[求助]协整滞后选择的问题？

半年不来大家越来越高深了

幼稚园级： (Introductory Econometrics 1st Edition, Wooldridge, pp68)

" Asymptotic analysis involves approximating the features of the sampling distribution of an estimator.

These approximations depend on the size of the sample. Unfortunately, we are necessarily limited in

what we can say about how “large” a sample size is needed for asymptotic analysis to be appropriate;

this depends on the underlying population distribution. But large sample approximations have been

known to work well for sample sizes as small as n ＝ 20. "

That is for undergraduate Econometrics, but not for modern Time series.

If you are really concerned with cointegration analysis, nonstationary time series analysis, do you really would like analyse a data set of sample size 40.

计量学者： 台湾中研院院士， PhD, UCSD (Prof. White 的学生)

" 许多书都强调样本规模必须大过 30 (或 50) 才够，但事实上这个问题是没有答案的。

因为：有时样本规模小于 30 时，参数与估计值便非常接近。有时即使样本规模大到 3000，

估计值仍不会接近参数。 所以我们只能说 n 越大，估计值愈有可能非常接近真实参数。

So that is why people will check the small sample property if the test statistics is asymptotic.

I think 30 is more concerned with statistics than with time series analysis. If your derivation starts from alpha-mixing, rho-mixing, functional Brownian motion, and then you deal with a 30-sample size data in your application section, will that be sensible?

Prof. White 的学生: I know White's students are all around the world. But this is not the point.

有时样本规模小于 30 时，参数与估计值便非常接近: the problem is that in nonstationary time series analysis this is not the case.

But large sample approximations have been

known to work well for sample sizes as small as n ＝ 20. ------------- that is also again not for cointegration, unit root. -----

[此贴子已经被作者于2006-2-13 19:56:54编辑过]

If you think about PPP, in general people find that in the long run, there is cointegration. Small sample size does not lead this conclusion in most cases. Well recently, people devise threshold cointegration which I think is much more intuitive. there is a growing literature of this kind. If you believe in such non-linear model,of course then large sample is welcome since normally  there are more parameters in the model. On the other hand if you think of the ADF, in order to get rid of the autocorrelation in the residual, quite a few lagged dependent variable need to be included(for example, sometimes, 15th lag turns out to be useful[OK, one can also delete the insignificant intermediate lagged variables]). Then with 40 obs, how many degrees of freedom can be left rendering the analysis really informative.

协整滞后期一般等于var最优滞后期-1

而Sims（1980）提出了决定VAR模型最优滞后阶数的似然比检验法。根据模型选择的似然比统计量LR的计算方程式为：LR（p，p+1）=-2（logLp-logLp+1）。似然比统计量服从卡方分布。

以下是引用shaowu_lj在2006-2-15 13:41:00的发言：

协整滞后期一般等于var最优滞后期-1

而Sims（1980）提出了决定VAR模型最优滞后阶数的似然比检验法。根据模型选择的似然比统计量LR的计算方程式为：LR（p，p+1）=-2（logLp-logLp+1）。似然比统计量服从卡方分布。

是的. 我用的就是这种方法, 就是找AIC和SC同时达到最小阶的VAR, 如果二者冲突, 则用对数似然比LR检验.

But there are some statistics can evalute how long the lag terms should be.you can find them in eviews and so on.

Maybe the software's suggestion is not like what you think, but it really can give you some guide. Now that you use the software,you should believe it.

Sometime the theory is not the same with the fact.

事实上，选择协整检验的滞后阶数，估计连johansen本人也没有确定的答案。好像有论文建议，通过增加滞后阶数，检验残差的白噪声性或正态性，滞后期越大，这些检验越容易通过，但需要估计的参数越多，自由度也就越少，具体操作中需要在两者间做出取舍。当然，有时也会遇到滞后期已经很长，残差仍然难以通过上述检验，此时就应该考虑模型构建问题，可能需要在Var模型中包含其他有解释能力的变量了！！