AUTOCORRELATION

Question 1

What is AC?

Answer 1

One of the CLRM assumptions is that error terms are not correlated, that is there is no covariance between error terms Cov(Ut, ut-1)=0. Autocorrelation violates this assumption because the error term in time series t, is correlated with the error term in time series t-1. This occurs mostly in time series data and is due to the strong correlation in the shock in t and shock in time period t-1.

Question 2

Non-formal detection of AC?

Answer 2

Graphical method:
- Plot the residuals, et, chronologically.
- Plot the residual et against et-1.
If a noticeable pattern occurs then AC may be present.

Question 3

The two formal detections of AC?

Answer 3

1. Durbin-Watson Test

2. Breusch-Godfrey Test

Question 4

What is the DW test? What does it test for?

Answer 4

The Durbin-Watson test, tests for the first-order autocorrelation which means it tests if consecutive error terms are correlated.

Question 5

D stat is defined as …

Answer 5

The sum of (et - et-1)^2/sum of et^2

Question 6

If D>DU

Answer 6

No autocorrelation exists

Question 7

If d less than DL

Answer 7

Have positive first-order autocorrelation - REJECT THE NULL

Question 8

If D is between DL and DU

Answer 8

Inconclusive

Question 9

If 4-DL less than D less than 4

Answer 9

Then negative first-order autocorrelation

Question 10

What D test can we reject the null?

Answer 10

D less than DL

Question 11

What are the assumptions of the Durbin-Watson Test?

Answer 11

1) Regression model must include an intercept in the OG model.
2) Variables are fixed in repeated sampling.
3) The error term, ut, follows an AR(1) scheme:
Ut = put-1 + Vt where P is the coefficient of AC and -1<=P<=1. This assumption means only the current error term and one period lagged error term is included.
4) Error terms follow a normal distribution
5) The regressors do not include lagged values of dependent variables. No Yt-1, Yt-2.

Question 12

The null hypothesis of the Durbin-Watson Test

Answer 12

H0: RESIDUALS from OLS regression are not AC.
H1: Residuals have a first order (normally positive) AC

Question 13

What is the BG test?

Answer 13

The BG test is a more general test for AC as it allows for more higher order AC schemes such as AR (2) and AR(3) so Ut-2 and Ut-3.
Ut = p1ut-1 + p2ut-2 + pput-p + Vt - current error term depends on the previous error term up to p-lags.
BG test also allows for lagged dependent variables.

Question 14

How to run BG test?

Answer 14

1. Run OLS and obtain residuals.
2. Regress et on the regressors and the p auto-regressive terms:
   et = A1 + A2lnDPIt + A3Dt + c1et-1 + C2et-2
3. Obtain R2 from above.

Question 15

What is the null hypothesis for the BG test?

Answer 15

Null H0:p1=p2=p3=pp=0 that is there is no AC

Alternative H1: Higher-order AC present

Question 16

How to determine the BG hypothesis?

Answer 16

If Chi2?Critical Chi2 or F-value>critical F-value can reject the null also look at p-values of F and X2 if they are low might be AC present (cannot reject the null).

Question 17

Solutions for AC?

Answer 17

The first difference transformation

Question 18

How does it the solution for AC work?

Answer 18

If autocorrelation is of first-order then take first difference of dependent and all regressors. Want to remove the AC.
Ut - put-1 = Vt (now free from AC).

Question 19

What if we know the value of p? What are the error term equation and the whole model equation

Answer 19

If we know the value of p, we can subtract p times the previous value of the error term from the current value.
Ut - Put-1 = Vt
Equation of the first difference transformation:
LnCt-pLnCt = B1(1-P) + B2(lnDt - plnDt-1) + b3(lnWt-plnWt-1) + (Ut-put-1) (which is now Vt and free from AC).

Question 20

What id p=1?

Answer 20

Triangle Ct = B2triangleLnDPI + B3triangle lnWt + Vt

Removed B1

Question 21

What is P(rho)

Answer 21

It is the correlation coefficient so by subtracting p we are removing first-order AC.

Question 22

Consequence of AC

Answer 22

Not BLUE - large standard errors and small t-stats makes hypothesis testing suspect as cannot rely on T or F stats even in large samples