Durbin h test (In Autoregressive Models)

Durbin h test.

We are familiar with the Durbin Watson test. Over there as we studied it in Masters in Economics as well, in the DW test the model should not contain lagged values of the dependent variable as an explanatory variable, the explanatory variables should be strictly exogenous.

However, to detect autocorrelation in Autoregressive models, if in case we apply OLS method, say d is almost 2 (Range of d os 0 to 4). We know if the value of d is around 2 there's no sign of autocorrelation.

In autoregressive model if we apply Durbin Watson to detect autocorrelation, we will erroneously declare that there's no autocorrelation in the model, even there's autocorrelation actually in the data. So, there the Durbin Watson test can't be used.

Durbin has suggested another large sample test to detect the first order autocorrelation in the autoregressive models. So the statistic is the Durbin h statistics.

h = rhohat * {n / (1 - n [Var alphahat])}

where, n = sample size.

             Var aplhahat = Variance of the coefficient of y t - 1.

              Rhohat = estimate of the coefficient of the 1st order autocorrelation.

Now, for large samples, Durbin ad shown that.

Ho : Rho = 0

Ha: Rho is not equal to 0

[ut = rho ut-1 + ephsilon t]

So, h asymp ~ N (0,1)

i.e. in large sample h is the standard normal variable.

In practice  rhohat = 1- d.

● Features of h stat are given as follows:

a) Here, it doesn't matter how many explanatory variables or lagged values are used in a model, the only concern is the requirement of the variance of coefficient of Y t-1, Y t-2, Y t -3, ... etc.

b) The test is not applicable when; n[Var (aplha)] > 1.

c) Since, its a large sample test it's application in small samples is not generally valid.

d) One can use BG-LM test as it's statistically powerful as sample size is very large. In sample (small) BG or LM is preferred over h test stats.

Now guys, if we get autocorrelation by Durbin h test or BG LM test then what should we do ?

The answer is, we should use " New West -HAC" procedure to estimate the parameters. 1st we have to solve the problem of correlation between Y t-1 and V t on the one hand using proxy, then we have to use "New West - HAC" standard errors to solve the problem of autocorrelation.

Thank you guys for reading this. I am sorry for the notations as i am writing these with my cell phone.

In the coming days, i will be writing about more.

Aditya Raz Pokhrel

MBA, MA Economics, MPA.