Week 2 Flashcards

1
Q

What is autocorrelation? Verbal and mathematical

A

Relationship between variable and its lag
E(εiεj) = σij, i!=j
E(εε’) = Ω = matrix of all different σij -> symmetric and positive definite

Also possible heteroskedasticity

Can see in plot of residual against residual lag - correlated

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2
Q

What are the properties of OLS under autocorrelation?

A
  • Unbiased
  • Consistent
  • Inefficient
  • Incorrect SE
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3
Q

What estimators should we use if autocorrelation?

A

Newey-West Estimator Covariance Matrix

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4
Q

Where do the weights in the Newey-West estimator come from?

A

The Kernel function

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5
Q

What are the properties of Newey-West SE?

A

HAC (Heteroskedastic and autocorrelation consistent)

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6
Q

What is the idea of the Cochrane-Orcutt procedure?

A

Errors are from an autoregressive model of order 1
You have the normal regression, the lag regression, and the regression of error term with lag
Find value of y(i) - py(i-1)

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7
Q

What are the alternatives to Cochrane-Orcutt procedure?

A

NLS for y(i) = py(i-1) + B1(1-p) + B2(xi-px(i-1)) + n(i)

In Eviews, AR(1)

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8
Q

What is the idea of GLS?

A

Transform data s.t. the conditions for efficient OLS hold

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9
Q

What is the Choleski decomposition?

A

PP’ = Ω

Transformed data: y* = P^(-1)y ; X* = P^(-1)X ; ε* = P^(-1)ε

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10
Q

Properties of GLS disturbances

A

Homoskedastic and no autocorrelation

=> OLS for transformed model efficient estimator for β

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11
Q

Compare GLS to Cochrane-Orcutt

A
  • In GLS 1st observation is included

- In GLS scaling factor 1/σ(n)

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12
Q

GLS estimator + expected value and variance

A
b = (X'Ω^(-1)X)^(-1)X'Ω^(-1)y
E(b) = β
Var(b) = (X'Ω^(-1)X)^(-1)
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13
Q

Why do we need feasible GLS?

A

In practice often Ω unknown and have to estimate it

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14
Q

What are the steps of FGLS?

A

1) Estimate the covariance matrix
a) Apply OLS in y=Xβ + ε -> b consistent
b) Estimate Ω using residuals e = y - Xb : Ω^ = ee’
2) Apply OLS on the transformed data
a) Use Ω^ to determine P^
b) Transform data with P^^(-1) : y=P^^(-1)y and X=P^^(-1)X
c) Estimate β with OLS in the model for the transformed data: y* = Xβ + ε -> b(FLGS)

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15
Q

What is the null hypothesis of the autocorrelation tests?

A

No autocorrelation

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16
Q

What is the equation for the autocorrelation of residuals?

A

r(k) = Σe(i)e(i-k)/Σe(i)^2 : first sum is from i=k+1 to n; second sum i=1 to n

17
Q

Durbin-Watson test

A

DW = Σ(i=2->n) (e(i) - e(i-1))^2/Σe(i)^2 ≈ 2(1 - r(1))
0 (r(1) = 1 => perfect correlation)
4 (r(1) = -1 => perfect negative correlation)
H0: Value should be around 2

18
Q

What are the disadvantages of the Durbin-Watson test?

A
  • Distribution under H0 depends on the properties of regressors
  • Not applicable when lagged dependent variables are included as regressors
19
Q

Box-Pierce Test

A

H0: No autocorrelation

BP = nΣ(k=1 -> p) r(k)^2 ≈ χ2(p)

20
Q

Ljung-Box Test

A

LB = nΣ(k=1 -> p) (n+2)/(n-k) r(k)^2 ≈ χ2(p)

21
Q

What type of test is a Breusch-Godfrey test?

A

Lagrange Multiplier (LM) test

22
Q

Which is the procedure for the Breusch-Godfrey test?

A

1) OLS on y(i) = x(i)’β + ε(i)
2) Run auxiliary regression
3) Under H0 (no autocorrelation) have nR^2 ≈ χ2(p)

23
Q

What is the main difference between the Box-Pierce and Ljung-Box test?

A

The Box-Pierce test is an approximated version of the Ljung-Box test

24
Q

What happens to the significance of the parameter of the independent variable with NW SE?

A

The significance may change

25
Q

What happens to the marginal effect of the independent variables with NW SE?

A

Doesn’t change

26
Q

Do NW SE automatically correct for possible heteroskedasticity?

A

Yes

27
Q

Do NW SE not harm i.e. should they always be used?

A

True - Ω = σ^2*I

False - We add uncertainly, less efficient