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)
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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.
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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.
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4
Q

Difference between a unit root test and a stationarity test

A
  • unit root: H0: unit root
  • stationarity: H0: stationary
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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
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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
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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)
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8
Q

Engle-Granger Procedure

A
  • test each individual time-series for stationarity
  • estimate the cointegration equation using OLS
  • test the residuals for stationarity
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9
Q

Engle-Granger Hypotheses

A
  • H0: residuals have a unit root
  • H1: residuals are stationary
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10
Q

Engle-Granger Decision Rule

A
  • If the residuals are stationary, reject null
  • otherwise, fail to reject
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