博客
关于我
Introduction of moving block bootstrap (MBB)algorithm
阅读量:243 次
发布时间:2019-03-01

本文共 2880 字,大约阅读时间需要 9 分钟。

Because we can not use usual bootstrap sampling method to get subsamples from time series dataset, then the MBB was proposed to address this issue.

Suppose we have the time series following :
X 1 X_1 X1, X 2 X_2 X2, . . . . .... ...., X 10 X_{10} X10. Note that you can extend the footnote with other number or a symbol.
First step is to split the series into several blocks in which one should figure out the size of each block. Assume we let the size of each block equal to 2, then our blocked data would look like :

X 1 , X 2 ⏞ b l o c k   1 , X 3 , X 4 ⏞ b l o c k   2 , . . . . . . X 9 , X 10 ⏞ b l o c k   5 \overbrace{X_1,X_2}^{block\,1},\overbrace{X_3,X_4}^{block\,2},......\overbrace{X_9,X_{10}}^{block\,5} X1,X2 block1,X3,X4 block2,......X9,X10 block5

with the above blocks we get, now we can apply the bootstrap algorithm by taking a random sample of the blocks with replacement. The order in which the blocks are drawn is the position that they are placed in the bootstrap series. Hence, one probably blocks might be

b l o c k   1 , b l o c k 3   , b l o c k   5 , b l o c k   1 , b l o c k   2 block\,1, block3\,, block \,5, block\,1,block\,2 block1,block3,block5,block1,block2
and the corresponding original time series is
X 1 , X 2 ,       X 5 , X 6       X 9 , X 10       X 1 , X 2 ,       X 3 , X 4 ,       X_1,X_2,\,\,\,\,\,X_5,X_6\,\,\,\,\,X_9,X_{10}\,\,\,\,\,X_1,X_2,\,\,\,\,\,X_3,X_4,\,\,\,\,\, X1,X2,X5,X6X9,X10X1,X2,X3,X4,

These are the basic process of MBB for time series data. This can help us to get a new sample series with similar short term dependence data structure to the original data.

In python, you can rely on the pkg of “arch”, following I present a simple toy code from the with a minor revision.

from arch.bootstrap import MovingBlockBootstrap from numpy.random import RandomState  from numpy.random import standard_normalimport numpy as npy = standard_normal((6, 1))# to generate a time series with standard norm distribution.bs = MovingBlockBootstrap(2, y,random_state=RandomState(1234))# 2 is block size, y is your time series data, random_state #                                                        														is for reproducibility when requiredi=0bs_x=[ ] # an empty list to store the bootstrap series#here for is to look what the bootstrap looks like for each iteration, in our demonstrated case, we do boostrap only for 2 times.for data in bs.bootstrap(2):    print(data)    bs_y.append(data[0][0])     print(bs_y)    i=i+1# fc is function to compute the bootstrap series mean value.,you can replace it with your own definitiondef fc(a):    return a.mean(0)results = bs.apply(fc,2) ###to apply  a function defined by yourself to the bootstrap replicated data, "2" means apply the fc 2times to calculate the average of the boostrap data. of course , you can figure it with any number you want. print(results)

Thx for ur reading.

转载地址:http://uaet.baihongyu.com/

你可能感兴趣的文章
MySQL 索引深入解析及优化策略
查看>>
MySQL 索引的面试题总结
查看>>
mysql 索引类型以及创建
查看>>
MySQL 索引连环问题,你能答对几个?
查看>>
Mysql 索引问题集锦
查看>>
Mysql 纵表转换为横表
查看>>
mysql 编译安装 window篇
查看>>
mysql 网络目录_联机目录数据库
查看>>
MySQL 聚簇索引&&二级索引&&辅助索引
查看>>
Mysql 脏页 脏读 脏数据
查看>>
mysql 自增id和UUID做主键性能分析,及最优方案
查看>>
Mysql 自定义函数
查看>>
mysql 行转列 列转行
查看>>
Mysql 表分区
查看>>
mysql 表的操作
查看>>
mysql 视图,视图更新删除
查看>>
MySQL 触发器
查看>>
mysql 让所有IP访问数据库
查看>>
mysql 记录的增删改查
查看>>
MySQL 设置数据库的隔离级别
查看>>