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???????MMB????????????

??????????????????????????????????Moving Block Bootstrap, MBB????????????MMB???????????????????????????????????????????????

????

??????????????????????????????????2???????????????????????????????

X?, X?, ..., X??

???????

• ?1?X?, X?
• ?2?X?, X?
• ...
• ?5?X?, X??

Bootstrap??

????????Bootstrap?????????????????????????????????????????????????????????????????????1??3??5??1??2?????????????????

block1, block3, block5, block1, block2

Python??

?Python????????arch??????????????????????

from arch.bootstrap import MovingBlockBootstrap
from numpy.random import RandomState
import numpy as np
# ???????????????
y = standard_normal((6, 1))  # shape (6, 1)
# ????????
bootstrap = MovingBlockBootstrap(2, y, random_state=RandomState(1234))  # ????2
# ??Bootstrap??
bs_y = []
# ??Bootstrap??
for _ in range(2):
    data = bootstrap.bootstrap(2)  # ??2?Bootstrap??
    bs_y.append(data[0][0])  # ???????
    print("Bootstrap??:", data)
    print("??????:", bs_y)
# ????????
def fc(a):
    return a.mean(0)  # ?????
# ?????????
results = bootstrap.apply(fc, 2)  # ?????????????
print("????:", results)

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