Autocorrelation

Question 1

What is autocorrelation

Answer 1

The values of the disturbance term u are not independent of each other

Question 2

What has to to hold to prevent autocorrelation

Answer 2

Cov(ui, uj ) = 0

Question 3

How many lags to use in time series data

Answer 3

Trial and error, but if they want a full year report then quarterly would have four lags
yt = β0 + β1xt + β2xt−1 + β3xt−2 + β4xt−3 + β5xt−4 + ut

Question 4

Why might we use lags of Y as a lagged dependent variable

Answer 4

If inertia effects are important - if this year is influenced by what you did last year
yt = β0 + β1xt + β2xt−1 + β3yt−1 + ut

Question 5

Types of autocorrelation

Answer 5

Autoregressive of order 1

Spatial autocorrelation

Question 6

What is AR (1)

Answer 6

Where the disturbance term in an observation is related to the disturbance term in the observation before

Question 7

What does ut = for AR (1)

Answer 7

put-1 + et

Question 8

Negative autocorrelation on a graph

Answer 8

Successive values tend to have different signs.

positive values followed by negative ones

Question 9

Positive autocorrelation on a graph

Answer 9

Positive values followed by positive and negative followed by negative

Question 10

What are the consequences of autocorrelation : Coefficients, standard errors, standard errors for regression coefficients

Answer 10

Does not bias the estimated coefficients
However they will be inefficient
Standard errors of the regression coefficients are estimated wrongly ( for AR(1) they are underestimated )
Any f and t tests are invalid

Question 11

Spatial autocorrelation

Answer 11

systematic pattern in the spatial distribution of a variable

Question 12

Difference between positive and negative spatial autocorrelation

Answer 12

Negative - Neighboring areas are unlike

Positive - neighboring areas are more alike

Question 13

Ways to test autocorrelation

Answer 13

Durbin-Watson test

With lagged dependent variable

Question 14

Durban watson formula

Answer 14

d =

t=1 uˆ2t

Question 15

Scores of durban watson tests

Answer 15

d=2 no autocorrelation
d=0 severe positive
d=4 severe negative

Question 16

Draw out Durban Watson test between 0-4

Answer 16

with dl du dcrit etc

Question 17

If d lies between dL and dU

Answer 17

we fail to reject the null

Question 18

If d lies between dU and 2

Answer 18

we would fail to reject the null

Question 19

If d is less than dL

Answer 19

Reject the null and conclude there is autocorrelation

Question 20

Reading a Durbin Watson test

Answer 20

N - number of observations

K - number of explanatory variables

Question 21

Why doesn’t a Durban Watson test work for Autocorrelation with a lagged dependent variable. Also what to do now?

Answer 21

It is biased towards the value 2 so therefore not of use. Use Durbin’s h test

Question 22

Durbin’s h test

Answer 22

h = ˆρ n
1 − ns2↓βˆyt−1
everything inside a square root apart from the p hat

Question 23

Three items required for test statistic. And how they are calculated

Answer 23

Number of observations in the regression n
An estimate of the variance of the coefficient of the lagged dependent variable - will be some letter t-1
An estimate for p. P hat = 1-o.5d

Question 24

In large samples what does d =

Answer 24

2-2p

Question 25

Ho p=0

Answer 25

no autocorrelation

Question 26

h statistic distribution and mean and variance

Answer 26

Normal
Mean = 0
Variance = 1
Therefore can use normal distribution table to test

Question 27

How to eliminate AR(1) autocorrelation

Answer 27

Use generalised least squares (GLS)

Cochrane-Orcutt Iterative method - used before computers

Question 28

Method of GLS

Answer 28

Multiply regression through by p, then put all variables to t-1

Subtract the new equation from the first

This reduces the disturbance term to Et

Question 29

Cochrane-Orcutt iterative process

Answer 29

Multiply regression through by p, then put all variable to t-1

Define new key terms to make the regression linear.
yt hat = yt-py↓t-1
xt hat = xt-px↓t-1
B’0 = B0(1-P)
1. Regress yt on xt using OLS.
2. Calculate uˆt = yt − βˆ0 − βˆ1x and regress uˆt on uˆt−1 to obtain an estimate of ρ.
3. Calculate y˜t and x˜t and regress y˜t on x˜t to obtain revised estimates
of β0 and β1.
4. Return to (2) and continue until convergence – i.e. get the same estimates for β0 and β1 that we obtained in the previous iteration.

Question 30

Common factor test

Answer 30

X^2 = n * ln(SSRr/SSRu)
n = number of observations - sample number - 1

Question 31

Causes of autocorrelation

Answer 31

• Something in the disturbance term that has a persistent effect – AR(1) autocorrelation.
• The omission of lagged variables that should be in the equation