# Quant Question

The regression results from fitting an AR(1) model to the first-differences in enrollment growth rates at a large university includes a Durbin-Watson statistic of 1.58. The number of quarterly observations in the time series is 60. At 5% significance, the critical values for the Durbin-Watson statistic are dl = 1.55 and du = 1.62. Which of the following is the most accurate interpretation of the DW statistic for the model? A) Since DW > dl, the null hypothesis of no serial correlation is rejected. B) Since DW < du, the null hypothesis of no serial correlation cannot be rejected. C) The Durbin-Watson statistic cannot be used with AR(1) models. D) Since dl < DW < du, the results of the DW test are inconclusive.

I’d go with c).

Is it C?

it is C you have to look at autocorrelations for AR

BTW - I’m not wild about answer c) either. The DW test is just going to biased and have low power but the statistic is biased toward 2 so your tables are conservative. That 1.58 number would move me and I would find it meaningful.

Ahh, Joey and maratikus have it right. I wanted to see how many people chose D as I did. I over looked the mentioning of AR.

with AR model you have to use t test not DW.

With AR model, can someone check that this is the right t equation to use to check autocorrelation: t = correlation / stand. error = correlation / [1 / (square root of # of observations)] ??

That looks right to me.

C and the equation is RIGHT!

I think I would have gone with D. Oops!

C, try to remember the graph on this…the line with the areas specified.