Two or more series are individually integrated (in the time series sense) but some linear combination of them has a lower order of integration, then the series are said to be cointegrated (所以这两个量不能为I(0))
One of the best explanations of cointegration is as follows: “A man leaves a pub to go home with his dog, the man is drunk and goes on a random walk, the dog also goes on a random walk. They approach a busy road and the man puts his dog on a lead, the man and the dog are now cointegrated. They can both go on random walks but the maximum distance they can move away from each other is fixed ie length of the lead”. So in essence the distance/spread between the man and his dog is fixed, also note from the story that the man and dog are still on a random walk, there is nothing to say if their movements are correlated or uncorrelated.With correlated stocks they will move in the same direction most of the time however the magnitude of the moves is unknown, this means that if you’re trading the spread between two stocks then the spread can keep growing and growing showing no signs of mean reversion. This is in contract to cointegration where we say the spread is “fixed” and that if the spread deviates from the “fixing” then it will mean revert.
1. 成对交易
涉及到的基础概念
Stationary - 平稳过程 2.1 严格平稳(或强平稳)
2.3 弱或者广义平稳过程(WSS)
Order of Integration -单整阶数 (I(d))(https://en.wikipedia.org/wiki/Order_of_integration)
Correlation-相关
Cointergration-协整
协整和相关的区别:
Buy, Sell, Long, Short的意义
Hedging-对冲
成对交易-Pairs trading
具体代码,见jupyter文件
几个比较好的时间序列参考文章