 # Serial correlation in AR model

It is present if the any of the augoregressive t stats are statistically significant.

How do u correct for it? I cant remember.

you mean if any lags are significant?

Use Hansen method?

If you find significant serial correlation between error terms and their one period lags, try an AR(2) model. If that doesnt work, try AR(3). Keep increasing the order until autocorrelation is not significant.

To test for autocorrelation in AR Model we have to use a t-test, not DW. The t-stat is given by [correlation of e(t) and e(t-k)] / [1(T)^(1/2)] and if its greater than t-crit, the t-stat is significant and autocorrelation is present.

I doubt we need to know formulas for the exam, most likely we will get the t-stats and t-crits or p-values, and it would be up to us to interpret whether autocorrelation is significant. If the p-values are really small, or if the absolute value of the t-stat is less than that of t-crit, autocorreltion in the AR model shouldn’t be a problem.

I believe the issue of seasonality receives similar treatment, except we dont increase the order of the AR§ model, but just adjust it for a seasonal lagged term, i.e. t-12 if the current value depends on previous period value as well as last year’s value.

Would appreciate if someone could confirm this. Think its correct.

they will give you the Autocorrelation but they probably won’t give you the std. error of it. you have to calculate it and it’s pretty straight forward whchi is n^(1/2)

if you run a regression like : xt = a +xt-1 +e

and lag 3, 6, 12 are significant. then you rerun the regression like this

xt = a +xt-1 +xt-3 +e

look at lags again, if 6 and 12 still significant you rerun this regression

xt = a +xt-1 +xt-3 +xt-6 +e

look at lags again, if 12 still significant you rerun this regression

xt = a +xt-1 +xt-3 +xt-6 +xt-12 +e

look at the lag again, if there is no more significant lag, then this is your model. i did those kind of model 2000 times in my M. Sc

Nice thanks.