6
k
k
0
covariance at lag k variance
obviously when k 0, 1 0
1 1 k
plot against k, the graph we obtain is known as the population correlogram k
• Returning to the example given in figure 21.8,the value of the Q statistic up to lag 25 is about 793,the LB statistic is about 891,both are highly significant, the probability of obtaining such a high
• We can rewrite the functions above as,
Yt ( 1)Yt1 ut
(21.9.1)
• or,
• Yt Yt 1 ut
(-1.96*0.1066,1.96*0.1066) or (0.2089,0.2089)
10
• In figure 21.8,the left two lines of dots represent the 95% confidence interval.
the joint hypothesis test of k H0 : all the k are simultaneo usly equal to zero.
• This can be done by using the Q statistic developed by Box and Pierce,