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Unit Root Test

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

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.

Testing for Unit root:

Testing for the order of integratingA 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 ∆ Yt = Yt - Yt-1

oStep 3: Take second difference of Yt as ∆2 Yt =∆ Yt -∆ Yt-1

Graphically

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

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.

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.∆ Yt = β + β1 t + δ Yt-1 + ∑ γ ∆ Yt-I + u

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, ∆ 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.

References:

www.timeseies.orgwww.wisegeek/dickey-fuller.orghttp://en.wikipedia.org/wiki/Phillips%E2%80%93Perron_test