The document outlines the concept of unit root tests, including definitions and methodologies for testing non-stationarity in time series data using tests such as the Dickey-Fuller, Augmented Dickey-Fuller, and Phillips-Perron tests. It provides a step-by-step approach to conducting these tests and highlights the differences among these tests regarding autocorrelation and heteroskedasticity. Additionally, it emphasizes the importance of graphical analysis as a preliminary step in time series analysis.

2. 2
Unit Root
Test

3. Objectives
:
 To explain the concept of Unit root test
 To highlight the different names of unit root test
 Explaining the,
Dickey Fuller unit root test
Augmented Dickey Fuller test
Phillips -Perron test

4. Overview:
A unit root is an attribute of a statistical model of a time series
whose autoregressive parameter is one.
Yt = ρ Yt + ut -1 ≤ ρ ≤ 1
Thus,
Non stationary, random walk and unit root are
synonymous.

5. Testing for Unit
root:
Testing for the order of integrating
A test for the order of integration is a test for the number of unit roots, and it
includes the following,
oStep 1: Test Yt to see if it is stationary.
oStep 2: Take first difference of Yt as Δ Yt = Yt - Yt-1
oStep 3: Take second difference of Yt as Δ2 Yt =Δ Yt -Δ Yt-1

6. Graphically

7. Hypothesis Testing for Unit
Root
 The basic objective of this test is to test null hypothesis that ρ = 1 in
the following model.
Yt = ρ Yt + ut

8. Dickey Fuller Test:
• Done by Dickey (1979) and Fuller (1976)
It is valid when time series is characterized by AR (1) with white noise
errors.
Testing Strategy:
Time series plot-Graphing variables against time should always
be the first step in any time series analysis.

9. Augmented Dickey Fuller test:
• Most widely used technique.
• It takes into account high order of correlation by adding ( p )
lags in the test.
• It is used when time series is AR (p) and error term is not
white noise.
Δ Yt = β + β1 t + δ Yt-1 + Σ γ Δ Yt-I + u

10. Phillips – Perron Test:
• Phillips and Perron (1988) developed a generalized for of ADF test procedure.
• Developed a number of unit root tests.
• PP test differs from the ADF in how they deal with serial correlation and
heteroscedsticity in the errors.
• When there is no autocorrelation, there PP test is identical to the DF test.
Test Regression:
For the PP test is the AR (1) process,
Δ Yt = α+ γ Yt-I + et
While ADF corrects high order serial correlation.
Advantages:
PP test are robust to general forms of heteroscedasticity.
User does not have to specify lag length for the test regression.

11. References:
www.timeseies.org
www.wisegeek/dickey-fuller.org
http://en.wikipedia.org/wiki/Phillips
%E2%80%93Perron_test