Lecture 7

Question 1

Describe Lemma 1, which is important for CLT of Time-Series Data. What does it imply?

Answer 1

It implies that if a r.v is made up of two r.v’s, one that converges in distribution to a normal and the other that has a very high probability of being small, then the random variable converges in distribution to a Normal.

Question 2

What is Theorem 30? Hint: It relates to finite MA models.

Answer 2

Question 3

Prove theorem 30 using the blocking method.

Answer 3

See notes for answer.

Question 4

What is theorem 31? Hint: it relates to infinite MA models.

Answer 4

Question 5

Prove theorem 31 using lemma 1.

Answer 5

See notes

Question 6

What is Theorem 32?

Answer 6

Covariance becomes small as the spacing between data increases. (Weak auto-covariance)

Question 7

State the asumptions needed for CLT to hold for time series.

Answer 7

See page 78 and Theorem 33 as well as remak 15

Question 8

State theorem 34

Answer 8