Week 2 - Serial Correlation Flashcards Preview

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Flashcards in Week 2 - Serial Correlation Deck (20)
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1
Q

What is serial correlation and what assumption does it go against?

A
  • Serial correlation is the presence of some from of linear dependence over time for some series z
  • This goes against assumption 3, which is Cov(et, et-j) = 0 for j does not equal, which is the idea that there is no serial correlation
2
Q

What is TheAutoCorrelationFunction (ACF)

A
  • The ACF is a pictorial representation of linear dependency over time which is measured in the form of the correlation between Z and Z t-k for different values of K
3
Q

What is TheAutoCorrelation Function (ACF) equal to?

A
  • Corr(Zt,Zt-k) = Gamma K / Gamma o = Pk, where Po=1, and Cov(Zt,Zt-k)=Gamma k, and V(Zt)=Gamma o
4
Q

What are the 4 different types of models we look at the ACF for?

A
  1. White Noise model
  2. Autoregressive model (AR)
  3. Moving average model (MA)
  4. Autoregressive moving average models (ARMA)
5
Q

What is Zt equal to for a white noise model?

A

Zt = et

6
Q

For a white noise model what is the E(Zt), V(Zt) , Cov(Zt,Zt-1), and Pj equal to?

A
  • E(Zt)=0
  • V(Zt)= Theta Squared
  • Cov(Zt,Zt-1)=0
  • Pj=0 for J not equal to 0
7
Q

For a white noise model what does the ACF look like when plotted?

A

See notes

8
Q

What is Zt equal to in an AR(1) model?

A

Zt = Phi Zt-1 + et

9
Q

What is E(Zt) V(Zt) and the Cov (Zt, Zt-1) equal to in an AR(1) model?

A
  • E(Zt)=0, See notes for derivation
  • V(Zt)= Theta squared / 1 + Theta Squared, for all values of T, See notes for derivation
  • Cov(Zt,Zt-1) = Phi^h, see notes for derivation
10
Q

What does the ACF look like for AR(1) model when plotted?

A

See notes zig zag up and down

11
Q

What can you conclude about the ACF for AR(1)

A
  • The ACF indicates we’ve got the condition of stationarity implying the correlation between 2 points gets closer to zero as the points are further away.
12
Q

What is Zt equal to for an AR(2) model?

A
  • Zt = Phi 1 Zt-1 + Phi 2 Zt-2 + et
13
Q

For an AR(2) model what is E(Zt) V(Zt) and Cov(Zt, Zt-1) equal to generally?

A
  • E(Zt)=0

- V(Zt)= E(Zt)^2= Gamma 0, generally Gamma j(the variance of Zt) = Phi 1 Gamma j-1 + Phi 2 Gamma j-2

14
Q

What does the ACF look like for an AR(2) model?

A

See notes

15
Q

What is Z equal to in a moving average MA(1) model?

A
  • Zt = Theta et-1 + et
16
Q

In a MA(1) model, what are E(Zt) , V(Zt) and Cov(Zt,Zt-1), and the Cov(Zt,Zt-2) equal to?

A
  • E(Zt)=0
  • V(Zt)= (1+Theta^2)sigma^2
  • Cov(Zt,Zt-1)= Gamma 1 = Theta Sigma^2
  • Cov(Zt,Zt-2)= Gamma 2 = 0, see notes for full derivation
17
Q

What does the ACF look like in an MA(1) model?

A

See notes

18
Q

In an MA(2) model what is Zt equal to?

A

Zt = Theta 1 et-1 + Theta 2 et-2 + et

19
Q

In an MA(2) model, What is the E(Zt) V(Zt) and the Cov(Zt,Zt-1) Cov(Zt,Zt-2) and Cov(Zt,Zt-3) equal to?

A
  • E(Zt)=0
  • V(Zt) = ( 1 + Theta 1^2 + Theta 2^2)Sigma^2
  • Cov(Zt,Zt-1)=Gamma 1 = (Theta 1 +Theta1 x Theta 2)Sigma^2
  • Cov(Zt,Zt-2)=Gamma 2 = Theta 1 x Sigma^2
  • Cov(Zt,Zt-3)=Gamma 3 = 0
20
Q

What does the ACF look like for the MA(2) model?

A

See notes