编程辅导 Financial Econometrics – Slides-08: Nonstationary Processes Identification

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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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests

Deterministic Non-stationarity

Deterministic Non-stationarity Process

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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests

Deterministic Non-stationarity

Deterministic Non-Stationary Process

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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests

Deterministic Non-stationarity

Deterministic Non-Stationary Process

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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests

Deterministic Non-stationarity

Deterministic Non-Stationary Process

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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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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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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 Process

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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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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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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests

The Augmented Dickey-Fuller test

Augmented DF Test

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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(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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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests

Model Selection

Model Selection for ADF

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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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Plan Stationarity versus Non-stationarity Unit Root Tests Power of ADF tests

A note on the power of ADF tests!

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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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