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Time Series Analysis - ARIMA Models - Unit Root Tests

[Home] [Up] [Basics] [AR(1) process] [AR(2) process] [AR(p) process] [MA(1) process] [MA(2) process] [MA(q) process] [ARMA(1,1) process] [ARMA(p,q) process] [Wold's decomp.] [Non stationarity] [Differencing] [Behavior] [Inverse Autocorr.] [Unit Root Tests]


o. Unit root tests

There are d unit roots in a non-stationary time series (with respect to the mean) if f(B) is stationary and q(B) invertible in

Time Series Analysis - ARIMA Models - Unit Root Tests

(V.I.1-252)

The most frequently used test for unit roots is the augmented Dickey-Fuller regression (ADF)

(V.I.1-253)

(V.I.1-254)

An example of the use of the ADF is the following LR-test

(V.I.1-255)

where

(V.I.1-256)

(V.I.1-257)

Some critical 95% values for this LR-test (K ³ 1) are: 7.24 (for T ³ 24), 6.73 (for T ³ 50), 6.49 (for T ³ 100), and 6.25 (for T ³ 120). It is also possible to perform an Engle-Granger cointegration test between the variables Xt,i.

This test estimates the cointegrating regression in a first step

(V.I.1-258)
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AR(1) process
AR(2) process
AR(p) process
MA(1) process
MA(2) process
MA(q) process
ARMA(1,1) process
ARMA(p,q) process
Wold's decomp.
Non stationarity
Differencing
Behavior
Inverse Autocorr.
Unit Root Tests
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