25, 1284.65, 1279.35, 1272.1, 1303.55, 1305.55, 1296.5, 1292.65, 1309.8, 1309.65, 1290.4, 1281.3, 1292.45, 1291.3, 1265.2, 1266.35, 1274.3, 1274.55, 1253.3, 1267, 1304.5, 1343.55, 1330.35, 1316.7, 1335.75, 1345.55, 1368.15, 1374.85, 1373.6, 1384, 1387, 1337.1, 1344.45, 1370.8, 1371.55, 1353.75, 1333.8, 1336.2, 1385.3, 1368.05, 1385.2, 1409.9, 1411.05, 1430.2, 1439.85, 1441.05, 1425.75, 1397.15, 1360.75, 1353.75, 1362.55, 1351.35, 1351.1, 1333.8, 1343.55, 1348.5, 1356, 1356.35, 1354.35, 1352.05, 1329.4, 1341.5, 1361.6, 1352.55, 1339.55, 1330.65, 1327, 1316.4, 1330.5, 1341, 1335.8, 1340.8, 1352.8]

y1 = [280.95, 281.55, 281.05, 278.2, 279.65, 277.4, 277.4, 279.65, 276.2, 277, 276.5, 281.95, 282.7, 279.75, 274.2, 273.35, 272.7, 269.95, 272.05, 272.35, 272.05, 271.3, 271.6, 273.7, 282.85, 276, 278.75, 282.55, 282.85, 284.55, 293.3, 307.2, 307.35, 312.15, 311.7, 316.5, 311.9, 312.25, 314.85, 304.7, 313.9, 311.55, 311.5, 313.55, 313.05, 333.95, 330.05, 335.3, 359.45, 374, 377.5, 375.95, 350.45, 341.6, 339.65, 343.2, 346.75, 343.45, 344.45, 342.4, 339.8, 334.05, 335.65, 337.45, 340.7, 334.8, 335.65, 342.95, 345.4, 345.75, 351.95, 342.3, 346.75, 345.55, 344.15, 345.45, 348.7, 345.3, 342.6, 346.3, 355.85, 355.5, 350, 354.85, 350.5, 352.85, 358.9, 360.3, 360.8, 358.45, 363.7, 359.5, 355.9, 353.5, 349.35, 352.7, 358.4, 356.9, 363.55, 353.95, 364.2, 385.55, 382.2, 382.9, 385, 384.4, 386.25, 388.1, 396.4, 406.3, 406.4, 406.75, 430.2, 446.8, 457.7, 459, 454.35, 438.55, 431.55, 430.25, 444.95, 445.8, 444.75, 437.25, 446.45, 431.9, 417.9, 421.5, 428.35, 433.5, 429.9, 425.55, 435.3, 439.35, 439, 437, 442, 439.7, 437.55, 430.2, 432.95, 429.95, 418.7, 415.5, 423.1, 421.3, 410.3, 414.4, 430.4, 435.5, 438.8, 420.85, 416.9, 419.2, 426.7, 425.2, 426.35, 429.3, 419.65, 410.15, 410.5, 414.45, 415.5, 411, 399.65, 403.9, 418.1, 414.15, 416.4, 425.45, 427.15, 438, 442.1, 450.1, 432.6, 418.95, 430.7, 469.2, 472.75, 470.1, 486.65, 475.7, 480.3, 485.05, 489.3, 489.85, 492.75, 487.35, 481.95, 490.6, 512.3, 515.25, 525.95, 518.4, 507.6, 498.45, 500.5, 509.2, 511.9, 508.65]
y2 = [281.55, 281.05, 278.2, 279.65, 277.4, 277.4, 279.65, 276.2, 277, 276.5, 281.95, 282.7, 279.75, 274.2, 273.35, 272.7, 269.95, 272.05, 272.35, 272.05, 271.3, 271.6, 273.7, 282.85, 276, 278.75, 282.55, 282.85, 284.55, 293.3, 307.2, 307.35, 312.15, 311.7, 316.5, 311.9, 312.25, 314.85, 304.7, 313.9, 311.55, 311.5, 313.55, 313.05, 333.95, 330.05, 335.3, 359.45, 374, 377.5, 375.95, 350.45, 341.6, 339.65, 343.2, 346.75, 343.45, 344.45, 342.4, 339.8, 334.05, 335.65, 337.45, 340.7, 334.8, 335.65, 342.95, 345.4, 345.75, 351.95, 342.3, 346.75, 345.55, 344.15, 345.45, 348.7, 345.3, 342.6, 346.3, 355.85, 355.5, 350, 354.85, 350.5, 352.85, 358.9, 360.3, 360.8, 358.45, 363.7, 359.5, 355.9, 353.5, 349.35, 352.7, 358.4, 356.9, 363.55, 353.95, 364.2, 385.55, 382.2, 382.9, 385, 384.4, 386.25, 388.1, 396.4, 406.3, 406.4, 406.75, 430.2, 446.8, 457.7, 459, 454.35, 438.55, 431.55, 430.25, 444.95, 445.8, 444.75, 437.25, 446.45, 431.9, 417.9, 421.5, 428.35, 433.5, 429.9, 425.55, 435.3, 439.35, 439, 437, 442, 439.7, 437.55, 430.2, 432.95, 429.95, 418.7, 415.5, 423.1, 421.3, 410.3, 414.4, 430.4, 435.5, 438.8, 420.85, 416.9, 419.2, 426.7, 425.2, 426.35, 429.3, 419.65, 410.15, 410.5, 414.45, 415.5, 411, 399.65, 403.9, 418.1, 414.15, 416.4, 425.45, 427.15, 438, 442.1, 450.1, 432.6, 418.95, 430.7, 469.2, 472.75, 470.1, 486.65, 475.7, 480.3, 485.05, 489.3, 489.85, 492.75, 487.35, 481.95, 490.6, 512.3, 515.25, 525.95, 518.4, 507.6, 498.45, 500.5, 509.2, 511.9, 508.65, 514.7]

x_train = np.array(x1).reshape((-1, 1))
y_train = np.array(y1)
model = LinearRegression().fit(x_train, y_train)
residues = stats.residuals(model, x_train, y_train, 'raw')
adf_result = adfuller(residues)
print(adf_result)

x_train = np.array(x2).reshape((-1, 1))
y_train = np.array(y2)
model = LinearRegression().fit(x_train, y_train)
residues = stats.residuals(model, x_train, y_train, 'raw')
adf_result = adfuller(residues)
print(adf_result)