You are given the following autocorrelations for a sample of 100 observations: Lag ACF 1 2 3 0

The test will be conducted for 3 seperate cases,

(i) m =1 (lag =1)

here, T = 100,  = 0.032,

Q* = 100*(100+2)*[(0.032)^2]/(100 - 1) = 0.1055

Q ~ X^2 with 1 degree of freedom

Q(0.05,1) = 3.841

Since, Q* < 3.841, We may accept the null, i.e there is no autocorrelation of order 1

(ii) m =2

here, Tau1 = 0.032 and Tau2 = 0.104

Q* = 100*(100+2)*{[(0.032)^2]/(100 - 1) + [(0.104)^2]/(100-2) } = 1.2312

Q ~ X^2 with 2 degrees of freedom

Q(0.05,2) = 5.991

Clearly Q* < 5.991, therefore we may reject the null hypothesis, and conclude

there is no significant autocorrelation at lag of order 2.

(iii) m =3

here, Tau1 = 0.032 Tau2 = 0.104, Tau3 = 0.420

Q* = 100*(100+2)*{[(0.032)^2]/(100 - 1) + [(0.104)^2]/(100-2) + [(0.420)^2]/(100-3) } = 19.7805

Q ~ X^2 with 3 degrees of freedom

Q(0.05,3) = 7.815

here, Q* >. 7.815, thus we may reject the null hypothesis and conclude that there is a significant autocorrelation at lag of order 3.

Thus option A is correct.