Stationarity, AR(1) Models & Unit Root Tests Flashcards

1
Q

What is stationary?

A

It is where statistical properties don’t change over time

This means:

1) the mean is constant over time

2) the variance is constant over time

) the covariance (correlation) between values depends only on the time gap, not the time itself

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2
Q

Why does stationary matter?

A

OLS only works properly on stationary data

Non-stationary data can lead to spurious regression (i.e false relationships)

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3
Q

What are the conditions for weak stationary

A

Yt is weak stationary if:

1) Mean does not depend on time

E(Yt) = u (constant mean)

2) Variance does not depend on time

Var(Yt) = σ2 (constant variance)

3) Covariance depends only on time difference

Cov(Yt,Yt-h) depends only on h (gap) not t

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4
Q

What is the AR(1) model?

A

The Autoregressive (AR) Model uses past values of Y to predict the present:

Yt=pYt-1 +ut

where:

p = autocorrelation coefficient

ut = white noise error term

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5
Q

What are the stationary conditions for AR(1)?

A

The process is stationary if ∣ρ∣<1.

if p = 1, the process is a random walk (non-stationary)

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6
Q

How can a time series have a unit root?

A

when p=1 it is a unit root meaning

Yt= Yt-1 +ut

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7
Q

What does a unit root cause?

A

It makes the series non stationary and randomly drift over time

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8
Q

How do we test for a unit root?

A

Use the Dickey-Fuller (DF) test, which tests:

H0: p=1 (unit root -> non stationary)

HA: P < 1 (stationary)

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9
Q

What is the dickey-Fuller test regression?

A

ΔYt=α+γYt−1+ut

(unit root is represented by the gamma symbol)

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10
Q

what do the results of the Dickey-Fuller test mean?

A

If the unit root is significantly negative then reject H0 = stationary

If the Unit root is not significant, fail to reject H0 = series has a unit root

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11
Q

How to interpret the DF test?

A

if the test statistic is more negative than the critical value, the series is stationary

if it is less negative than the critical value, the series has a unit root

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