Topic 11: Autocorrelation Flashcards Preview

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Flashcards in Topic 11: Autocorrelation Deck (15)
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1

Why can autocorrelation occur?

-Inertia

-Specification, excluding a variable

-Lag, regressor dependent on previous period

-Manipulation / smoothing of data

-Data transformation

2

Show teh Autoregressive 1 ( AR(1) ) model?

x

3

Show the Moving Average ( MA(1) ) model

x

4

How does uncorrected Autocorrelation affect our results?

-Estimators still linear & unbiased, not BLUE

-No minimum variance

-Variance ill estimated, likely under

-Tests not valid

5

What can be done to test for autocorrelation?

-Graph of u^i v time

-Durbin-Watson test

-Breusch-Godfrey test

6

How is the durbin watson test calculated?

x

7

What does the Durbin-Watson test assume?

-Regression has intercept

-Nonstochastic Xi's

-AR(1)

-Normal errors

-no lagged regressant in the model

-No missing observations

8

How is rho related to the d stat in the DW test?

d ~= (2(1-ρ))

-1

When d = 0, p = 1.

When d = 2, ρ = 0

When d = 4, ρ = -1

9

How does one check a durbin watson d stat?

 

Look up dL & dU from tables

if d L or 4-dL < d -> then autocorrelation

if dU < d < 4-DU then no autocorrelation

Otherwise undecisive

DU & DL are dependent on n & k-1

10

How is the Breusch-Godfrey test run?

1. Run the normal regression, may include lagged regressants

2. Regress ut on Xi, ρ1ut-1 ρ2ut-p other Xi's

3. For large samples, nR2 ~ Chi(p), or F(k,n-k-p-1)

- Works for MA,

- p must be assumed / guessed

- might want to choose a yearly p, so montly data would have p=12 

11

How might we correct AR(1) for known ρ?

Because ut = ρut-1 + ϵ

We can tranform our model by -ρYt-1

So Yt - ρYt-1 = B1(1-ρ)+B2(Xt-ρXt-1) + ϵt

or Yi*=B1*+B2*xt*+ ϵt

Coefficients are now blue

We must remember to adjust coefficients for interpretation

12

How can we use the durbin watson test to estimate ρ?

ρ = 1 - d/2

13

What is the Cochrane-Orcut procedure?

1. Run the normal model, get ut

2. Then run the model ut = ρ1ut-1 + vt

3. use ρto use the tranformed model, get new residuals

4. Use the new residuals to resestimate ρ1

5. Continue until ρ does not change much with each iteration

14

What are the Newey-West errors?

Like whites errors, but for autocorrelation. Not BLUE but valid tests

15

What is ARCH?

Autoregressive Conditional Heteroscedasticity Model

Yt = B1 + B2X2t+ut

ut ~ N(0, α0 + α1 u2t-1)

run u2t ~ α0+ α2u2t-1 ... αku2k-x

Use nR~ Chi(k)