http://www.hylt.net/vb/showpost.php?p=59492&postcount=2 世上的路很多，也很少。 无意中看到了tom-sh兄两年前的帖子，提到了cointegration.
而hylt兄去年介绍的Carol Alexander在cointegration方面也有一些论文。 Carol Alexander brings many new insights to the pricing and hedging of options with her understanding of volatility and correlation, and the uncertainty which surrounds these key determinants of option portfolio risk. Modelling the market risk of portfolios is covered where the main focus is on a linear algebraic approach; the covariance matrix and principal component analysis are developed as key tools for the analysis of financial systems. The traditional time series econometric approach is also explained with coverage ranging from the application cointegration to long-short equity hedge funds, to high-frequency data prediction using neural networks and nearest neighbour algorithms. Carol Alexander还有一篇论文，研究方向正好与我的一个思路重合。正在琢磨着怎么借鉴一下她的方法。
2005年，hylt兄与itfin兄华山论剑、讨论统计套利，列出了一大堆有价值的资源。 其中当然也不会少了cointegration。 世上本没有路，走的人多了，就成了路。 老外的大马路，到了国内，成了山间小路。 “人住层崖嫌洞浅，鸟鸣春磵觉山幽。”
cointegration，协整，一个统计概念。描述变量之间的关系。 pair trading，配对交易，针对品种之间的价差关系进行操作。有些pair trading策略是以cointegration为理论基础的。 pair trading目前可能更多是机构采用较多。
再支持一下。 http://www.wilmott.com/messageview.cfm?catid=4&threadid=48032 http://www.trade2win.com/boards/mechanical-systems-trading/11209-co-integration-pairs-trading.html
HOOK 的困惑也是我的对cointegration 的困惑。 Since cointegration gives a linear relationship between non-stationary variables, that it is itself stationary, you could create a portfolio (given by the weights in the cointegration vector) that is stationary and mean reverting. In this sense you should short the portflio if it is above the (estimated) mean and go long in case it is below the (estimated) mean. The difficulty is finding these portfolios that will maintain this stationary relationship for a long time out of sample. Unfortunatellyit is easy to find spurius cointegrations in the sample that won´t stand for long when you decide to go trading
这是华尔街喜欢cointegration的一个重要原因。 这是一些对冲基金的基本操作策略。包括著名的LTCM。 他所讲的困难，我理解，本质上不在于"finding these portfolios"，不在于组合的构建。而是找到在未来仍会持续一段时间让你赚钱的cointegration。 事实上，有很多cointegration是必然的，比如说，上证50ETF和上证50指数之间。再比如说，香港利率与美国利率之间。在比如说，汇丰在香港的股价和在英国的股价之间。 因为它的必然性，所以它的价差就会较小，无风险套利的空间就会较小。你必须放大到足够的杠杆，才有足够的净利润。事实上，杠杆放大的过程，也是风险提高的过程。风险、收益的规律在起作用。
使用http://www.spatial-econometrics.com/的matlab toolbox验证上证50指数和50ETF收盘价过去一年的cointegration(CADF)检验，结果不显著（如下），哪位懂的评价一下？ res=cadf(a,b,-1,1) // a=上证50指数,b=50ETF prt(res) Augmented DF test for co-integration variables: variable 1,variable 2 CADF t-statistic # of lags AR(1) estimate -1.46630294 1 -0.022661 1% Crit Value 5% Crit Value 10% Crit Value -3.357 -2.775 -2.466
最后还是tom_sh兄来吃这个“螃蟹”了 辛苦了。 1. 参数p和nlag的取值可能还可以试试其它数值。 2. 对原始数据取个对数，再来试试？ 3. 如果还不行，建议先对它书中的例子做个计算。然后再计算自己的数据，可能更好。 因为它的cadf()函数对参数可能有自己的要求。
cadf(50指数,50ETF,3,0)在95%上显著，观察历史叠加曲线，ETF始终有折价，应该是长电停牌的原因，或许应该把这个因素考虑进去。 cadf(上证指数,深证成指,1,2)在99%上显著。 cadf(50ETF,50ETF净值,-1,0)在99%上显著。
Hi, One suggestion is that you need to do de-trend first, which will increase the test significantly.
If I use johansen method instead of cadf, how to interpret the testing result, in investment terms or concepts, such as ones obtained from Le Sage matlab routines as follows: % USAGE: result = johansen(x,p,k) % ------------------------------------------------------- % RETURNS: a results structure: % result.eig = eigenvalues (m x 1) % result.evec = eigenvectors (m x m), where first % r columns are normalized coint vectors % result.lr1 = likelihood ratio trace statistic for r=0 to m-1 % (m x 1) vector % result.lr2 = maximum eigenvalue statistic for r=0 to m-1 % (m x 1) vector % result.cvt = critical values for trace statistic % (m x 3) vector [90% 95% 99%] % result.cvm = critical values for max eigen value statistic % (m x 3) vector [90% 95% 99%] % result.ind = index of co-integrating variables ordered by % size of the eigenvalues from large to small
How : estimate Cointegration Vector ? I run the johansen function of the Spatial Econometrics Toolbox and get the eigenvectors. Is there anybody can tell me how to estimate the Cointegration Vector? Thanks! if for two equations and two lags egenvector will be [ b11 b12; b21 b22]