※ 引述《liton (歐吉桑留學生)》之銘言： : ※ 引述《wwwwwww (哪個王八蛋一天上十九次됩》之銘言： : : Instrument variables is mainly used to deal with the difficulty : : that the explanatory variables and error terms are correlated. : : AR models have no such difficulty. : : But ARMA models do have and can be treated by instrument variables. : : For example, in the ARMA(1,1) case, you cannot get a consistent estimator of : : AR coeff. by regressing x_{t} on x_{t-1}. : : But you can get a consistent estimator of the AR coff. by regressing : : x_{t} on x_{t-2}. Now x_{t-2} is the instrument variable. : Well, I just take one example to overcome the correlation problem in : cross section. : In practice, there are many methods to handle with the problem. : For example, I can drop the independent variables in the regression. : A best practice for cross section model always includes testing the : correlation between independend variables. : The key is that correlation in cross section is a serios problem, no matter : in theories or practice. Correlation will result in at least three : kinds of trouble: : 1.measurement error or errors in variables : 2.endogeneity : 3.omitted variables : However, it seems that time series care more about unit roots. : I think that's another problem in time series, but the unit :roots theory has not resolve the correlation problem. In the AR case, the LSE is consistent regardless of whether there are units in the model. Theotetically, correlations between explanatory variables are not serious problems only if the Fisher information meets certain regularity conditions. Take the AR model with unit roots for example. The LSE is consistent (and even has super efficiency) even if the correlations between explanatory variables converge to 1. Of course, no one will oppose you to do ridge regression (or other fancy estimation procedures, e.g. Boosting, LASSO,..) to combat high correlations between explanatory variables. But this is another issue. The more serious problem occurs in situations where there are correlations between the explanatory variables and error (note that the latter is unobservable), which sometimes can be resolved by IV. --

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