Financial Econometrics – Slides-08: Nonstationary Processes Identification, Testing and Estimation
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Financial Econometrics
Slides-08: Nonstationary Processes
Identification, Testing and Estimation
School of Economics1
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
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1 Stochastic and Deterministic Non-stationary Processes
• Properties of Deterministic Non-stationary Process
• Properties of Stochastic Non-stationary Process
1 Random Walk Process
2 Random Walk Process with a drift
• Transformation to achieve Stationarity
2 Unit Root Tests
1 Test: Basic
2 Test: Intercept
3 Test: Intercept and Trend
4 Augmented Dickey-
3 Power consideration
4 Selection of model for testing
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Stationarity versus Non-stationarity
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Deterministic Non-stationarity
Deterministic Non-stationarity Process
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Deterministic Non-stationarity
Deterministic Non-Stationary Process
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Deterministic Non-stationarity
Deterministic Non-Stationary Process
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Deterministic Non-stationarity
Deterministic Non-Stationary Process
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Stochastic Non-stationarity
Stochastic Non-Stationary Process
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Univariate Time Series Analysis
Stationarity versus Non-stationarity
Stochastic non-stationarity
Consider the AR(1) process:
yt = α0 + α1yt−1 + εt
The MA representation is given by:
Depending on the value for α1, two cases can be distinguished:
I Stationary case: |α1| < 1 ⇒ αi1 → 0 as i →∞
→ shocks gradually die out.
I Unit root case: |α1| = 1 ⇒ αi1 = 1 ∀i
→ shocks persist in the system.
I Explosive case: |α1| > 1 ⇒ αi1 →∞ as i →∞
→ shocks have an increasingly large influence.
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Stochastic Non-stationarity
Stochastic Non-Stationary Process
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Random Walk Model
Random Walk Process
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Random Walk Model
Random Walk Process
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Random Walk Model
Random Walk Process
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Random Walk Model
Random Walk: Simulated example
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Random Walk Model
Random Walk: Simulated example
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Random Walk Model
Random Walk with a Drift
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Random Walk Model
Random Walk with a Drift: Properties
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Random Walk Model
Random Walk with a Drift: Properties
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Transformation to Stationarity
Transformation to Stationarity
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Transformation to Stationarity
Transformation to Stationarity
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Unit Root Tests
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
How do we test for a unit root?
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Basic Dickey-
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Basic Dickey-
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Basic Dickey- : Alternative τ statistic
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Basic Dickey- : Distribution
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Basic Dickey- : Example
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Example of DF test: Australian GDP
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
DF Test with Intercept
Dickey- : Intercept
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
DF Test with Intercept
Dickey- with Intercept: Example
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Example of DF test: Australian GDP
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
DF Test: Intercept and Trend
Dickey- : Intercept and Trend
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
DF Test: Intercept and Trend
Dickey- with Intercept: Example
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Example of DF test: Australian GDP
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
The Augmented Dickey-Fuller test
Augmented DF Test
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
The Augmented Dickey-Fuller test
Augmented DF Test
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
The Augmented Dickey-Fuller test
Augmented Dickey- : Example
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Example of ADF(1) test: Australian GDP
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
The Augmented Dickey-Fuller test
Augmented Dickey- : Example
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Example of ADF(3) test: Australian GDP
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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Model Selection
Model Selection for ADF
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Model Selection
Model Selection for ADF
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
Model Selection
Model Selection for ADF
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
A note on the power of ADF tests!
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Slides-07 UNSW
Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests
A note on the power of ADF tests!
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Slides-07 UNSW
Stationarity versus Non-stationarity
Deterministic Non-stationarity
Stochastic Non-stationarity
Random Walk Model
Transformation to Stationarity
Unit Root Tests
DF Test with Intercept
DF Test: Intercept and Trend
The Augmented Dickey-Fuller test
Model Selection
Power of ADF tests
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