COINTEGRATION

Question 1

What is cointegration?

Answer 1

Cointegration is when a regression of one non-stationary series on another does not result in spurious regression. If two-time series have a stochastic trend they will cancel each other our which suggests a long-run equilibrium.

Question 2

How is it non-formally detected?

Answer 2

Graphically. If you have two drunks walking aimlessly together than it is a long-run E.
“Even though the two trends are stochastic, they do not drift apart substantially.

Question 3

How do we detect spurious regression?

Answer 3

R2>d

Question 4

What is the formal test?

Answer 4

Engle-Granger test

Question 5

How is the formal test performed?

Answer 5

1. Get the ECM and perform the cointegration
   - Estimate the cointegrating equation:
   LC= cons + B1ly + error (reg ly lc)
   - Generate the ECM term:
   error = lc - constant - B1ly
   error = lc - 0.180 - 0.990ly
2. Identify whether the equation is for consumption or income?
   - The function where EMC1 (lagged error) that is negative and stat significant indicates the variable that should be the dependent. reg dlc emc1 and reg dly on emc1.
3. Specify the ARDL
   -General model equation = Yt = B0 + B1Xt + B2Xt-1 + BqXt-q + B4Yt + B5Yt-1 + BpYt-p
4. Search for parsimonious ARDL
   - Estimate the first difference model without E correction term.

Question 6

How do you identify whether the equation is for consumption or income?

Answer 6

The function where emc1 (lagged error term) is negative and statistically significant indicates the variable that should be the dependent.
reg dlc emc1 = emc1 (-0.072) (p=0.008)
reg dly emc1 = emc1 (0.0315) (p=0.118)
So, consumption is the independent variable.

Question 7

What is the ARDL model? Includes the general equation.

Answer 7

ARDL is the auto-regressive distributive lag model.

General equation = Yt = B0 + B2Xt + B3Xt-1 + BqXt-q + B5Yt-1 + B6Yt-2 + BpYt-p + Ut.

Question 8

What is AR

Answer 8

Only dependent

Question 9

What is DL

Answer 9

Only independent

Question 10

I(1)

Answer 10

Non-stationary

Question 11

I(0)

Answer 11

Stationary

Question 12

What is the cointegrating equation?

Answer 12

Lc = cons + ly + error

Question 13

What test is used in the Engle-Granger test

Answer 13

Cointegrating regression augmented Dickey-Fuller test, it is a modified version of ADF.

Question 14

What is the null of CRADF?

Answer 14

Null: H0: Unit root - no cointegration
Alternative: H1: Stationarity - Cointegrating relationshipo

Question 15

What does a unit root mean in terms of cointegration?

Answer 15

Means that there is no cointegration

Question 16

If we reject then null what do we have?

Answer 16

The two time-series are stationary and therefore cointegrated. That is they have a long-run E.

Question 17

What is the Granger Theorem?

Answer 17

If two-time series are cointegrating then their short-run relationship can be expressed as the error correction model.

Question 18

Whats another solution for non-stationary time series?

Answer 18

Transform the original model by using the first difference to remove the non-stationarity.

Question 19

How does the first difference in transformation work? Why do we do it?

Answer 19

It is non-stationary so we cant use OLS and have to use time-series metrics.
By taking the first difference we can use OLS as taking the first-difference in lags always leave us with stationarity.
Ut - Put-1 = Vt
LnC-pLnCt-1 = B1(1-p) + B2(lnY-pLnYt-1) + Ut-pUt-1.
if p = 1
triangle Ct = B2triangleYt + Vt (remove B1)