In AR models, does the significance of lagged variables still matter?

CFA Level II Quant
#1

It seems that in an AR model, the significance of the actual lagged variables doesn’t matter, as long as you have no serial correlation in the residuals. Is this correct?

For instance, in Reading 13, Q17 on page 488 of the 2014 CFAI book 1, part A only addresses the fact that none of the autocorrelations are significant, therefore the model is correctly specified. Yet the lag 1 variable has a t-stat of -.8757 (not significant).

Also in Part b, how does a difference of sales of 1% from lnSales(t-1) - lnSales(t-2) translate to 1.01 and a difference of sales of 2% from lnSales(t-4)-lnSales(t-5) translate to 1.02? Wouldn’t we have to know the actualy sales figures figures? Or is there some mathematical property for exponents that I’m missing?

Thanks for your help.

#2

Any help would be appreciated! Thanks

#3

I believe that the significance of the lagged variables does matter; if the t-stat for one coefficient is insignificant, I’d say that you could remove the corresponding variable from your model.

For the second,

ln(x) – ln(y) = ln(x/y)

So, if sales increase 1% from month t-2 to month t-1, then

ln(sales(t-1)) – ln(sales(t-2))

= ln(sales(t-1)/sales(t-2))

= ln(1.01)

≈ 0.00995

#4

Thanks s2000 you are insightful as always

#5

Glad to be of some small help.