Unit Roots and Co-integration Flashcards
1
Q
Briefly discuss how you can test if yt is indeed I(1)
A
- test for the presence of a unit root in levels, using ADF or PP
- test yt and Δyt, if yt has a unit root and Δyt is stationary then you can conclude that yt is I(1)
2
Q
Explain what is meant by co-integration of two variables
A
- cointegration refers to a situation where two or more variables, each individually non-stationary and integrated of the same order, form a linear combination that is stationary.
3
Q
Using an example from finance, explain what is meant by co-integration
A
- The spot price and futures price of a commodity are often I(1). However, they share a long-run equilibrium relationship due to arbitrage. If futures prices deviate too far from spot prices, arbitrage forces correct the spread, making their combination stationary (I(0)). This co-integration reflects their short-term fluctuations but long-term linkage.
4
Q
Difference between a unit root test and a stationarity test
A
- unit root: H0: unit root
- stationarity: H0: stationary
5
Q
Why use both a unit root and stationarity test?
A
- low power of the ADF test (type 2 error)
- cross-checking
- allows you to minimise type 1 and type 2 errors
6
Q
When to use ADF over DF
A
- when serial correlation is present in residuals as the assumption of white noise errors is violated
7
Q
How are the lags chosen for an ADF?
A
- typically using information criteria like Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC)
8
Q
Engle-Granger Procedure
A
- test each individual time-series for stationarity
- estimate the cointegration equation using OLS
- test the residuals for stationarity
9
Q
Engle-Granger Hypotheses
A
- H0: residuals have a unit root
- H1: residuals are stationary
10
Q
Engle-Granger Decision Rule
A
- If the residuals are stationary, reject null
- otherwise, fail to reject
